Recent zbMATH articles in MSC 70https://zbmath.org/atom/cc/702024-03-13T18:33:02.981707ZWerkzeugA toolbox of averaging theorems. Ordinary and partial differential equationshttps://zbmath.org/1528.340012024-03-13T18:33:02.981707Z"Verhulst, Ferdinand"https://zbmath.org/authors/?q=ai:verhulst.ferdinandThe book is intended to present a concise survey of averaging theorems as a toolbox for applied mathematicians, physicists and engineers, with emphasis on the practical use. For this reason, proofs are mostly omitted, although an extensive source of bibliographic references is provided. Some discussion on the results is added and examples, from the most elementary to the most complex, are included to illustrate the theoretical results.
The book is organized as follows. The first chapter discusses, at a very elementary level, possible approaches to perturbation problems. Chapters 2--4 introduce the first and second order periodic averaging, with several examples and some qualitative statements. Chapter 5 is devoted to the general first and second order averaging theory, with several applications. New theory and new applications can be found in Chapters 6--9, which include averaging on large timescales, averaging over spatial variables, applications to Hamiltonian systems and the study of more general dynamics, e.g. invariant manifolds and quasi-periodic solutions. Finally, in Chapter 10 an account of the averaging methods for PDEs is given.
In summary, this is an enjoyable and very clear textbook for scientists, engineers, students and practitioners, which reflects the author's vast expertise on the subject.
Reviewer: Pablo Amster (Buenos Aires)Oscillators at resonancehttps://zbmath.org/1528.340352024-03-13T18:33:02.981707Z"Rojas, David"https://zbmath.org/authors/?q=ai:rojas.davidSummary: An oscillator is isochronous if all motions are periodic with a common period. When the system is forced by a time-dependent periodic perturbation with the same period, the dynamics may change drastically and the phenomenon of resonance can appear. In this article we will study which properties the perturbations must fulfil in order to obtain unbounded solutions. We will consider different oscillators, from harmonic to nonlinear generalizations, and we will set out a number of remarks about the concept of auto-parametric resonance.Attractors of a weakly dissipative system allowing transition to the stochastic web in the conservative limithttps://zbmath.org/1528.370412024-03-13T18:33:02.981707Z"Golokolenov, Alexander V."https://zbmath.org/authors/?q=ai:golokolenov.alexander-v"Savin, Dmitry V."https://zbmath.org/authors/?q=ai:savin.dmitrii-vladimirovichSummary: This article deals with the dynamics of a pulse-driven self-oscillating system -- the Van der Pol oscillator -- with the pulse amplitude depending on the oscillator coordinate. In the conservative limit the ``stochastic web'' can be obtained in the phase space when the function defining this dependence is a harmonic one. The paper focuses on the case where the frequency of external pulses is four times greater than the frequency of the autonomous system. The results of a numerical study of the structure of both parameter and phase planes are presented for systems with different forms of external pulses: the harmonic amplitude function and its power series expansions. Complication of the pulse amplitude function results in the complication of the parameter plane structure, while typical scenarios of transition to chaos visible in the parameter plane remain the same in different cases. In all cases the structure of bifurcation lines near the border of chaos is typical of the existence of the Hamiltonian type critical point. Changes in the number and the relative position of coexisting attractors are investigated while the system approaches the conservative limit. A typical scenario of destruction of attractors with a decrease in nonlinear dissipation is revealed, and it is shown to be in good agreement with the theory of 1:4 resonance. The number of attractors of period 4 seems to grow infinitely with the decrease of dissipation when the pulse amplitude function is harmonic, while in other cases all attractors undergo destruction at certain values of dissipation parameters after the birth of high-period periodic attractors.The \(0:1\) resonance bifurcation associated with the supercritical Hamiltonian pitchfork bifurcationhttps://zbmath.org/1528.370472024-03-13T18:33:02.981707Z"Zhou, Xing"https://zbmath.org/authors/?q=ai:zhou.xingSummary: We consider the non-semisimple \(0:1\) resonance (i.e. the unperturbed equilibrium has two purely imaginary eigenvalues \(\pm i\alpha\; (\alpha \in\mathbb{R}\) and \(\alpha >0)\) and a non-semisimple double-zero one) Hamiltonian bifurcation with one distinguished parameter, which corresponds to the supercritical Hamiltonian pitchfork bifurcation. Based on BCKV singularity theory established by \textit{H. W. Broer} et al. [Z. Angew. Math. Phys. 44, No. 3, 389--432 (1993; Zbl 0805.58047)], this bifurcation essentially triggered by the reversible universal unfolding
\[
M=\frac{1}{2} p^2 +\frac{1}{4}q^4 +(\lambda +I_1) q^2
\]
with respect to BCKV-restricted morphisms of the planar non-semisimple singularity \(\frac{1}{2}p^2 +\frac{1}{4}q^4\) (the \(I_1\) is regarded as distinguished parameter with respect to the external parameter \(\lambda)\). We first give the plane bifurcation diagram of the integrable Hamiltonian on each level of integral in detail, which is related to the usual supercritical Hamiltonian pitchfork bifurcation. Then, we use the \(S_1\)-symmetry generated by the additional pair of imaginary eigenvalues \(\pm i\alpha\) to reconstruct the above plane bifurcation phenomenon caused by the zero eigenvalue pair into the case with two degrees of freedom. Finally, we prove the persistence of typical bifurcation scenarios (e.g. 2-dimensional invariant tori and the symmetric homoclinic orbit) under the small Hamiltonian perturbations, as proposed by H. W. Broer et al. [loc. cit.]. An example system (the coupled Duffing oscillator) with strong linear coupling and weak local nonlinearity is given for this bifurcation.Topological analysis of pseudo-Euclidean Euler top for special values of the parametershttps://zbmath.org/1528.370492024-03-13T18:33:02.981707Z"Altuev, Murat K."https://zbmath.org/authors/?q=ai:altuev.murat-k"Kibkalo, Vladislav A."https://zbmath.org/authors/?q=ai:kibkalo.vladislav-aleksandrovichSummary: An analogue of the Euler top is considered for a pseudo-Euclidean space is under consideration. In the cases when the geometric integral or area integral vanishes the bifurcation diagrams of the moment map are constructed and the homeomorphism class of each leaf of the Liouville foliation is determined. For each arc of the bifurcation diagram, for one of the two possible cases of the mutual arrangement of the moments of inertia, the types of singularities in the preimage of a small neighbourhood of this arc (analogues of Fomenko 3-atoms) are determined, and for nonsingular isoenergy and isointegral surfaces an invariant of rough Liouville equivalence (an analogue of a rough molecule) is constructed. The pseudo-Euclidean Euler system turns out to have noncompact noncritical bifurcations.Periodic solutions, KAM tori, and bifurcations in the planar anisotropic Schwarzschild-type problemhttps://zbmath.org/1528.370502024-03-13T18:33:02.981707Z"Alberti, Angelo"https://zbmath.org/authors/?q=ai:alberti.angelo"Vidal, Claudio"https://zbmath.org/authors/?q=ai:vidal.claudio"Vidarte, Jhon"https://zbmath.org/authors/?q=ai:vidarte.jhonThe anisotropic Schwarzschild-type problem in the plane considered here is determined by the Hamiltonian
\[
H=\frac 12 (p_x^2+p_y^2)-\frac 1{\sqrt{\mu x^2+y^2}}-\frac b{(\mu x^2+y^2)^{\frac 32}}, \quad \mu>0.
\]
This becomes the standard Schwarzschild Hamiltonian for \(\mu=0\). Here the anisotropy is assumed to be small, namely \(\mu\) close to 1 and \(b\) small. In this case, a small parameter \(\epsilon\) can be introduced such that \(b=\epsilon B\) and \(\mu=1-\mu_0\epsilon\) for suitable \(B\) and \(\mu_0\). The Hamiltonian \(H\) is then written as a perturbation of the Kepler problem by developing it in Taylor series in \(\epsilon\). By using polar and Delauney coordinates, \(H\) is normalized by averaging perturbations over the periodic solutions of the Kepler system. The normalized Hamiltonian is then reduced, by truncating terms of degree \(\geq 2\) in \(\epsilon\), to the reduced space of the planar Kepler problem, which is diffeomorphic to \(\mathbb S^2\). The critical points of the equations of motion are then determined. Symplectic coordinates are introduced in the neighborhoods of the critical points. In these coordinates periodic solutions are found via Reeb's theorem and their stability is discussed. Moreover, periodic bifurcations and symmetric periodic solutions are studied. It is remarked that certain symmetric solutions of the system found in literature depend on \(\epsilon\), while the ones determined here do not. The existence of KAM tori enclosing some periodic solutions is proved for certain values of the energy, by using a theorem by \textit{Y. Han} et al. [Ann. Henri Poincaré 10, No. 8, 1419--1436 (2010; Zbl 1238.37018)]. At last, for a Hill-type Hamiltonian obtained from \(H\), the existence of periodic solutions and their stability is discussed.
Reviewer: Giovanni Rastelli (Vercelli)Complex Arnol'd-Liouville mapshttps://zbmath.org/1528.370512024-03-13T18:33:02.981707Z"Biasco, Luca"https://zbmath.org/authors/?q=ai:biasco.luca"Chierchia, Luigi"https://zbmath.org/authors/?q=ai:chierchia.luigiThis paper considers Arnol'd-Liouville action-angle variables that depend on adiabatic invariants for real analytic Hamiltonian systems with one degree-of-freedom. The specific goal is studying the holomorphic properties of the complex continuation of these action-angle variables, and especially their behavior near separatrices.
Two primary results are as follows. The first shows that, in the vicinity of the separatrices, the actions -- considered as functions of the energy -- have a special representation in terms of the affine functions of the logarithm with coefficients that are analytic functions. This result allows estimation of derivatives of the action function.
The second result allows the computation of the analyticity radii of the action-angle variables in arbitrary neighborhoods of the separatrices and their behavior in a suitably scaled distance from separatrices.
Later in the paper the authors consider the convexity of the inverse of the action functions near separatrices. It is also shown that there are inflection points within separatrices.
Reviewer: William J. Satzer Jr. (St. Paul)A nonholonomic model and complete controllability of a three-link wheeled snake robothttps://zbmath.org/1528.370552024-03-13T18:33:02.981707Z"Artemova, Elizaveta M."https://zbmath.org/authors/?q=ai:artemova.elizaveta-markovna"Kilin, Alexander A."https://zbmath.org/authors/?q=ai:kilin.aleksandr-aleksandrovichSummary: This paper is concerned with the controlled motion of a three-link wheeled snake robot propelled by changing the angles between the central and lateral links. The limits on the applicability of the nonholonomic model for the problem of interest are revealed. It is shown that the system under consideration is completely controllable according to the Rashevsky-Chow theorem. Possible types of motion of the system under periodic snake-like controls are presented using Fourier expansions. The relation of the form of the trajectory in the space of controls to the type of motion involved is found. It is shown that, if the trajectory in the space of controls is centrally symmetric, the robot moves with nonzero constant average velocity in some direction.Retraction maps: a seed of geometric integratorshttps://zbmath.org/1528.370702024-03-13T18:33:02.981707Z"Barbero-Liñán, María"https://zbmath.org/authors/?q=ai:barbero-linan.maria"de Diego, David Martín"https://zbmath.org/authors/?q=ai:martin-de-diego.davidThe authors propose a generalization of the classical concept of retraction map. Retraction maps provide a means to select a smooth curve on a differentiable manifold given an initial position and velocity; a curve like this is an approximation of the Riemannian exponential map. The classical version of retraction map can be used in many ways, including approximating geodesics on a Riemannian manifold. More background and additional references for retraction maps are provided in [\textit{P.-A. Absil} et al., in Optimization algorithms on matrix manifolds. Princeton Unversity Press, Princeton NJ (2008; Zbl 1147.65043)].
In this paper the original idea is extended to construct geometric integrators that can take the form of a discretization map. Lifts of such discretization maps to the tangent and cotangent bundles turn out to inherit the properties of the original map, and therefore continue to be discretization maps.
It turns out that the cotangent lift of a discretization map is also a natural symplectomorphism. This is particularly useful for creating geometric integrators for systems defined by either Hamiltonian or Lagrangian functions. The authors show how well-known geometric methods can be derived in their general framework. Furthermore, they believe that their work can enable other geometric integrators, even higher order ones, that might be applied to more complex mechanical systems.
Reviewer: William J. Satzer Jr. (St. Paul)Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equationshttps://zbmath.org/1528.600682024-03-13T18:33:02.981707Z"Röckner, Michael"https://zbmath.org/authors/?q=ai:rockner.michael"Xie, Longjie"https://zbmath.org/authors/?q=ai:xie.longjie"Yang, Li"https://zbmath.org/authors/?q=ai:yang.li.7The paper studies asymptotic behavior of stochastic hyperbolic-parabolic equations with slow-fast time scales, and establish both the strong and weak convergence in the averaging principle setting. The stochastic fluctuations of the original system around its averaged equation is investigated as well. It turns out that the normalized difference converges weakly to the solution of a linear stochastic wave equation. Also, sharp rates for the above convergence have been obtained.
Reviewer: Anatoliy Swishchuk (Calgary)On the Gröbner basis of the ideal of Lyapunov quantities of the Kukles systemhttps://zbmath.org/1528.700012024-03-13T18:33:02.981707Z"Rudenok, A. E."https://zbmath.org/authors/?q=ai:rudenok.a-e"Vasilevich, M. N."https://zbmath.org/authors/?q=ai:vasilevich.m-nSummary: The center problem and the cyclicity of singular points of the Kukles system are studied. The necessary conditions for the center at the origin are obtained as the variety of the ideal of Lyapunov quantities calculated by direct solution of the polynomial system whose left-hand sides form the Gröbner basis of the ideal. This ideal is also used to calculate the cyclicity of the centers and foci of the system. A theorem is proved that allows one to find the cyclicity of the centers of polynomial systems by using its Gröbner basis instead of the ideal of Lyapunov quantities.On the relative rotation of rigid parts and the visco-elastic torsion bushing elementhttps://zbmath.org/1528.700022024-03-13T18:33:02.981707Z"Lidström, Per"https://zbmath.org/authors/?q=ai:lidstrom.perSummary: In this paper the interaction between two rigid parts of a multibody, connected by an ideal spherical joint equipped with a visco-elastic torsion bushing element, is derived. The model allows for arbitrary relative rotations of the parts and involves a non-linear torsion stiffness of the bushing. An expression for the interaction between the parts is derived and a specialization to the isotropic bushing element is presented.The kinematics and kinetics of multi-closed-chain mechanisms in the impact and non-impact stageshttps://zbmath.org/1528.700032024-03-13T18:33:02.981707Z"Shafei, A. M."https://zbmath.org/authors/?q=ai:shafei.a-m"Sadeghi, Z."https://zbmath.org/authors/?q=ai:sadeghi.zahraSummary: The chief objective of the current research is to outline an automated technique for deriving the governing equations and also simulating the motions of the multi-closed-chain mechanisms. To this end, the behavior of a mechanical system, whose straight and rigid links are hinged together by perfect rotary joints to make an array of closed loops, will be studied in the two phases of impact and non-impact. For the non-impact phase, in which the said mechanism is only affected by the Earth's gravity, the relevant differential equations will be derived by the recursive Gibbs-Appell (G-A) methodology (which is a simple approach with fewer partial derivatives to worry about, especially when dealing with the holonomic systems); while for the impact phase, in which at least one joint of the mechanism collides with the surrounding curved wall, the algebraic equations of the system will be obtained by the Newton's kinematic impact law. One of the most formidable challenges in the current research is the presence of the holonomic constraints that govern the kinematics of the problem. The number of these constraints goes up linearly with the increase in the number of system loops. The other challenges and issues that have been successfully addressed by the presented technique include the oblique impact of the joints of the said mechanism with the surrounding curved wall and the relatively large number of the dependent generalized coordinates needed to define the system configuration. In the suggested approach, after deriving the inverse kinetic equations of the considered mechanism, they are converted to the forward dynamics form in a graphical procedure to simulate the system's dynamic responses. To demonstrate the capability and the efficacy of the presented technique in deriving the kinetic equations of multi-closed-loop systems, the dynamic behavior of a 5RRR mechanism with 4 closed loops and 10 rigid links is simulated. The simulation results are then validated by means of the work and energy principles.Gyrostatic Suslov problemhttps://zbmath.org/1528.700042024-03-13T18:33:02.981707Z"Maciejewski, Andrzej J."https://zbmath.org/authors/?q=ai:maciejewski.andrzej-j"Przybylska, Maria"https://zbmath.org/authors/?q=ai:przybylska.mariaSummary: In this paper, we investigate the gyrostat under influence of an external potential force with the Suslov nonholonomic constraint: the projection of the total angular velocity onto a vector fixed in the body vanishes. We investigate cases of free gyrostat, the heavy gyrostat in the constant gravity field, and we discuss certain properties for general potential forces. In all these cases, the system has two first integrals: the energy and the geometric first integral. For its integrability, either two additional first integrals or one additional first integral and an invariant \(n\)-form are necessary. For the free gyrostat we identify three cases integrable in the Jacobi sense. In the case of heavy gyrostat three cases with one additional first integral are identified. Among them, one case is integrable and the non-integrability of the remaining cases is proved by means of the differential Galois methods. Moreover, for a distinguished case of the heavy gyrostat a co-dimension one invariant subspace is identified. It was shown that the system restricted to this subspace is super-integrable, and solvable in elliptic functions. For the gyrostat in general potential force field conditions of the existence of an invariant \(n\)-form defined by a special form of the Jacobi last multiplier are derived. The class of potentials satisfying them is identified, and then the system restricted to the corresponding invariant subspace of co-dimension one appears to be integrable in the Jacobi sense.Signatures of physical constraints in rotating rigid bodieshttps://zbmath.org/1528.700052024-03-13T18:33:02.981707Z"Gutierrez Guillen, G. J."https://zbmath.org/authors/?q=ai:gutierrez-guillen.g-j"Arroyo, E. Aldo"https://zbmath.org/authors/?q=ai:arroyo.e-aldo"Mardešić, P."https://zbmath.org/authors/?q=ai:mardesic.pavao"Sugny, D."https://zbmath.org/authors/?q=ai:sugny.dominiqueSummary: We study signatures of physical constraints on free rotations of rigid bodies. We show analytically that the physical or non-physical nature of the moments of inertia of a system can be detected by qualitative changes both in the Montgomery phase and in the tennis racket effect.On the descent of a skier down a straight trackhttps://zbmath.org/1528.700062024-03-13T18:33:02.981707Z"Lokshin, B. Ya."https://zbmath.org/authors/?q=ai:lokshin.boris-yakovlevich"Samsonov, V. A."https://zbmath.org/authors/?q=ai:samsonov.vitaly-a(no abstract)Stability of stationary motions of mechanical systems with a particular Goryachev-Chaplygin integralhttps://zbmath.org/1528.700072024-03-13T18:33:02.981707Z"Novikov, M. A."https://zbmath.org/authors/?q=ai:novikov.m-a(no abstract)Dynamic modeling and analysis of hybrid driven multi-link press mechanism considering non-uniform wear clearance of revolute jointshttps://zbmath.org/1528.700082024-03-13T18:33:02.981707Z"Chen, Xiulong"https://zbmath.org/authors/?q=ai:chen.xiulong"Tang, Yuefei"https://zbmath.org/authors/?q=ai:tang.yuefei"Gao, Shun"https://zbmath.org/authors/?q=ai:gao.shunSummary: The multi-link press mechanism is developing in the direction of high speed and high precision. However, the non-uniform wear of joint clearance seriously affects the output motion accuracy of mechanism. In order to accurately predict the impact of wear clearance on precision press mechanism, this paper takes the hybrid drive seven-bar press mechanism as an example, a method of dynamic modeling and analysis for the press mechanism with non-uniform wear clearance is developed. First, the contact force and friction force at the clearance are solved based on the L-N model and modified Coulomb friction model respectively, and the dynamic model of press mechanism with clearances is developed by Lagrangian multiplier method. Then, the wear characteristics of joint clearance are predicted by Archard model. Finally, the influences of factors such as wear times, friction coefficient and driving velocities on wear characteristics of kinematic pair and the dynamic response of press mechanism are discussed respectively. This study offers a theoretical basis for dynamic behavior prediction of press mechanism with multiple non-uniform wear clearances, and lays a foundation for the design and manufacture of high-precision press.Dynamic characteristics of helical gears incorporating the effects of coupled sliding frictionhttps://zbmath.org/1528.700092024-03-13T18:33:02.981707Z"Jiang, Hanjun"https://zbmath.org/authors/?q=ai:jiang.hanjun"Liu, Fuhao"https://zbmath.org/authors/?q=ai:liu.fuhaoSummary: Sliding friction is an important source of excitation for gear vibration and noise. However, the axial friction caused by the axial mesh force of the helical gear may excite the gear vibration, which is often ignored by researchers. In this study, firstly, an analytical model of mesh stiffness for helical gears incorporating the friction force and mesh force is proposed. And then, a dynamic model of helical gears with coupled sliding friction is established. The dynamic model includes the transverse friction, the axial friction and the effect of friction on mesh stiffness. Finally, the effect of coupled sliding friction on the dynamic characteristics of helical gears incorporating the proposed analytical mesh stiffness model is investigated. The results show that friction leads to the increase or reduction of mesh stiffness before or after the mesh position where the direction of the friction force is reversed. The oscillations of the dynamic responses become more significant incorporating the effects of coupled sliding friction, especially with the increase of friction coefficient. The developed dynamic model of helical gears incorporating the effects of coupled sliding friction may lead to a more realistic dynamic response.Calculation method of mesh stiffness for helical gear pair with manufacturing errors, assembly errors and tooth modificationshttps://zbmath.org/1528.700102024-03-13T18:33:02.981707Z"Liu, Chang"https://zbmath.org/authors/?q=ai:liu.chang.1|liu.chuang|liu.chang"Shi, Wankai"https://zbmath.org/authors/?q=ai:shi.wankai"Liu, Kun"https://zbmath.org/authors/?q=ai:liu.kunSummary: For the accurate calculation of the time-varying mesh stiffness (TVMS) of helical gear pairs, a novel method is proposed in this paper. This proposed method can predict the TVMS based on the gear accuracy grade or the measurement coordinates of the tooth surface. The abnormal meshing phenomena caused by manufacturing errors (MEs), assembly errors (AEs), and tooth modifications (TMs), such as the loss of contact of tooth pairs, out-of-line meshing, and eccentric loads, are considered in the calculation process. The proposed method was verified to be effective for both spur and helical gear pairs. The effects of MEs, AEs, and TMs on the TVMS of helical gear pairs were also investigated. The results showed that the pitch, helix, and misalignment deviations were the main influencing factors of the TVMS in MEs and AEs. Both profile modification and lead crowning reduced the mean of the TVMS. The proposed method is expected to provide accurate TVMS excitation data of gear transmission systems for dynamic analysis.A dynamic model as a tool for design and optimization of propulsion systems of transport meanshttps://zbmath.org/1528.700112024-03-13T18:33:02.981707Z"Peruń, Grzegorz"https://zbmath.org/authors/?q=ai:perun.grzegorzSummary: Designing power transmission systems is a complex and often time-consuming problem. In this task, various computational tools make it possible to speed up the process and verify a great many different solutions before the final one is developed. It is widely possible today to conduct computer simulations of the operation of various devices before the first physical prototype is built. The article presents an example of a dynamic model of power transmission systems, which has been developed to support work aimed at designing new and optimizing existing systems of that type, as well as to help diagnose them by designing diagnostic algorithms sensitive to early stages of damage development. The paper also presents sample results of tests conducted with the model, used at the gear design stage. In the presented model, the main goal is to reproduce the phenomena occurring in gears as well as possible, using numerous experiments in this direction featured in the literature. Many already historical models present different ways of modeling, but they often made significant simplifications, required by the limitations of the nature of computational capabilities. Differences also result from the purpose of the models being developed, and the analysis of these different ways of doing things makes it possible to choose the most appropriate approach.Changing the spatial orientation of a rigid body using one moving mass in the presence of external forceshttps://zbmath.org/1528.700122024-03-13T18:33:02.981707Z"Shmatkov, Anton M."https://zbmath.org/authors/?q=ai:shmatkov.anton-mSummary: The problem of changing the spatial orientation of a rigid body according to a given program using a movable mass interacting with it in the presence of external forces is considered. An equation is obtained that describes the motion of this mass. The properties that the statement of the problem must satisfy in order for it to have a solution are revealed. Equations for calculating the reorientation program are obtained. They are based on the properties of the vector, which is the difference between the vector of the derivative of the angular momentum of a rigid body, determined by a given reorientation program, and the vector of the moment of external forces acting on the solid during the implementation of this program. It is shown that this difference determines three main variants of the algorithm. For the most complicated case, an example of the spatial reorientation of a mechanical system is considered. The resulting relationships can be used to control spacecraft and robotic systems.Robot workspace approximation with modified bicentered Krawczyk methodhttps://zbmath.org/1528.700132024-03-13T18:33:02.981707Z"Maminov, Artem"https://zbmath.org/authors/?q=ai:maminov.artem"Posypkin, Mikhail"https://zbmath.org/authors/?q=ai:posypkin.mikhail-aSummary: The article considers the application of numerical method based on bicentered Krawczyk operator for solving the problem of the robot workspace approximation with box constraints. We applied several modifications for approximation of the solution sets of the indeterminate system of nonlinear equations and compare it with basic method. All methods were tested on a passive orthosis robot, which is part of the lower limb rehabilitation system. A mathematical model of the mechanism kinematics is presented. We evaluate the efficiency of the considered approaches, compute and visualize the robot workspace for different parameters sets.
For the entire collection see [Zbl 1516.90004].Estimation of robot states with Poisson process based on EKF approximate of Kushner filter: a completely coordinate free Lie group approachhttps://zbmath.org/1528.700142024-03-13T18:33:02.981707Z"Rana, Rohit"https://zbmath.org/authors/?q=ai:rana.rohit"Gaur, Prerna"https://zbmath.org/authors/?q=ai:gaur.prerna"Agarwal, Vijyant"https://zbmath.org/authors/?q=ai:agarwal.vijyant"Parthasarathy, Harish"https://zbmath.org/authors/?q=ai:parthasarathy.harishSummary: In this paper, a Lie coordinate-free torque based Euler-Lagrange equations of motion are developed for a 3-D link (3-DOF) robot. Intentional torque and jerky torque (non-intentional torque) are considered as the inputs to the dynamic profile of the robot. The jerky torque is modelled as a superposition of compound Poisson processes, which is a unique feature. The state vector of the robot, i.e., angular position and angular velocity vector, is thus a Markov process whose transition probability generator can be expressed in terms of the rate of the compound Poisson process that defines the jerky torque. Proof of frame invariance is provided to support the coordinate-free robot dynamics profile. Noise-free measurement is investigated as an ideal case. Angular position measurement is considered with white Gaussian noise. Further, an implementable finite-dimensional EKF approximate to Kushner-Kallianpur filter is obtained to estimate the robot state vector. Finally, the simulations are implemented on commercially available Omni bundle robot.Three-body relative equilibria on \(\mathbb{S}^2\)https://zbmath.org/1528.700152024-03-13T18:33:02.981707Z"Fujiwara, Toshiaki"https://zbmath.org/authors/?q=ai:fujiwara.toshiaki"Pérez-Chavela, Ernesto"https://zbmath.org/authors/?q=ai:perez-chavela.ernestoSummary: We study relative equilibria \((RE)\) for the three-body problem on \(\mathbb{S}^2\), under the influence of a general potential which only depends on \(\cos\sigma_{ij}\) where \(\sigma_{ij}\) are the mutual angles among the masses. Explicit conditions for masses \(m_k\) and \(\cos\sigma_{ij}\) to form relative equilibrium are shown. Using the above conditions, we study the equal masses case under the cotangent potential. We show the existence of scalene, isosceles, and equilateral Euler \(RE\), and isosceles and equilateral Lagrange \(RE\). We also show that the equilateral Euler \(RE\) on a rotating meridian exists for general potential \(\sum_{i<j}m_im_jU(\cos\sigma_{ij})\) with any mass ratios.Finiteness of spatial central configurations with fixed subconfigurationshttps://zbmath.org/1528.700162024-03-13T18:33:02.981707Z"Deng, Yiyang"https://zbmath.org/authors/?q=ai:deng.yiyang"Hampton, Marshall"https://zbmath.org/authors/?q=ai:hampton.marshallFor a generalized \(N\)-body problem with a rational homogeneous central potential, by using some techniques of tropical geometry, the authors show that ``any fixed configuration of \(N-1\) masses in space with no three points collinear and no four points cocircular can be extended to a central configuration of \(N\) masses by adding a specified additional mass only in finitely many ways.''
Reviewer: Xiang Yu (Chengdu)Braids, metallic ratios and periodic solutions of the \(2n\)-body problemhttps://zbmath.org/1528.700172024-03-13T18:33:02.981707Z"Kajihara, Yuika"https://zbmath.org/authors/?q=ai:kajihara.yuika"Kin, Eiko"https://zbmath.org/authors/?q=ai:kin.eiko"Shibayama, Mitsuru"https://zbmath.org/authors/?q=ai:shibayama.mitsuruSummary: Periodic solutions of the planar \(N\)-body problem determine braids through the trajectory of \(N\) bodies. Braid types can be used to classify periodic solutions. According to the Nielsen-Thurston classification of surface automorphisms, braids fall into three types: periodic, reducible and pseudo-Anosov. To a braid of pseudo-Anosov type, there is an associated stretch factor greater than 1, and this is a conjugacy invariant of braids. In [Nonlinearity 19, No. 10, 2441--2453 (2006; Zbl 1260.70006)], the third author discovered a family of multiple choreographic solutions of the planar \(2n\)-body problem. We prove that braids obtained from the solutions in the family are of pseudo-Anosov type, and their stretch factors are expressed in metallic ratios. New numerical periodic solutions of the planar \(2n\)-body problem are also provided.Analysis of the natural orbits around Iohttps://zbmath.org/1528.700182024-03-13T18:33:02.981707Z"Caritá, G. A."https://zbmath.org/authors/?q=ai:carita.g-a"Aljbaae, S."https://zbmath.org/authors/?q=ai:aljbaae.s"Prado, A. F. B. A."https://zbmath.org/authors/?q=ai:prado.antonio-fernando-bertachini-de-almeida"Signor, A. C."https://zbmath.org/authors/?q=ai:signor.a-c"Morais, M. H. M."https://zbmath.org/authors/?q=ai:morais.maria-helena-moreira|morais.m-h-m"Sanchez, D. M."https://zbmath.org/authors/?q=ai:sanchez.diogo-merguizoSummary: The natural satellite of Jupiter, Io, is one of the most interesting bodies in the solar system and deserves to be studied in detail. Up to now, no man-made vehicle has orbited Io because the level of radiation is too high for an orbiter to stay nearby for longer periods of time. In that sense, only flyby missions have studied this body. With the advance of technology, an important step in Solar System research is to develop shields that are strong enough to make orbiter missions around Io possible in the near future. With that in mind, the present paper has the goal, as first step, of mapping possible stable orbits around Io that can accommodate a spacecraft and that do not require station-keeping maneuvers to survive. The dynamical system considers the gravity fields of the Sun, Jupiter, Saturn, Europa, Ganymede, Callisto and the non-spherical shape of Jupiter and Io. To help in this search and to better explain the reasons of stability, integral indices are used to map the less perturbed orbits to guide the numerical searches for stable orbits. We observe several regions of bounded orbits around Io. In these orbits, a relation between the perturbation indices and the duration of stability is found, demonstrating the importance of this tool in mission analyses. Several regions of bounded orbits are found in this system.A variational approach to frozen planet orbits in heliumhttps://zbmath.org/1528.700192024-03-13T18:33:02.981707Z"Cieliebak, Kai"https://zbmath.org/authors/?q=ai:cieliebak.kai"Frauenfelder, Urs"https://zbmath.org/authors/?q=ai:frauenfelder.urs-adrian"Volkov, Evgeny"https://zbmath.org/authors/?q=ai:volkov.evgeny\textit{Frozen planet orbits} are periodic orbits in the helium atom which play an important role in its semiclassical treatment. In such an orbit both electrons lie on a line on the same side of the nucleus. The inner electron undergoes consecutive collisions with the nucleus while the outer electron (the actual ``frozen planet'') stays almost stationary at some distance.
In this paper the authors present a variational approach to frozen planet orbits with instantaneous or mean interaction. One difficulty lies in the collisions of the inner electron with the nucleus, which need to be regularized in order to obtain a good functional analytic setup. In the case of mean interactions, the problem has delay and the application of the traditional Levi-Civita regularization becomes problematic. However, the authors address this issue by considering the novel nonlocal regularization discovered by \textit{V. Barutello} et al. [Adv. Math. 383, Article ID 107694, 64 p. (2021; Zbl 1482.70016)], which is defined in the loop space and therefore fits well with the problem under study.
The two non-local approaches to the orbits of frozen planets, namely, the Lagrangian and the Hamiltonian, are presented. Within the variational setup, the authors transform the helium problem into one where two electrons interact only based on their mean values and use this to infer the existence of frozen planetary orbits. They study two functionals \({\mathcal B}_{av}\) and \({\mathcal B}_{in}\) arising from regularizing frozen planet configurations for the mean and instantaneous interaction, respectively, as well as their linear interpolation \({\mathcal B}_{r} = r {\mathcal B}_{in} + (1-r) {\mathcal B}_{av}\), \(r\in [0,1]\).
The regularized action functional \({\mathcal B}_{r}\) has an intriguing structure. It consists of two terms. The first term can be interpreted as a kinetic energy, but for a nonlocal metric which depends on the whole loop. The second term can be interpreted as the negative of a nonlocal potential which is defined on the loop space of the configuration space. The authors explain how in this situation a nonlocal Legendre transform can be carried out which produces a nonlocal Hamiltonian.
In particular, the following theorems are proven.
\textbf{Theorem A.} For each \(r\in [0,1]\), critical points of the regularized action functional \({\mathcal B}_{r}\) correspond precisely to frozen planet orbits for the interpolated interaction.
\textbf{Theorem B.} The regularized action functional \({\mathcal B}_{r}\) is invariant under an involution such that the critical points fixed by the involution are precisely the symmetric frozen planet orbits.
\textbf{Theorem D.} After applying the nonlocal Legendre transform to the regularized action functional \({\mathcal B}_{r}\), the corresponding Hamiltonian delay equation reproduces frozen planet orbits.
Reviewer: Martha Alvarez-Ramírez (Ciudad de México)Rotation of a planet in a three-body system: a non-resonant casehttps://zbmath.org/1528.700202024-03-13T18:33:02.981707Z"Podvigina, Olga M."https://zbmath.org/authors/?q=ai:podvigina.olga-mikhailovnaSummary: We investigate the temporal evolution of the rotation axis of a planet in a system comprised of the planet (which we call an exo-Earth), a star (an exo-Sun) and a satellite (an exo-Moon). The planet is assumed to be rigid and almost spherical, the difference between the largest and the smallest principal moments of inertia being a small parameter of the problem. The orbit of the planet around the star is a Keplerian ellipse. The orbit of the satellite is a Keplerian ellipse with a constant inclination to the ecliptic, involved in two types of slow precessional motion, nodal and apsidal. Applying time averaging over the fast variables associated with the frequencies of the motion of exo-Earth and exo-Moon, we obtain Hamilton's equations for the evolution of the angular momentum axis of the exo-Earth. Using a canonical change of variables, we show that the equations are integrable. Assuming that the exo-Earth is axially symmetric and its symmetry and rotation axes coincide, we identify possible types of motions of the vector of angular momentum on the celestial sphere. Also, we calculate the range of the nutation angle as a function of the initial conditions. (By the range of the nutation angle we mean the difference between its maximal and minimal values.)The mean-field limit for particle systems with uniform full-rank constraintshttps://zbmath.org/1528.700212024-03-13T18:33:02.981707Z"Plunder, Steffen"https://zbmath.org/authors/?q=ai:plunder.steffen"Simeon, Bernd"https://zbmath.org/authors/?q=ai:simeon.berndSummary: We consider a particle system with uniform coupling between a macroscopic component and individual particles. The constraint for each particle is of full rank, which implies that each movement of the macroscopic component leads to a movement of all particles and vice versa. Skeletal muscle tissues share a similar property which motivates this work. We prove convergence of the mean-field limit, well-posedness and a stability estimate for the mean-field PDE. This work generalises our previous results from
[\textit{S. Plunder} and \textit{B. Simeon}, in: Progress in differential-algebraic equations II. Proceedings of the 9th workshop on descriptor systems, Paderborn, Germany, March 17--20, 2019. Cham: Springer. 357--395 (2020; Zbl 1456.34051)] to the case of nonlinear constraints.On symplectic and isospectral integration of the stationary Landau-Lifshitz (Neumann oscillator) equationhttps://zbmath.org/1528.700222024-03-13T18:33:02.981707Z"Krešić-Jurić, Saša"https://zbmath.org/authors/?q=ai:kresic-juric.sasa"Martinić-Bilać, Tea"https://zbmath.org/authors/?q=ai:martinic-bilac.teaSummary: In this paper we discuss numerical integration of the stationary Landau-Lifshitz (LL) equation. Using a Lax pair representation of the LL equation, we propose an isospectral algorithm that preserves the geometric structure of the system. The algorithm computes a discrete flow of a pair of matrices satisfying Lax-type equations and projects the flow on the phase space of the system. Since the stationary LL equation is equivalent to an integrable Hamiltonian system on the cotangent bundle of the unit sphere, we show that it can be also integrated by a symplectic method for constrained Hamiltonian systems. Comparison of the two methods demonstrates that they are similar in terms of accuracy and stability over long-time integration, but the isospectral method is much faster since it avoids solving a system of nonlinear equations required at each iteration of the symplectic algorithm.On the combination of multiple harmonics in direct and parametric forcing of an oscillator: new results on parametric amplificationhttps://zbmath.org/1528.700232024-03-13T18:33:02.981707Z"Abboud, Eddy"https://zbmath.org/authors/?q=ai:abboud.eddy"Grolet, Aurélien"https://zbmath.org/authors/?q=ai:grolet.aurelien"Mahe, Hervé"https://zbmath.org/authors/?q=ai:mahe.herve"Thomas, Olivier"https://zbmath.org/authors/?q=ai:thomas.olivierSummary: In this article, we focus on the study of a forced single degree of freedom Hill-type differential equation, which can be found in particular in the modeling of gear interactions. We consider that the variable part of the stiffness is composed of several harmonics, and that the forcing term contains a constant part and a single harmonic component. The response of the equation is estimated using methods such as the multiple scale method and the harmonic balance method, and the results are compared to the ones obtained using numerical time integration. The phenomenon of parametric amplification, classically observed when the second harmonic of the parametric driving interacts with the first harmonic of the direct driving, is here observed and quantitatively investigated in the case of more complex direct and parametric interactions. The simplest case is the one with a constant direct forcing, seldom described in the literature. Then, more complex situations with both harmonic and constant forcing leads to parametric amplification with more complex behavior.Compound pendulum pivot forcehttps://zbmath.org/1528.700242024-03-13T18:33:02.981707Z"Hinrichsen, Peter F."https://zbmath.org/authors/?q=ai:hinrichsen.peter-f(no abstract)Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effecthttps://zbmath.org/1528.700252024-03-13T18:33:02.981707Z"Shami, Zein Alabidin"https://zbmath.org/authors/?q=ai:shami.zein-alabidin"Shen, Yichang"https://zbmath.org/authors/?q=ai:shen.yichang"Giraud-Audine, Christophe"https://zbmath.org/authors/?q=ai:giraud-audine.christophe"Touzé, Cyril"https://zbmath.org/authors/?q=ai:touze.cyril"Thomas, Olivier"https://zbmath.org/authors/?q=ai:thomas.olivierSummary: This article considers the nonlinear dynamics of coupled oscillators featuring strong coupling in 1:2 internal resonance. In forced oscillations, this particular interaction is the source of energy exchange, leading to a particular shape of the response curves, as well as quasi-periodic responses and a saturation phenomenon. These main features are embedded in the simplest system which considers only the two resonant quadratic monomials conveying the 1:2 internal resonance, since they are the proeminent source allowing one to explain these phenomena. However, it has been shown recently that those features can be substantially modified by the presence of non-resonant quadratic terms. The aim of the present study is thus to explain the effect of the non-resonant quadratic terms on the dynamics. To that purpose, the normal form up to the third order is used, since the effect of the non-resonant quadratic terms will be transferred into the resonant cubic terms. Analytical solutions are detailed using a second-order mutliple scale expansion. A thorough investigation of the backbone curves, their stability and bifurcation, and the link to the forced-damped solutions, is detailed, showing in particular interesting features that had not been addressed in earlier studies. Finally, the saturation effect is investigated, and it is shown how to correct the detuning effect of the cubic terms thanks to a specific tuning of non-resonant quadratic terms and resonant cubic terms. This choice, derived analytically, is shown to extend the validity of the saturation effect to larger amplitudes, which can thus be used in all applications where this effect is needed e.g. for control.Dynamic effect of the parametric excitation force on an autoparametric vibration absorberhttps://zbmath.org/1528.700262024-03-13T18:33:02.981707Z"Atepor, Lawrence"https://zbmath.org/authors/?q=ai:atepor.lawrence"Akoto, Richard Nii Ayitey"https://zbmath.org/authors/?q=ai:akoto.richard-nii-ayiteySummary: Autoparametric vibration absorber is a machine invented to suppress vibration and has been widely employed in many fields of engineering. Previous works reported by various researchers have shown that dangerous motions, like the full rotation of the pendulum subsystem or chaotic motion, can emerge due to small perturbations of initial conditions or system parameters. To tackle this problem, a new model of the autoparametric vibration absorber with an attached piezoelectric actuator exciter is proposed in this paper. Under the effects of parametric excitation forces produced by the exciter, the vibration absorber will absorb more vibration energy. The dynamic response of the new system is studied analytically using the method of multiple scales and the results validated numerically using the continuation method and detailed bifurcation analysis. The results show that the vibration amplitudes of the subsystems are reduced, the region over which the absorption takes place gets widened and chaotic regions are removed with the introduction of parametric excitation forces in contrast to that of the original model of the autoparametric vibration absorber.Time-varying piecewise nonlinear dynamic model of the vibrating machinery with elliptical trajectory consider the interactions between its frame and particleshttps://zbmath.org/1528.700272024-03-13T18:33:02.981707Z"Li, Lingxuan"https://zbmath.org/authors/?q=ai:li.lingxuan"Zhang, Haonan"https://zbmath.org/authors/?q=ai:zhang.haonan"Zhong, Hao"https://zbmath.org/authors/?q=ai:zhong.haoSummary: Vibrating machinery with an elliptical trajectory widely exists. The bulk particles show a regular sliding motion and throwing motion under the periodic vibration of the frame. It is essential for the theoretical design and engineering application of such machinery to study the particle's motion theory based on considering the interactions between particles and frame in detail. In the first, a time-varying piecewise nonlinear dynamic model of the system is established based on the force analysis of the particles in the state of sliding and throwing motion. The dimensionless equations of systems with nonlinear terms are deduced. After that, the feasibility of using a single particle to study the particle flow's movement is verified by the discrete element method. Then, the system's approximate steady-state analytical solution is obtained by the incremental harmonic balance method. Its numerical solutions are solved by the Newmark-\(\beta\) method, and the solutions obtained by the three methods are verified mutually. In addition, the Sommerfeld effect in vibration system and the system's related parameters are analyzed. Finally, an experimental platform of particles' movement is built. The feasibility of the theoretical analysis in this article was verified by particle's movement experiments.
{{\copyright} 2022 John Wiley \& Sons Ltd.}A note on forced oscillations in systems on a planehttps://zbmath.org/1528.700282024-03-13T18:33:02.981707Z"Polekhin, I. Yu."https://zbmath.org/authors/?q=ai:polekhin.ivan-yuSummary: A sufficient condition for the existence of forced oscillations in nonautonomous systems on a plane is presented under the assumption that the magnitude of the nonautonomous perturbation is small. An advantage of the results presented over analytic methods is that they can be applied in degenerate systems as well.Novel multi-stable energy harvester by exploring the benefits of geometric nonlinearityhttps://zbmath.org/1528.700292024-03-13T18:33:02.981707Z"Yang, Tao"https://zbmath.org/authors/?q=ai:yang.tao.3"Cao, Qingjie"https://zbmath.org/authors/?q=ai:cao.qingjieSummary: This paper proposes the theoretical model and dynamical investigations of a novel multi-stable energy harvester using geometric nonlinearity technique. Among present energy harvesters one of them uses the elastic steel slices and springs, rather than the usual magnetic attraction and repulsion effects. Such a harvester is shown to outperform conventional linear harvesters and to overcome some of the most severe limitations of present approaches. By adjusting the geometric nonlinearity parameters, the energy harvester can possess multi-stable potential energy functions, ranging from mono-stable to quad-stable. The results show that the combined geometric nonlinearity can not only make jumping between potential wells easier, but also improve the efficiency of energy harvesting under low intensity excitations.On the dynamics of vibro-impact systems with ideal and non-ideal excitationhttps://zbmath.org/1528.700302024-03-13T18:33:02.981707Z"Zukovic, Miodrag"https://zbmath.org/authors/?q=ai:zukovic.miodrag"Hajradinovic, Dzanko"https://zbmath.org/authors/?q=ai:hajradinovic.dzanko"Kovacic, Ivana"https://zbmath.org/authors/?q=ai:kovacic.ivanaSummary: This study is concerned with modelling and analyses of a vibro-impact system consisting of a crank-slider mechanism and one oscillator attached to it, where the system is exposed to a non-ideal excitation. The impact occurs during the motion of the oscillator when it fits a base, and the excitation of the driving source is affected by this behaviour. The aim is to determine the interaction between a driving torque and the motion of the oscillator. To achieve this aim in a methodologically sound manner, both vibrating and vibro-impact systems with an ideal and non-ideal excitation are analysed. Analytical and numerical solutions are obtained for the vibrating system with the ideal excitation. Numerical analyses of the vibrating system with the non-ideal excitation is then conducted, where the characteristic curves for this system are found analytically. Numerical simulations are also carried out for other two systems and the results obtained are shown in terms of frequency-response diagrams, time-displacement diagrams and basins of attraction. The results found for different systems are compared mutually, and the differences between them are pointed out. Impact solutions for different regions of the excitation frequency are shown. For the vibro-impact system with the non-ideal excitation, the average value of its frequency is used.Heteroclinic chaos detecting in dissipative mechanical systems: chaotic regimes of compound nanosatellites dynamicshttps://zbmath.org/1528.700312024-03-13T18:33:02.981707Z"Doroshin, Anton V."https://zbmath.org/authors/?q=ai:doroshin.anton-v"Eremenko, Alexandr V."https://zbmath.org/authors/?q=ai:eremenko.alexandr-vSummary: The problem of heteroclinic chaos detecting is considered with the help of the Melnikov method. This paper presents the Melnikov method adaptation based on investigation of a nanosatellite attitude dynamics in the presence of internal dissipation properties. The need for this adaptation is determined by dynamical aspects of perturbing oscillations acting with damping amplitudes. In this case formal analytical exponential growth of perturbations values in reverse time takes place while the classical Melnikov integral does not converge.
The adaptation of the Melnikov method allows investigating the heteroclinic chaos in mechanical systems with internal dissipation properties. As a prime example of this adaptation, the research presents the complete study of chaotic attitude dynamics of a nanosatellite with a slightly movable unit under action of its damped oscillations considered as perturbations. Moreover, the considered research of the nanosatellite attitude dynamics discovers a range of important tasks in the area of a rigid body dynamics under different perturbations with damping.Energy analysis of the single impulsive Earth-Moon transfer with the temporary lunar capturehttps://zbmath.org/1528.700322024-03-13T18:33:02.981707Z"Tan, Minghu"https://zbmath.org/authors/?q=ai:tan.minghu"Li, Haoyu"https://zbmath.org/authors/?q=ai:li.haoyuSummary: The single impulsive planar Earth-Moon transfer strategy is investigated by analyzing the energy change of the lunar capture. A planar bicircular model of the restricted four-body problem is applied to define the single impulsive trajectory to the Moon from the Earth. Then analytical expressions are derived to describe the energy changes of the lunar capture in the Sun-Earth rotating frame. Accordingly, the eccentricity at the perilune of the single impulsive transfer trajectory can be calculated analytically to explore the lunar escape and capture conditions. The error analysis shows that the theoretical solutions serve as good approximations of the energy changes of the single impulsive transfer. Furthermore, it has been found that the perilune angle and the perilune radius are the critical factors for lunar capture. Finally, the theoretical results are successfully employed to find a series of single impulsive planar Earth-Moon transfers.Modified toric code models with flux attachment from Hopf algebra gauge theoryhttps://zbmath.org/1528.700332024-03-13T18:33:02.981707Z"Conlon, A."https://zbmath.org/authors/?q=ai:conlon.aaron|conlon.a-s-c|conlon.alexandre|conlon.anna"Pellegrino, D."https://zbmath.org/authors/?q=ai:pellegrino.daniel-marinho"Slingerland, J. K."https://zbmath.org/authors/?q=ai:slingerland.johannes-kSummary: Kitaev's toric code is constructed using a finite gauge group from gauge theory. Such gauge theories can be extended with the gauge group generalized to any finite-dimensional semisimple Hopf algebra. This also leads to extensions of the toric code. Here we consider the simple case where the gauge group is unchanged but furnished with a non-trivial quasitriangular structure (R-matrix), which modifies the construction of the gauge theory. This leads to some interesting phenomena; for example, the space of functions on the group becomes a non-commutative algebra. We also obtain simple Hamiltonian models generalizing the toric code, which are of the same overall topological type as the toric code, except that the various species of particles created by string operators in the model are permuted in a way that depends on the R-matrix. In the case of \(\mathbb{Z}_N\) gauge theory, we find that the introduction of a non-trivial R-matrix amounts to flux attachment.On conservation laws in nonlocal elasticity associated with internal long-range interactionshttps://zbmath.org/1528.740172024-03-13T18:33:02.981707Z"Huang, Zaixing"https://zbmath.org/authors/?q=ai:huang.zaixingSummary: A Lagrangian formulation with nonlocality is investigated in this paper. The nonlocality of the Lagrangian is introduced by a new nonlocal argument that is defined as a nonlocal residual satisfying the zero mean condition. The nonlocal Euler-Lagrangian equation is derived from the Hamilton's principle. The Noether's theorem is extended to this Lagrangian formulation with nonlocality. With the help of the extended Noether's theorem, the conservation laws relevant to energy, linear momentum, angular momentum and the Eshelby tensor are determined in the nonlocal elasticity associated with the mechanically based constitutive model. The results show that the conservation laws exist only in the form of the integral over the whole domain occupied by the body. The localization of the conservation laws is discussed in detail. We demonstrate that not every conservation law corresponds to a local equilibrium equation. Only when the nonlocal residual of conservation current exists, can a conservation law be transformed into a local equilibrium equation by localization.Integration of variable stiffness actuators in a five-bar device to assist in active rehabilitation of the armhttps://zbmath.org/1528.740772024-03-13T18:33:02.981707Z"Contreras-Calderón, M. G."https://zbmath.org/authors/?q=ai:contreras-calderon.m-g"Castillo-Castañeda, E."https://zbmath.org/authors/?q=ai:castillo-castaneda.eduardo"Laribi, M. A."https://zbmath.org/authors/?q=ai:laribi.m-aSummary: Active arm rehabilitation involves restoring muscle tone by applying force to the arm to produce traction and compression on the muscles. Devices for rehabilitation assistance can be exoskeleton or end-effector type. This paper uses an end-effector type device, which provides an opposing force to the patient's arm's movement to tone their muscles during active rehabilitation. To provide that force, large and expensive motors with high torque are required. In order to avoid the use of motors, it is proposing a variable stiffness actuator integrated into a five-bar mechanism for active arm rehabilitation assistance in this work. The five-bar mechanism has a pantograph attached to amplify the workspace and emulates the arm rehabilitation trajectories, the patient holding onto the end-effector to trace the trajectories. The end-effector provides a constant opposing force to the patient's arm's movement, which activates the muscles. Thus, our proposal is the integration of an actuator with variable stiffness to replace the motors. The mechanism synthesis is presented to determine the parameters to vary the stiffness that provides a constant force in the five-bar mechanism end-effector.On coupled envelope evolution equations in the Hamiltonian theory of nonlinear surface gravity waveshttps://zbmath.org/1528.760102024-03-13T18:33:02.981707Z"Li, Yan"https://zbmath.org/authors/?q=ai:li.yan.72|li.yan.19|li.yan.2|li.yan.9|li.yan.7|li.yan.21|li.yan.12|li.yan.14|li.yan.16|li.yan|li.yan.25|li.yan.28|li.yan.5|li.yan.41|li.yan.15|li.yan.10|li.yan.11|li.yan.24|li.yan.43Summary: This paper presents a novel theoretical framework in the Hamiltonian theory of nonlinear surface gravity waves. The envelope of surface elevation and the velocity potential on the free water surface are introduced in the framework, which are shown to be a new pair of canonical variables. Using the two envelopes as the main unknowns, coupled envelope evolution equations (CEEEs) are derived based on a perturbation expansion. Similar to the high-order spectral method, the CEEEs can be derived up to arbitrary order in wave steepness. In contrast, they have a temporal scale as slow as the rate of change of a wave spectrum and allow for the wave fields prescribed on a computational (spatial) domain with a much larger size and with spacing longer than the characteristic wavelength at no expense of accuracy and numerical efficiency. The energy balance equation is derived based on the CEEEs. The nonlinear terms in the CEEEs are in a form of the separation of wave harmonics, due to which an individual term is shown to have clear physical meanings in terms of whether or not it is able to force free waves that obey the dispersion relation. Both the nonlinear terms that can only lead to the forcing of bound waves and those that are capable of forcing free waves are demonstrated, in the case of the latter through the analysis of the quartet and quintet resonant interactions of linear waves. The relations between the CEEEs and two other existing theoretical frameworks are established, including the theory for a train of Stokes waves up to second order in wave steepness
[\textit{J. D. Fenton}, J. Waterway Port Coast. Ocean Eng. 111, No. 2, 216--234 (1985; \url{doi:10.1061/(ASCE)0733-950X(1985)111:2(21})] and a semi-analytical framework for three-dimensional weakly nonlinear surface waves with arbitrary bandwidth and large directional spreading by
\textit{Y. Li} and \textit{X. Li} [Phys. Fluids 33, No. 7, Article ID 076609 (2021; \url{doi:10.1063/5.0057215})].Information-theoretic interpretation of quantum formalismhttps://zbmath.org/1528.810082024-03-13T18:33:02.981707Z"Feldmann, Michel"https://zbmath.org/authors/?q=ai:feldmann.michel.1Summary: We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued probability space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic.Gauge is quantum?https://zbmath.org/1528.810132024-03-13T18:33:02.981707Z"Patrascu, Andrei T."https://zbmath.org/authors/?q=ai:patrascu.andrei-tudorAuthor's abstract: In this article I discuss a proposed equivalence between quantum mechanics and gauge theory. The evolution of the idea of gauge invariance is very interesting to follow even historically. The idea that gauge transformations have in general no impact on the physics described, leading to even calling gauge variant observables as ``unphysical'' has transformed quite significantly in the past. Now we know large gauge transformations become sensitive to topological (homotopical) structures of thling group, as is the case of the SU(2) anomaly, and that gauge degrees of freedom do play a role, for example in the problem of confinement, via the Gribov ambiguity. The evolution of the concept of gauge is continued here, by the main claim, that gauge and quantum have equivalent origins and behave similarly to the point that they can be considered dual representations of the same physical ideas.
Reviewer: Laure Gouba (Trieste)A new entanglement monotone based on min-relative entropyhttps://zbmath.org/1528.810312024-03-13T18:33:02.981707Z"Cui, Shijie"https://zbmath.org/authors/?q=ai:cui.shijie"Li, Junqing"https://zbmath.org/authors/?q=ai:li.junqing"Huang, Li"https://zbmath.org/authors/?q=ai:huang.liSummary: Quantum relative entropy has been studied extensively, and many forms have been derived due to different parameters. Maximum relative entropy and minimum relative entropy are obtained by taking specific conditions for parameters. Our goal in this paper is to propose a new bipartite entanglement monotone based on minimum relative entropy of any bipartite quantum entanglement state. We also demonstrate that entanglement monotone satisfies some basic properties as an entanglement measure.Mentor initiated controlled bi-directional remote state preparation scheme for \((2 \iff 4)\)-qubit entangled states in noisy channelhttps://zbmath.org/1528.810362024-03-13T18:33:02.981707Z"Choudhury, Binayak S."https://zbmath.org/authors/?q=ai:choudhury.binayak-samadder"Mandal, Manoj Kumar"https://zbmath.org/authors/?q=ai:mandal.manoj-kumar"Samanta, Soumen"https://zbmath.org/authors/?q=ai:samanta.soumenSummary: In this paper we present a bi-directional protocol for mutual remote preparation of a two and a four-qubit non-maximally entangled state where the parties intending to remotely prepare the respective states are not initially entangled. There is a controller of the protocol who oversees the performances of other parties and acts to signal for the execution of the final step in the protocol. There is a Mentor whose action creates entanglement between the rest of the parties and also determines one of the several possible courses of the communication scheme. After that the Mentor quits. The effect of three different noises, namely, Bit-flip, Phase-flip and Amplitude-damping noises are analyzed using the Kraus operator on the otherwise perfect protocol. The decreased fidelity in the presence of noise is numerically studied with respect to noise and other parameters. It is found that in all the three cases the fidelity tends to one as the noise parameter tends to zero.Preparation of two-qubit entangled states on a spin-1/2 Ising-Heisenberg diamond spin cluster by controlling the measurementhttps://zbmath.org/1528.810372024-03-13T18:33:02.981707Z"Kuzmak, A. R."https://zbmath.org/authors/?q=ai:kuzmak.andrij-rSummary: The preparation of entangled quantum states is an inherent and indispensable step for the implementation of many quantum information algorithms. Depending on the physical system, there are different ways to control and measure them, which allow one to achieve the predefined quantum states. The diamond spin cluster is the system that can be applied for this purpose. Moreover, such a system appears in chemical compounds such as the natural mineral azurite, where the \(\operatorname{Cu}^{2 +}\) are arranged in a spin-\( 1 / 2\) diamond chain. Herein, we propose the method of preparation of pure entangled states on the Ising-Heisenberg spin-\( 1 / 2\) diamond cluster. We suppose that the cluster consists of two central spins which are described by an anisotropic Heisenberg model and interact with the side spins via Ising interaction. Controlling the measurement direction of the side (central) spins allows us to achieve predefined pure quantum states of the central (side) spins. We show that this directly affects the entanglement and fidelity of the prepared states. For example, we obtain conditions and fidelities for preparations of the Bell states.Can multipartite entanglement be characterized by two-point connected correlation functions?https://zbmath.org/1528.810392024-03-13T18:33:02.981707Z"Lepori, Luca"https://zbmath.org/authors/?q=ai:lepori.luca"Trombettoni, Andrea"https://zbmath.org/authors/?q=ai:trombettoni.andrea"Giuliano, Domenico"https://zbmath.org/authors/?q=ai:giuliano.domenico"Kombe, Johannes"https://zbmath.org/authors/?q=ai:kombe.johannes"Malo, Jorge Yago"https://zbmath.org/authors/?q=ai:malo.jorge-yago"Daley, Andrew J."https://zbmath.org/authors/?q=ai:daley.andrew-j"Smerzi, Augusto"https://zbmath.org/authors/?q=ai:smerzi.augusto"Chiofalo, Maria Luisa"https://zbmath.org/authors/?q=ai:chiofalo.maria-luisaSummary: We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.Multi-party entanglement generation through superconducting circuitshttps://zbmath.org/1528.810452024-03-13T18:33:02.981707Z"Shahmir, Syed"https://zbmath.org/authors/?q=ai:shahmir.syed"Khan, Mughees Ahmad"https://zbmath.org/authors/?q=ai:khan.mughees-ahmad"Abbas, Tasawar"https://zbmath.org/authors/?q=ai:abbas.tasawar"Alvi, Sajid Hussain"https://zbmath.org/authors/?q=ai:alvi.sajid-hussain"Islam, Rameez-ul"https://zbmath.org/authors/?q=ai:ul-islam.rameezSummary: In this article multipartite entanglement generation schemes are suggested using Circuit Quantum Electrodynamics (Circuit-QED). These proposed setups are achieved by building an interactive connection among many charge qubits, which act as an artificial atom as well as coupler. By initializing these charge qubits in a circuit, one can obtain the multiparty entanglement among these qubits. Further, the charge qubits used for coupling the circuit are traced out. These maximally entangled states are experimentally feasible and can exhibit good fidelity and can further be utilized for quantum information processing tasks.Asymmetric bidirectional hierarchical controlled quantum information transmissionhttps://zbmath.org/1528.810672024-03-13T18:33:02.981707Z"Yang, Benchao"https://zbmath.org/authors/?q=ai:yang.benchaoSummary: This scheme proposes for the first time a hierarchical quantum information transmission scheme for asymmetric bidirectional transmission of unknown single particle quantum states and two particle quantum states with four communication participants. During the communication process, the communication party undertaking ordinary tasks can only complete information transmission under the supervision of one controller, while the communication party performing important tasks can only complete information transmission with the permission and assistance of two controllers. The scheme also discusses the selection of participants who communicate with Alice while the quantum channel remains unchanged.Cost-effective bidirectional controlled quantum teleportation scheme by using nine-qubit entangled statehttps://zbmath.org/1528.810792024-03-13T18:33:02.981707Z"Zhang, Xuehua"https://zbmath.org/authors/?q=ai:zhang.xuehua"Jin, Wentao"https://zbmath.org/authors/?q=ai:jin.wentao"Zeng, Haoxian"https://zbmath.org/authors/?q=ai:zeng.haoxian"Feng, Junlan"https://zbmath.org/authors/?q=ai:feng.junlan"Yang, Chunsheng"https://zbmath.org/authors/?q=ai:yang.chunshengSummary: Quantum communication scheme can play an important role in quantum teleportation. In this paper, an improved asymmetric scheme for bidirectional controlled quantum teleportation of special three-qubit entangled state by using the nine-qubit entangled state as a quantum channel is presented theoretically. In this scheme, two distant parties, Annie and Ben, are both senders and receivers. While Annie wants to send a special three-qubit entangled state to Ben, Ben wishes to transmit another special three-qubit entangled state back to Annie. This scheme only requires the Von Neumann type measurements, controlled-not (CNOT) operations and appropriate unitary operations. By introducing the appropriate unitary transformation and auxiliary particles, Annie and Ben may reconstruct the initial state to achieve quantum teleportation successfully.Detection of the genuine non-locality of any three-qubit statehttps://zbmath.org/1528.810832024-03-13T18:33:02.981707Z"Garg, Anuma"https://zbmath.org/authors/?q=ai:garg.anuma"Adhikari, Satyabrata"https://zbmath.org/authors/?q=ai:adhikari.satyabrataSummary: It is known that the violation of Svetlichny inequality by any three-qubit state described by the density operator \(\rho_{ABC}\) witness the genuine non-locality of \(\rho_{ABC}\). But it is not an easy task as the problem of showing the genuine non-locality of any three-qubit state reduces to the problem of a complicated optimization problem. Thus, the detection of genuine non-locality of any three-qubit state may be considered a challenging task. Therefore, we have taken a different approach and derived the lower and upper bound of the expectation value of the Svetlichny operator with respect to any three-qubit state to study this problem. The expression of the obtained bounds depends on whether the reduced two-qubit entangled state is detected by the CHSH witness operator or not. It may be expressed in terms of the following quantities such as (i) the eigenvalues of the product of the given three-qubit state and the composite system of single qubit maximally mixed state and reduced two-qubit state and (ii) the non-locality of reduced two-qubit state. We then achieve the inequality whose violation may detect the genuine non-locality of any three-qubit state. A few examples are cited to support our obtained results. Lastly, we discuss its possible implementation in the laboratory.Security analysis and improvement of a blind semi-quantum signaturehttps://zbmath.org/1528.811062024-03-13T18:33:02.981707Z"Cao, Jie"https://zbmath.org/authors/?q=ai:cao.jie"Xin, Xiangjun"https://zbmath.org/authors/?q=ai:xin.xiangjun"Li, Chaoyang"https://zbmath.org/authors/?q=ai:li.chaoyang"Li, Fagen"https://zbmath.org/authors/?q=ai:li.fagenSummary: Recently, Xia et al. proposed a semi-quantum blind signature protocol based on five-particle GHZ state. Their protocol can reduce the computation burden of the communicants. However, their protocol is not secure against forgery attack. We prove that the message sender and the signature receiver may conspire to forge the signer's signature, because they master all the private keys of the signer. Then, both the signer and the signature receiver can deny a valid signature. Then, based on the three-particle GHZ state, an improved semi-quantum blind signature protocol is proposed. In the improved protocol, the signer shares the signing key with the trusted arbitrator. Even the message sender and the signature receiver conspire, it is infeasible for them to forge the signer's signature. The improved scheme is secure against the disavowal attack. It has the better efficiency and practicability than the old version as well.Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limithttps://zbmath.org/1528.811312024-03-13T18:33:02.981707Z"Mounaix, Philippe"https://zbmath.org/authors/?q=ai:mounaix.philippeSummary: We study the tail of \(p(U)\), the probability distribution of \(U = |\psi(0, L)|^2\), for \(\ln U \gg 1\), \(\psi(x, z)\) being the solution to \(\partial_z\psi - \frac{i}{2m}\nabla^2_\perp\psi = g|S|^2\psi\), where \(S(x, z)\) is a complex Gaussian random field, \(z\) and \(x\) respectively are the axial and transverse coordinates, with \(0 \leqslant z \leqslant L\), and both \(m \neq 0\) and \(g > 0\) are real parameters. We perform the first instanton analysis of the corresponding Martin-Siggia-Rose action, from which it is found that the realizations of \(S\) concentrate onto long filamentary instantons, as \(\ln U \to +\infty\). The tail of \(p(U)\) is deduced from the statistics of the instantons. The value of \(g\) above which \(\langle U \rangle\) diverges coincides with the one obtained by the completely different approach developed in [\textit{P. Mounaix} et al., Commun. Math. Phys. 264, No. 3, 741--758 (2006; Zbl 1111.35310)]. Numerical simulations clearly show a statistical bias of \(S\) towards the instanton for the largest sampled values of \(\ln U\). The high maxima -- or `hot spots' -- of \(|S(x, z)|^2\) for the biased realizations of \(S\) tend to cluster in the instanton region.Quasimonochromatic dynamical system and optical soliton cooling with triple-power law of self-phase modulationhttps://zbmath.org/1528.811402024-03-13T18:33:02.981707Z"Biswas, Anjan"https://zbmath.org/authors/?q=ai:biswas.anjan"Bagchi, Bijan K."https://zbmath.org/authors/?q=ai:bagchi.bijan-kumar"Yıldırım, Yakup"https://zbmath.org/authors/?q=ai:yildirim.yakup"Khan, Salam"https://zbmath.org/authors/?q=ai:khan.salam"Asiri, Asim"https://zbmath.org/authors/?q=ai:asiri.asim-mSummary: Soliton perturbation theory is used in this paper to uncover the adiabatic conservation laws. The effect of soliton cooling arises from a fixed point in the corresponding dynamical system.First order approximate conserved quantities induced by the approximate symmetries of the perturbed Lagrangianhttps://zbmath.org/1528.811412024-03-13T18:33:02.981707Z"Rehman, Haseeb Ur"https://zbmath.org/authors/?q=ai:rehman.haseeb-ur"Feroze, Tooba"https://zbmath.org/authors/?q=ai:feroze.toobaSummary: The conserved quantities of the approximate symmetries of perturbed Lagrange systems are investigated in this article. The research first finds new conserved quantities directly, which are induced by the approximate Lie symmetry of perturbed Lagrange systems, and sheds light on their precise form and prerequisites for existing. The second part of the article looks at the relationships between Noether, Mei, and Lie approximate symmetries and emphasizes how these approximate symmetries can be used to infer these novel kinds of conserved quantities. The piece concludes with an illustration of some examples.Existence condition for the eigenvalue of a three-particle Schrödinger operator on a latticehttps://zbmath.org/1528.811452024-03-13T18:33:02.981707Z"Abdullaev, J. I."https://zbmath.org/authors/?q=ai:abdullaev.janikul-i"Khalkhuzhaev, A. M."https://zbmath.org/authors/?q=ai:khalkhuzhaev.ahmad-m"Khujamiyorov, I. A."https://zbmath.org/authors/?q=ai:khujamiyorov.i-aSummary: A three-particle discrete Schrödinger operator \({{H}_{{\mu ,\gamma }}}({\mathbf{K}})\), \({\mathbf{K}} \in{{\mathbb{T}}^3}\) associated with a system of three particles (two fermions with the mass 1 and one more particle with the mass \(m = 1/\gamma < 1)\) interacting through pairwise repulsive zero-range potentials \(\mu > 0\) on the three-dimensional lattice \({{\mathbb{Z}}^3}\) is considered. The operator \({{H}_{{\mu ,\gamma }}}({\boldsymbol{\pi }})\), \({\boldsymbol{\pi }} = (\pi ,\pi ,\pi )\) is proved to have no eigenvalues for \(\gamma \in (1,{{\gamma }_0}) ({{\gamma }_0} \approx 4.7655)\) and have the unique eigenvalue with multiplicity three for \(\gamma > {{\gamma }_0} \), which lies to the right of the essential spectrum for sufficiently big \(\mu \).Optical conductivity of multi-Weyl node semimetals due to electromagnetic and axial pseudogauge fieldshttps://zbmath.org/1528.811462024-03-13T18:33:02.981707Z"Schmeltzer, D."https://zbmath.org/authors/?q=ai:schmeltzer.d"Saxena, Avadh"https://zbmath.org/authors/?q=ai:saxena.avadh-behariSummary: We compute the optical conductivity of a multi-Weyl semimetal in the presence of electromagnetic and axial fields. In the first part of the paper we use a U(1) gauge field to compute the current of a multi-Weyl semimetal. The current is used in the computation of the optical conductivity within the Kubo-Matsubara formalism. We consider a multi-Weyl semimetal with two nodal points in the \(z\)-direction. The multi-Weyl semimetal has a width \(D\) in the transverse direction which is smaller than the length \(L\) in the longitudinal direction. Due to the width \(D\) we replace the model by a sum of transverse modes in 1+1 dimensions. We then regularize the model in 1+1 dimensions. The nodal points are responsible for a constant axial field and a static anomalous Hall effect. In the second part we study the effect of dynamic axial fields. An elastic deformation couples to the two electronic chiralities, and represents the axial pseudogauge field \(\vec{a}^5\). As a consequence, the system is excited by two kinds of field, the electromagnetic one and the axial strain field. For a Weyl system this is represented by the triangle diagram, which is responsible for the anomalous Hall effect. We can obtain the anomalous Hall effect also by a chiral transformation in 1+1 dimensions using regularization. The chiral transformation modifies the path integration measure and is the source of the induced anomalous Hall effect. The latter is controlled by a combination of strain waves and electromagnetic fields.How distorting the trajectories of quantum particles shapes the statistical properties of their ensemblehttps://zbmath.org/1528.811512024-03-13T18:33:02.981707Z"Shushi, Tomer"https://zbmath.org/authors/?q=ai:shushi.tomerSummary: We present universal statistical relations between the center of mass of a quantum ensemble and its sub-ensembles when the Bohmian trajectories of the particles are distorted. These relations break the additivity property of the expectation into subadditivity of the distorted expectation, which obtains an evident difference between the various ways to infer quantum expectations. The results do not depend on the form of the Hamiltonian, and do not have a classical parallel. While an experimentalist can arrange the distortion of the trajectories to produce the proposed relations, such distortion may naturally appear in standard experimental setups.Solutions of noncommutative two-dimensional position-dependent mass Dirac equation in the presence of Rashba spin-orbit interaction by using the Nikiforov-Uvarov methodhttps://zbmath.org/1528.811632024-03-13T18:33:02.981707Z"Haouam, Ilyas"https://zbmath.org/authors/?q=ai:haouam.ilyasSummary: We study the combined effects of both position-dependent mass (PDM) and Rashba spin-orbit interaction (RSOI) on the Dirac equation of a spin 1/2 particle moving in a plane and in the presence of a magnetic field within noncommutative (NC) phase-space. The eigenvalues of the two-dimensional system are calculated and the corresponding eigenstates are obtained. The model is solved using NU method then some numerical results are given and used to extensively investigate the behavior of the system under the various influences of linear potential (involved in PDM), magnetic field and RSOI in both commutative and NC frameworks.Pointillisme à la Signac and construction of a quantum fiber bundle over convex bodieshttps://zbmath.org/1528.811802024-03-13T18:33:02.981707Z"de Gosson, Maurice"https://zbmath.org/authors/?q=ai:de-gosson.maurice-a"de Gosson, Charlyne"https://zbmath.org/authors/?q=ai:de-gosson.charlyneSummary: We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase space. The total space of this fiber bundle consists of geometric quantum states, products of convex bodies carried by Lagrangian planes by their polar duals with respect to a second transversal Lagrangian plane. Using the theory of the John ellipsoid we relate these geometric quantum states to the notion of ``quantum blobs'' introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle. We show that the set of equivalence classes of unitarily related geometric quantum states is in a one-to-one correspondence with the set of all Gaussian wavepackets. We emphasize that the uncertainty principle appears in this paper as geometric property of the states we define, and is not expressed in terms of variances and covariances, the use of which was criticized by \textit{J. B. M. Uffink} and \textit{J. Hilgevoord} [Found. Phys. 15, No. 9, 925--944 (1985; \url{doi:10.1007/BF00739034})].Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalismhttps://zbmath.org/1528.811902024-03-13T18:33:02.981707Z"Miyakawa, Yuki"https://zbmath.org/authors/?q=ai:miyakawa.yuki"Sonoda, Hidenori"https://zbmath.org/authors/?q=ai:sonoda.hidenori"Suzuki, Hiroshi"https://zbmath.org/authors/?q=ai:suzuki.hiroshi.1|suzuki.hiroshiSummary: The gradient flow exact renormalization group (GFERG) is an idea that incorporates gauge-invariant gradient flows into the formalism of the exact renormalization group (ERG). GFERG introduces a Wilson action with a cutoff while keeping the vector gauge invariance manifestly. The details of the formalism are still to be worked out. In this paper, we apply GFERG to construct the Wilson action of massless Dirac fermions under the background chiral gauge fields. By formulating the chiral anomaly as a ``composite operator'', we make the scale invariance of the anomaly manifest. We argue that the same result extends to QCD.Pseudogauge freedom and the SO(3) algebra of spin operatorshttps://zbmath.org/1528.811962024-03-13T18:33:02.981707Z"Dey, Sourav"https://zbmath.org/authors/?q=ai:dey.sourav"Florkowski, Wojciech"https://zbmath.org/authors/?q=ai:florkowski.wojciech"Jaiswal, Amaresh"https://zbmath.org/authors/?q=ai:jaiswal.amaresh"Ryblewski, Radoslaw"https://zbmath.org/authors/?q=ai:ryblewski.radoslawSummary: The energy-momentum and spin tensors for a given theory can be replaced by alternative expressions that obey the same conservation laws for the energy, linear momentum, as well as angular momentum but, however, differ by the local redistribution of such quantities (with global energy, linear momentum, and angular momentum remaining unchanged). This arbitrariness is described in recent literature as the pseudogauge freedom or symmetry. In this letter, we analyze several pseudogauges used to formulate the relativistic hydrodynamics of particles with spin \(\frac{1}{2}\) and conclude that the canonical version of the spin tensor has an advantage over other forms as only the canonical definition defines the spin operators that fulfill the SO(3) algebra of angular momentum. This result sheds new light on the results encountered in recent papers demonstrating pseudogauge dependence of various physical quantities. It indicates that for spin-polarization observables, the canonical version is fundamentally better suited for building a connection between theory and experiment.Duality symmetry of quantum electrodynamics and magnetic chargeshttps://zbmath.org/1528.812152024-03-13T18:33:02.981707Z"Yang, Li-Ping"https://zbmath.org/authors/?q=ai:yang.liping"Xu, Dazhi"https://zbmath.org/authors/?q=ai:xu.dazhiSummary: The duality symmetry between electricity and magnetism hidden in classical Maxwell equations suggests the existence of dual charges, which have usually been interpreted as magnetic charges and have not been observed in experiments. In quantum electrodynamics (QED), the electric and magnetic fields are unified into a single gauge field, which makes this symmetry inconspicuous. Here, we revisit the duality symmetry of QED by introducing a dual gauge field and a dual symmetric Lagrangian. Within the framework of gauge-field theory, we show that the electric-magnetic duality symmetry cannot give any new conservation law. By checking the charge-charge interaction and the quantum Lorentz-force equation, we find that the introduced dual charges are electric charges, not magnetic charges. Notably, we show that genuine magnetic charges are incompatible with the traditional QED gauge-field framework, as the interaction between a magnetic charge and an electric charge cannot be mediated via the exchange of gauge photons.Non-SUSY lepton flavor model with the three Higgs doublet modelhttps://zbmath.org/1528.812162024-03-13T18:33:02.981707Z"Izawa, Yukimura"https://zbmath.org/authors/?q=ai:izawa.yukimura"Shimizu, Yusuke"https://zbmath.org/authors/?q=ai:shimizu.yusuke"Takei, Hironori"https://zbmath.org/authors/?q=ai:takei.hironoriSummary: We propose a simple non-supersymmetric lepton flavor model with \(A_4\) symmetry. The \(A_4\) group is a minimal one that includes triplet irreducible representation. We introduce three Higgs doublets, which are assigned as a triplet of the \(A_4\) symmetry. It is natural that there are three generations of the Higgs fields, as with the standard model fermions. We analyze the potential and find the vacuum expectation values for the local minimum. In the vacuum expectation values, we obtain the charged lepton, Dirac neutrino, and right-handed Majorana neutrino mass matrices. By using the type-I seesaw mechanism, we get the left-handed Majorana neutrino mass matrix. In the NuFIT 5.1 data, we predict the Dirac CP phase and the Majorana phases for the only inverted neutrino mass hierarchy. In particular, the Dirac CP phase and lepton mixing angle \(\theta_{23}\) are strongly correlated. If \(\theta_{23}\) is more precisely measured, the Dirac CP phase is more precisely predicted, and vice versa. We also predict the effective mass for neutrinoless double beta decay \(m_{ee} \simeq 47.1\) [meV] and the lightest neutrino mass \(m_3 \simeq 0.789\)--1.43 [meV]. This will be testable with our model in near-future neutrino experiments.Consistency of new CDF-II W boson mass with 123-modelhttps://zbmath.org/1528.812182024-03-13T18:33:02.981707Z"Ouazghour, B. Ait"https://zbmath.org/authors/?q=ai:ouazghour.b-ait"Benbrik, R."https://zbmath.org/authors/?q=ai:benbrik.rachid"Ghourmin, E."https://zbmath.org/authors/?q=ai:ghourmin.e"Ouchemhou, M."https://zbmath.org/authors/?q=ai:ouchemhou.m"Rahili, L."https://zbmath.org/authors/?q=ai:rahili.lSummary: Following the recent update measurement of the W boson mass performed by the CDF-II experiment at Fermilab which indicates \(7\sigma\) deviation from the SM prediction. As a consequence, the open question is whether there are extensions of the SM that can carry such a remarkable deviation or what phenomenological repercussions this has. In this paper, we investigate what the theoretical constraints reveal about the 123-model. Also, we study the consistency of a CDF W boson mass measurement with the 123-model expectations, taking into account theoretical and experimental constraints. Both fit results of \(S\) and \(T\) parameters before and after \(m_W^{\mathrm{CDF}}\) measurement are, moreover, considered in this study. Under these conditions, we found that the 123-model prediction is consistent with the measured \(m_W^{\mathrm{CDF}}\) at a 95\% Confidence Level (CL).Molecular dynamics simulations for quasicrystals under the Born-Gauss potentialshttps://zbmath.org/1528.812252024-03-13T18:33:02.981707Z"Zhao, Sheng"https://zbmath.org/authors/?q=ai:zhao.sheng"Fu, Xiujun"https://zbmath.org/authors/?q=ai:fu.xiujunSummary: Molecular dynamics simulations are a tool for the study of the microscopic dynamics in quasicrystals. By choosing suitable potentials, such as the Dzugutov potential and the Lennard-Jones-Gauss potential, two-dimensional quasicrystals with 8-, 10- and 12-fold symmetries have been formed. In this work, we propose a Born-Gauss type potential with more adjusting parameters to do simulations in two dimensions. Decagonal and dodecagonal quasicrystals are successfully obtained. The structural properties are analyzed and the phase transitions between different structures are discussed.An alternative to the Born rule: spectral quantizationhttps://zbmath.org/1528.812272024-03-13T18:33:02.981707Z"Dvorak, Marc"https://zbmath.org/authors/?q=ai:dvorak.marcSummary: We show that there is a hidden freedom in quantum many-body theory associated with overcompleteness of the time evolution through the single-particle subspace of a many-body system. To fix the freedom, an additional constraint is necessary. We argue that the appropriate constraint on the time evolution through the subspace is to quantize the propagation of entangled pairs of particles, represented by the single-particle spectral function, instead of individual particles. This solution method creates a surface that indicates the multiplicity of every solution to the inverse problem defined by matching the freedom to the constraint. Upon measurement, the system collapses nonlocally onto a single quantized solution. In addition to a combinatoric multiplicity, each solution acquires a multiplicity due to its stability when subject to a small variation in the microscopic degrees of freedom. Numerical calculations for a two-level system show that our theory improves upon standard theory in the description of non-quasiparticle spectral features. Our reinterpretation of quantum many-body theory is not based on the Born rule and offers a more faithful representation of experiments than current theory by modeling individual, quantized events with an explicit collapse model.From symmetries to commutant algebras in standard Hamiltonianshttps://zbmath.org/1528.812292024-03-13T18:33:02.981707Z"Moudgalya, Sanjay"https://zbmath.org/authors/?q=ai:moudgalya.sanjay"Motrunich, Olexei I."https://zbmath.org/authors/?q=ai:motrunich.olexei-iSummary: In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras. In particular, we start with families of Hamiltonians defined by parts that are local, and study the algebra of operators that separately commute with each part. The families of models we discuss include the spin-1/2 Heisenberg model and its deformations, several types of spinless and spinful free-fermion models, and the Hubbard model. This language enables a decomposition of the Hilbert space into dynamically disconnected sectors that reduce to the conventional quantum number sectors for regular symmetries. In addition, we find examples of non-standard conserved quantities even in some simple cases, which demonstrates the need to enlarge the usual definitions of symmetries and conserved quantities. In the case of free-fermion models, this decomposition is related to the decompositions of Hilbert space via irreducible representations of certain Lie groups proposed in earlier works, while the algebra perspective applies more broadly, in particular also to arbitrary interacting models. Further, the von Neumann Double Commutant Theorem (DCT) enables a systematic construction of local operators with a given symmetry or commutant algebra, potentially eliminating the need for ``brute-force'' numerical searches carried out in the literature, and we show examples of such applications of the DCT. This paper paves the way for both systematic construction of families of models with exact scars and characterization of such families in terms of non-standard symmetries, pursued in a parallel paper \textit{S. Moudgalya} and \textit{O. I. Motrunich} [``Exhaustive characterization of quantum many-body scars using commutant algebras'', Preprint, \url{arXiv:2209.03377}].Domain formation of modulation instability in spin-orbit-Rabi coupled Gross-Pitaevskii equation with cubic-quintic interactionshttps://zbmath.org/1528.812332024-03-13T18:33:02.981707Z"Sasireka, Rajmohan"https://zbmath.org/authors/?q=ai:sasireka.rajmohan"Sabari, Subramaniyan"https://zbmath.org/authors/?q=ai:sabari.subramaniyan"Uthayakumar, Ambikapathy"https://zbmath.org/authors/?q=ai:uthayakumar.ambikapathy"Tomio, Lauro"https://zbmath.org/authors/?q=ai:tomio.lauroSummary: The effect of two- and three-body interactions on the modulation instability (MI) domain formation of a spin-orbit (SO) and Rabi-coupled Bose-Einstein condensate is studied within a quasi-one-dimensional model. To this aim, we perform numerical and analytical investigations of the associated dispersion relations derived from the corresponding coupled Gross-Pitaevskii equation. The interplay between the linear (SO and Rabi) couplings with the nonlinear cubic-quintic interactions are explored in the mixture, considering miscible and immiscible configurations, with a focus on the impact in the analysis of experimental realizations with general binary coupled systems, in which nonlinear interactions can be widely varied together with linear couplings.Angular momentum inheritance from the Schwinger effect in (chromo)electromagnetic fieldshttps://zbmath.org/1528.812342024-03-13T18:33:02.981707Z"Copinger, Patrick"https://zbmath.org/authors/?q=ai:copinger.patrick"Hidaka, Yoshimasa"https://zbmath.org/authors/?q=ai:hidaka.yoshimasaSummary: The angular momentum of fermion pairs generated by the Schwinger effect is studied in homogeneous (chromo)electromagnetic fields, mimicking the early stages of a heavy-ion collision. It is demonstrated that the angular momentum density of produced pairs is proportional to that of the background fields. This is argued both heuristically in a virtual breaking condensate model by evaluating Wong's equations, and out-of-equilibrium to one-loop using the in-in formalism.TT deformations in general dimensionshttps://zbmath.org/1528.830042024-03-13T18:33:02.981707Z"Taylor, Marika"https://zbmath.org/authors/?q=ai:taylor.marikaSummary: It has recently been proposed that Zamoldchikov's \(T\bar{T}\) deformation of two-dimensional CFTs describes the holographic theory dual to \(\mathrm{AdS}_3\) at finite radius. In this note we use the Gauss-Codazzi form of the Einstein equations to derive a relationship in general dimensions between the trace of the quasi-local stress tensor and a specific quadratic combination of this stress tensor, on constant radius slices of AdS. We use this relation to propose a generalization of Zamoldchikov's \(T\bar{T}\) deformation to conformal field theories in general dimensions. This operator is quadratic in the stress tensor and retains many but not all of the features of \(T\bar{T}\). To describe gravity with gauge or scalar fields, the deforming operator needs to be modified to include appropriate terms involving the corresponding R currents and scalar operators and we can again use the Gauss-Codazzi form of the Einstein equations to deduce the forms of the deforming operators. We conclude by discussing the relation of the quadratic stress tensor deformation to the stress energy tensor trace constraint in holographic theories dual to vacuum Einstein gravity.Revisiting the renormalization of Einstein-Maxwell theory at one-loophttps://zbmath.org/1528.830082024-03-13T18:33:02.981707Z"Park, I. Y."https://zbmath.org/authors/?q=ai:park.il-young|park.inyong-ySummary: In a series of recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the presence of the trace mode, with the four-dimensional covariance. A subtlety in the background field method also requires careful handling. This status of the matter motivated us to revisit an Einstein-scalar system in one of the sequels. Continuing the endeavors, we revisit the one-loop renormalization of an Einstein-Maxwell system in the present work. The systematic renormalization of the cosmological and Newton constants is carried out by applying the refined background field method. The one-loop beta function of the vector coupling constant is explicitly computed and compared with the literature. The longstanding problem of the gauge choice dependence of the effective action is addressed, and the manner in which gauge choice independence is restored in the present framework is discussed. The formalism also sheds light on background independent analysis. The renormalization involves a metric field redefinition originally introduced by 't Hooft; with the field redefinition the theory should be predictive.Polarized gravitational waves in the parity violating scalar-nonmetricity theoryhttps://zbmath.org/1528.830112024-03-13T18:33:02.981707Z"Chen, Zheng"https://zbmath.org/authors/?q=ai:chen.zheng|chen.zheng.1"Yu, Yang"https://zbmath.org/authors/?q=ai:yu.yang"Gao, Xian"https://zbmath.org/authors/?q=ai:gao.xian(no abstract)A peak in the power spectrum of primordial gravitational waves induced by primordial dark magnetic fieldshttps://zbmath.org/1528.830132024-03-13T18:33:02.981707Z"Kanno, Sugumi"https://zbmath.org/authors/?q=ai:kanno.sugumi"Mukuno, Ann"https://zbmath.org/authors/?q=ai:mukuno.ann"Soda, Jiro"https://zbmath.org/authors/?q=ai:soda.jiro"Ueda, Kazushige"https://zbmath.org/authors/?q=ai:ueda.kazushige(no abstract)Post-Keplerian waveform model for binary compact object as sources of space-based gravitational wave detector and its implicationshttps://zbmath.org/1528.830142024-03-13T18:33:02.981707Z"Li, Li-Fang"https://zbmath.org/authors/?q=ai:li.lifang"Cao, Zhoujian"https://zbmath.org/authors/?q=ai:cao.zhoujianSummary: Binary compact objects will be among the important sources for the future space-based gravitational wave detectors. Such binary compact objects include stellar massive binary black hole, binary neutron star, binary white dwarf and mixture of these compact objects. Regarding to the relatively low frequency, the gravitational interaction between the two objects of the binary is weak. Post-Newtonian approximation of general relativity is valid. Previous works about the waveform model for such binaries in the literature consider the dynamics for specific situations which involve detailed complicated matter dynamics between the two objects. We here take a different idea. We adopt the trick used in pulsar timing detection. For any gravity theories and any detailed complicated matter dynamics, the motion of the binary can always be described as a post-Keplerian expansion. And a post-Keplerian gravitational waveform model will be reduced. Instead of object masses, spins, matter's equation of state parameters and dynamical parameters beyond general relativity, the involved parameters in our post-Keplerian waveform model are the Keplerian orbit elements and their adiabatic variations. Respect to current planning space-based gravitational wave detectors including LISA, Taiji and Tianqin, we find that the involved waveform model parameters can be well determined. And consequently the detail matter dynamics of the binary can be studied then. For binary with purely gravitational interactions, gravity theory can be constrained well.Primordial gravity waves in a rainbow backgroundhttps://zbmath.org/1528.830162024-03-13T18:33:02.981707Z"Salti, M."https://zbmath.org/authors/?q=ai:salti.mustafa|salti.mehmet"Aydogdu, O."https://zbmath.org/authors/?q=ai:aydogdu.oktay|aydogdu.omerSummary: The dawn of the epoch of gravitational wave (GW) astronomy, which initiated with the detection of a fundamental noise, was the period when the search for a theory in which gravity could be quantized began to increase significantly. In this paper, we have mainly intended to focus on the polar modes of GWs in the formalism of gravity's rainbow, which is based on the product of the disparity between quantum mechanics and general relativity (GR). For this purpose, we have perturbed the spatially flat conformal Friedmann-Lemaitre-Robertson-Walker metric, material distribution and the components of four-velocity by making use of the polar Regge-Wheeler gauge and formulated the corresponding field equations for both the zeroth-order (unperturbed) and the first-order (perturbed) cases of the metric. Subsequently, these field equations have been taken into account simultaneously to get exact expressions of the gauge functions. From a graphical perspective, we have studied the impact of rainbow parameters on the amplitude of GWs. In the last step, discussing the Huygens Principle, we have concluded that the GWs obey the principle only in the radiation-dominated era and the principle is broken otherwise.Testing the post-Newtonian expansion with GW170817https://zbmath.org/1528.830172024-03-13T18:33:02.981707Z"Shoom, Andrey A."https://zbmath.org/authors/?q=ai:shoom.andrey-a"Gupta, Pawan K."https://zbmath.org/authors/?q=ai:gupta.pawan-k"Krishnan, Badri"https://zbmath.org/authors/?q=ai:krishnan.badri"Nielsen, Alex B."https://zbmath.org/authors/?q=ai:nielsen.alex-b"Capano, Collin D."https://zbmath.org/authors/?q=ai:capano.collin-dSummary: Observations of gravitational waves from compact binary mergers have enabled unique tests of general relativity in the dynamical and non-linear regimes. One of the most important such tests is constraints on the post-Newtonian (PN) corrections to the phase of the gravitational wave signal. The values of the PN coefficients can be calculated within standard general relativity, and these values are different in many alternate theories of gravity. It is clearly of great interest to constrain the deviations based on gravitational wave observations. In the majority of such tests which have been carried out, and which yield by far the most stringent constraints, it is common to vary these PN coefficients individually. While this might in principle be useful for detecting certain deviations from standard general relativity, it is a serious limitation. For example, we would expect alternate theories of gravity to generically have additional parameters. The corrections to the PN coefficients would be expected to depend on these additional non-GR parameters, whence, we expect that the various PN coefficients to be highly correlated. We present an alternate analysis here using data from the binary neutron star coalescence GW170817. Our analysis uses an appropriate linear combination of non-GR parameters that represent absolute deviations from the corresponding post-Newtonian inspiral coefficients in the TaylorF2 approximant phase. These combinations represent uncorrelated non-GR parameters which correspond to principal directions of their covariance matrix in the parameter subspace. Our results illustrate good agreement with GR. In particular, the integral non-GR phase is \(\Psi_{\tiny int-non-GR} = 0.0447\pm 25.3000\) and the deviation from GR percentile is \(p^{\tiny Dev-GR}_n=25.85\%\).Odd-parity perturbations of the wormhole-like geometries and quasi-normal modes in Einstein-æther theoryhttps://zbmath.org/1528.830192024-03-13T18:33:02.981707Z"Zhang, Chao"https://zbmath.org/authors/?q=ai:zhang.chao.1|zhang.chao.11|zhang.chao.2|zhang.chao.17|zhang.chao|zhang.chao.5|zhang.chao.3|zhang.chao.12"Wang, Anzhong"https://zbmath.org/authors/?q=ai:wang.anzhong"Zhu, Tao"https://zbmath.org/authors/?q=ai:zhu.tao(no abstract)Influence of anisotropic matter on the alcubierre metric and other related metrics: revisiting the problem of negative energyhttps://zbmath.org/1528.830202024-03-13T18:33:02.981707Z"Abellán, Gabriel"https://zbmath.org/authors/?q=ai:abellan.gabriel"Bolivar, Nelson"https://zbmath.org/authors/?q=ai:bolivar.nelson"Vasilev, Ivaylo"https://zbmath.org/authors/?q=ai:vasilev.ivayloSummary: Negative energy scenarios are the most widely studied for the warp metric. In fact, the prevailing view in the community so far has been that the warp metric necessarily has negative energies. In this work it is shown that the issue of negative energy densities associated with the Alcubierre warp metric with a general form function and similar metrics can be addressed when the whole non-vacuum Einstein equations of the system are examined. To this end, we have considered matter content in the form of anisotropic fluids. We have succeeded in writing the Einstein equations in such a way that some general constraints on the material content become evident. This means that, in rectangular coordinates, the energy density depends necessarily on the tangential pressures of the fluid. For matter such as dust or isotropic fluids we find that that density and other related quantities become identically zero. This makes the negative energy problem spurious. It is also revealed that constructing Alcubierre-based metrics using cylindrical and spherical coordinates results in a system of equations that are amenable to more systematic analysis. The field equations constrain the dependence of the form function and how this impacts the matter content. In all cases we determine that energy density is not mandatory negative, despite the recurrent claims in the literature. This result prompts a reevaluation of the negative energy requirements and underscore the importance of cylindrical and spherical type-warps to demonstrate that negative energy density is not an intrinsic unavoidable feature of warp drives.Broken scale invariance and the regularization of a conformal sector in gravity with Wess-Zumino actionshttps://zbmath.org/1528.830232024-03-13T18:33:02.981707Z"Corianò, Claudio"https://zbmath.org/authors/?q=ai:coriano.claudio"Cretì, Mario"https://zbmath.org/authors/?q=ai:creti.mario"Maglio, Matteo Maria"https://zbmath.org/authors/?q=ai:maglio.matteo-mariaSummary: We elaborate on anomaly induced actions of the Wess-Zumino (WZ) form and their relation to the renormalized effective action, which is defined by an ordinary path integral over a conformal sector, in an external gravitational background. In anomaly - induced actions, the issue of scale breaking is usually not addressed, since these actions are obtained only by solving the trace anomaly constraint and are determined by scale invariant functionals. We investigate the changes induced in the structure of such actions once identified in dimensional renormalization (DR) when the \(\epsilon = d - 4 \to 0\) limit is accompanied by the dimensional reduction (DRed) of the field dependencies. We show that operatorial nonlocal modifications (\(\sim\square^\epsilon\)) of the counterterms are unnecessary to justify a scale anomaly. In this case, only the ordinary finite subtractions play a critical role in the determination of the scale breaking. This is illustrated for the WZ form of the effective action and its WZ consistency condition, as seen from a renormalization procedure. Logarithmic corrections from finite subtractions are also illustrated in a pure \(d = 4\) (cutoff) scheme. The interplay between two renormalization schemes, one based on dimensional regularization (DR) and the second on a cutoff in \(d = 4\), illustrates the ambiguities of DR in handling the quantum corrections in a curved background. Therefore, using DR in a curved background, the scale and trace anomalies can both be obtained by counterterms that are Weyl invariant only at \(d = 4\).The Jacobi metric approach for dynamical wormholeshttps://zbmath.org/1528.830262024-03-13T18:33:02.981707Z"Duenas-Vidal, Álvaro"https://zbmath.org/authors/?q=ai:duenas-vidal.alvaro"Lasso Andino, Oscar"https://zbmath.org/authors/?q=ai:lasso-andino.oscarSummary: We present the Jacobi metric formalism for dynamical wormholes. We show that in isotropic dynamical spacetimes, a first integral of the geodesic equations can be found using the Jacobi metric, and without any use of geodesic equation. This enables us to reduce the geodesic motion in dynamical wormholes to a dynamics defined in a Riemannian manifold. Then, making use of the Jacobi formalism, we study the circular stable orbits in the Jacobi metric framework for the dynamical wormhole background. Finally, we also show that the Gaussian curvature of the family of Jacobi metrics is directly related, as in the static case, to the flare-out condition of the dynamical wormhole, giving a way to characterize a wormhole spacetime by the sign of the Gaussian curvature of its Jacobi metric only.Wormhole solution in modified teleparallel-Rastall gravity and energy conditionshttps://zbmath.org/1528.830332024-03-13T18:33:02.981707Z"Nazavari, N."https://zbmath.org/authors/?q=ai:nazavari.n"Saaidi, K."https://zbmath.org/authors/?q=ai:saaidi.kh|saaidi.khaled"Mohammadi, A."https://zbmath.org/authors/?q=ai:mohammadi.ahmad|mohammadi.adeleh|mohammadi.abbas|mohammadi.arman|mohammadi.arash|mohammadi.anwar|mohammadi.abdolreza|mohammadi.aliasghar|mohammadi.abbasali|mohammadi.abdulqader|mohammadi.ali|mohammadi.aref-zadehgol|mohammadi.atousa-h-s|mohammadi.amin|mohammadi.anvar|mohammadi.amir-hossein-mousavi|mohammadi.ashkan|mohammadi.atieh|mohammadi.amir|mohammadi.alireza|mohammadi.abolhassan|mohammadi.azadeh|mohammadi.abumoslem|mohammadi.arefeh|mohammadi.amir-amjad.1Summary: The possibility of static and spherically symmetric traversable wormhole solution in modified teleparallel Rastall gravity in a non-diagonal tetrad is investigated. Rastall assumption modifies the field equations and energy-momentum conservation law. These modifications lead to different exact asymptotically flat traversable wormhole solutions. By imposing different constraints on modified energy-momentum conservation law, different exact solutions are found and the obtained results for teleparallel Rastall gravity, with specific choices of \(f(T)\), are studied. It is shown that the Rastall parameters have a key role in these model and in all of those exact traversable wormhole solutions the null energy condition and weak energy condition of matter or energy which has surrounded the wormhole are valid at the throat of the wormhole and through the space time as well.Black-bounce in \(f(T)\) gravityhttps://zbmath.org/1528.830342024-03-13T18:33:02.981707Z"Rodrigues, Manuel E."https://zbmath.org/authors/?q=ai:rodrigues.manuel-e"Junior, Ednaldo L. B."https://zbmath.org/authors/?q=ai:junior.ednaldo-l-b-junSummary: We study new solutions of black-bounce spacetimes formulated in \(f(T)\) gravity in four dimensions. First, we present the case of diagonal tetrad where a restriction appears in the equations of motion that is divided into the cases of zero torsion, constant torsion and teleparallel. The Null Energy Condition (NEC) is still always violated, which implies that the other energy conditions are also violated. The solutions are regular throughout spacetime and the zero torsion solution presents discontinuity between the energy conditions inside and outside the event horizon. Second, we present the case of non-diagonal tetrads. This case is divided into a Simpson-Visser type model and a quadratic model in \(T\). The NEC continues to be violated, implying the violation of the other energy conditions. The solutions are regular in all spacetimes. An interesting result is that due to the possibility that the area associated with the metric is different from \(4\pi r^2\), the no-go output theorem established in the usual \(f(T)\) is violated, resulting in the new possibility \(g_{00}=-g^{11}\), for metric components.Reassessing the problem of time of quantum gravityhttps://zbmath.org/1528.830392024-03-13T18:33:02.981707Z"Mozota Frauca, Álvaro"https://zbmath.org/authors/?q=ai:mozota-frauca.alvaroSummary: In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for which the problem can be solved, while I argue in this paper that there are good reasons for doubting about these resolutions when the theory is not deparametrizable, which is the case of general relativity. I introduce an example of a non-deparametrizable model, a double harmonic oscillator system expressed by its Jacobi action, and argue that the problem of time for this model is not solvable, in the sense that its canonical quantization doesn't lead to the quantum theory of two harmonic oscillators and the standard resolutions of the problem of time don't work for this case. I argue that as general relativity is strongly analogous to this model, one should take seriously the view that the canonical quantization of general relativity doesn't lead to a meaningful quantum theory. Finally, I comment that this has an impact on the foundations of different approaches to quantum gravity.Graviton loop contribution to Higgs potential in gauge-Higgs unificationhttps://zbmath.org/1528.830402024-03-13T18:33:02.981707Z"Nishikawa, Yasunari"https://zbmath.org/authors/?q=ai:nishikawa.yasunariSummary: We study the two-loop finiteness of an effective potential for a Higgs boson that is the fifth component of a gauge field in a \(U(1)\) gauge theory coupled to quantum gravity on the five-dimensional space-time \(M^4\times S^1\). There are two types of diagrams including quantum gravitational corrections. We find that only one type of diagram contributes to the effective potential for the Higgs boson, and its magnitude is finite.A note on the canonical formalism for gravityhttps://zbmath.org/1528.830412024-03-13T18:33:02.981707Z"Witten, Edward"https://zbmath.org/authors/?q=ai:witten.edwardSummary: We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a relationship of the phase space of gravity in asymptotically Anti de Sitter spacetime to a cotangent bundle. We describe what is known about this relationship and some extensions that might plausibly be true. A key fact is that, under certain conditions, the Einstein Hamiltonian constraint equation can be viewed as a way to gauge fix the group of conformal rescalings of the metric of a Cauchy hypersurface. An analog of the procedure that we follow for Anti de Sitter gravity leads to standard results for a Klein-Gordon particle.Dynamics of self-gravitating systems in non-linearly magnetized chameleonic Brans-Dicke gravityhttps://zbmath.org/1528.830442024-03-13T18:33:02.981707Z"Yousaf, Z."https://zbmath.org/authors/?q=ai:yousaf.z"Bhatti, M. Z."https://zbmath.org/authors/?q=ai:bhatti.muhammad-zaeem-ul-haq"Rehman, S."https://zbmath.org/authors/?q=ai:rehman.salim-u|rehman.semeen|ur-rehman.shafiq.1|rehman.shaista-amat-ur|rehman.sajjad-ur|rehman.shakeel-ul|rehman.sana|rehman.sirajur|rehman.shafiq-ur|rehman.sajid|rehman.sumaira|rehman.shafqat-ur|ur-rehman.shafiq"Bamba, Kazuharu"https://zbmath.org/authors/?q=ai:bamba.kazuharuSummary: We study the effects of magnetic fields of non-linear electrodynamics in chameleonic Brans-Dicke theory under the existence of anisotropic spherical fluid. In particular, we explore dissipative and non-dissipative self-gravitating systems in the quasi-homologous regime with the minimal complexity constraint. As a result, under the aforementioned circumstances, several analytic solutions are found. Furthermore, by analyzing the dynamics of a dissipative fluid, it is demonstrated that a void covering the center can satisfy the Darmois criteria. The temperature of the self gravitating systems is also investigated.Test of conformal theory of gravity as an alternative paradigm to dark matter hypothesis from gravitational lensing studieshttps://zbmath.org/1528.830472024-03-13T18:33:02.981707Z"Ghosh, Shubhrangshu"https://zbmath.org/authors/?q=ai:ghosh.shubhrangshu"Bhattacharya, Mahasweta"https://zbmath.org/authors/?q=ai:bhattacharya.mahasweta"Sherpa, Yanzi"https://zbmath.org/authors/?q=ai:sherpa.yanzi"Bhadra, Arunava"https://zbmath.org/authors/?q=ai:bhadra.arunava(no abstract)Geodesic structure of a rotating regular black holehttps://zbmath.org/1528.830682024-03-13T18:33:02.981707Z"Bautista-Olvera, Brandon"https://zbmath.org/authors/?q=ai:bautista-olvera.brandon"Degollado, Juan Carlos"https://zbmath.org/authors/?q=ai:degollado.juan-carlos"German, Gabriel"https://zbmath.org/authors/?q=ai:german.gabrielSummary: We examine the dynamics of particles around a rotating regular black hole. In particular we focus on the effects of the characteristic length parameter of the spinning black hole on the motion of the particles by solving the equation of orbital motion. We have found that there is a fourth constant of motion that determines the dynamics of orbits out the equatorial plane similar as in the Kerr black hole. Through detailed analyses of the corresponding effective potentials for massive particles the possible orbits are numerically simulated. A comparison with the trajectories in a Kerr spacetime shows that the differences appear when the black holes rotate slowly for large values of the characteristic length parameter.Junction conditions in bi-scalar Poincaré gauge gravityhttps://zbmath.org/1528.830712024-03-13T18:33:02.981707Z"Casado-Turrión, Adrián"https://zbmath.org/authors/?q=ai:casado-turrion.adrian"de la Cruz-Dombriz, Álvaro"https://zbmath.org/authors/?q=ai:de-la-cruz-dombriz.alvaro"Jiménez Cano, Alejandro"https://zbmath.org/authors/?q=ai:jimenez-cano.alejandro"Maldonado Torralba, Francisco José"https://zbmath.org/authors/?q=ai:maldonado-torralba.francisco-jose(no abstract)Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickershttps://zbmath.org/1528.830732024-03-13T18:33:02.981707Z"Destounis, Kyriakos"https://zbmath.org/authors/?q=ai:destounis.kyriakos"Huez, Giulia"https://zbmath.org/authors/?q=ai:huez.giulia"Kokkotas, Kostas D."https://zbmath.org/authors/?q=ai:kokkotas.kostas-dSummary: Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical dark objects lurking in galactic centers are black holes. Sgr A\(^*\), one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. Nevertheless, the well-established presence of accretion disks and astrophysical environments around supermassive compact objects can significantly deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that transverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.Energy condition and cosmic censorship conjecture in the perfect fluid collapsehttps://zbmath.org/1528.830752024-03-13T18:33:02.981707Z"Firouzjaee, Javad T."https://zbmath.org/authors/?q=ai:firouzjaee.javad-tSummary: The hypothesis of cosmic censorship plays a crucial role in classical general relativity, as an aspect of the strong version it expresses that naked singularities would never occur from the black hole singularity. In this paper, we will present how energy conditions prohibit forming the local naked singularity in the spherical perfect fluid collapse, and thus we get one step closer to the strong cosmic censorship conjecture proof. We also show that this result can be extended to the cosmological constant background.Circular strings in Kerr-\(AdS_5\) black holeshttps://zbmath.org/1528.830762024-03-13T18:33:02.981707Z"Geytota, O. V."https://zbmath.org/authors/?q=ai:geytota.o-v"Golubtsova, A. A."https://zbmath.org/authors/?q=ai:golubtsova.anastasia-a"Dimov, H."https://zbmath.org/authors/?q=ai:dimov.hristo"Nguyen, Vu H."https://zbmath.org/authors/?q=ai:nguyen.vu-hoang-vuong|nguyen.vu-hieu"Rashkov, R. C."https://zbmath.org/authors/?q=ai:rashkov.radoslav-cSummary: The quest for extension of holographic correspondence to the case of finite temperature naturally includes Kerr-AdS black holes and their field theory duals. We probe the five-dimensional Kerr-AdS space time by pulsating strings. First we find particular pulsating string solutions and then semi-classically quantize the theory. For the string with large values of energy, we use the Bohr-Sommerfeld analysis to find the energy of the string as a function of a large quantum number. From the dual theory viewpoint, the constraint for the string energy can be considered as the dispersion relation of stationary thermal states. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which according to the holographic dictionary are related to anomalous dimensions of certain operators in the dual gauge theory.Dynamics of test particles around hairy black holes in Horndeski's theoryhttps://zbmath.org/1528.830792024-03-13T18:33:02.981707Z"Lin, Hou-Yu"https://zbmath.org/authors/?q=ai:lin.hou-yu"Deng, Xue-Mei"https://zbmath.org/authors/?q=ai:deng.xuemeiSummary: We investigate charged particles' motions around a hairy black hole of Horndeski's theory immersed in an external magnetic field. Although the critical energy \(\mathcal{E}_\ast^2\) divides the charged particle's bounded trajectory into three types just like the situation in the classical Schwarzschild black hole, it still suggests that the values of the angular momentum and the energy for the charged particle around the hairy black hole are smaller than the ones of the classical hole. The epicyclic frequencies of the charged particle around the hairy black hole immersed in the external magnetic field are compared with the results of the observed microquasars' results. It indicates that the influences of the hairy black hole best fits the data of the observations with a non-vanishing magnetic field. Our present work might provide hints for distinguishing the hairy black hole in Horndeski's theory from the classical Schwarzschild black hole by using the test charged particles' dynamics around the strong gravitational field.Gyroscopic precession in the vicinity of a static blackhole's event horizonhttps://zbmath.org/1528.830802024-03-13T18:33:02.981707Z"Majumder, Paulami"https://zbmath.org/authors/?q=ai:majumder.paulami"Nayak, K. Rajesh"https://zbmath.org/authors/?q=ai:nayak.k-rajeshSummary: In this article, we investigate gyroscopic precession in the vicinity of a spherically symmetric static event horizon. Our goal is to address whether the gyroscopic precession frequency diverges when approaching an event horizon. To do so, we employ the Frenet-Serret formalism of gyroscopic precession, which provides a complete covariant formalism, and extend it to include arbitrary timelike curves. We analyze the precession frequency near the Schwarzschild and Schwarzschild-anti-de-Sitter black holes, using horizon-penetrating Kerr-Schild coordinates to eliminate coordinate singularities near the horizon. Our study shows that a diverging gyroscopic precession frequency is not a universal feature for a trajectory crossing an event horizon. As a counter-example, we construct a timelike curve passing through the event horizon along which the gyroscopic precession frequency remains finite at the horizon.Impact of multiple modes on the evolution of self-interacting axion condensate around rotating black holeshttps://zbmath.org/1528.830812024-03-13T18:33:02.981707Z"Omiya, Hidetoshi"https://zbmath.org/authors/?q=ai:omiya.hidetoshi"Takahashi, Takuya"https://zbmath.org/authors/?q=ai:takahashi.takuya"Tanaka, Takahiro"https://zbmath.org/authors/?q=ai:tanaka.takahiro"Yoshino, Hirotaka"https://zbmath.org/authors/?q=ai:yoshino.hirotaka(no abstract)Energy formula, surface geometry and energy extraction for Kerr-Sen black holehttps://zbmath.org/1528.830822024-03-13T18:33:02.981707Z"Pradhan, Parthapratim"https://zbmath.org/authors/?q=ai:pradhan.parthapratimSummary: We evaluate the \textit{surface energy \((\mathcal{E}_s^\pm)\), rotational energy} \((\mathcal{E}_r^\pm)\) \textit{and electromagnetic energy} \((\mathcal{E}_{em}^\pm)\) for a \textit{Kerr-Sen black hole (BH)} having the event horizon \((\mathcal{H}^+)\) and the Cauchy horizon \((\mathcal{H}^-)\). Interestingly, we find that the \textit{sum of these three energies is equal to the mass parameter i.e.}\(\mathcal{E}_s^\pm +\mathcal{E}_r^\pm +\mathcal{E}_{em}^\pm =\mathcal{M}\) . Moreover in terms of the \textit{ scale parameter} \((\zeta_\pm)\), \textit{the distortion parameter} \((\xi_\pm)\) \textit{and a new parameter} \((\sigma_\pm)\) which corresponds to the area \((\mathcal{A}_\pm)\), the angular momentum \((J)\) and the charge parameter \((Q)\), we find that the \textit{mass parameter in a compact form} \(\mathcal{E}_s^\pm +\mathcal{E}_r^\pm +\mathcal{E}_{em}^\pm =\mathcal{M} =\frac{\zeta_\pm}{2} \sqrt{\frac{1+2 \sigma_\pm^2}{1-\xi_\pm^2}}\) which is valid through all the horizons \(( \mathcal{H}^\pm)\). We also compute the \textit{equatorial circumference and polar circumference} which is a gross measure of the BH surface deformation. It is shown that when the spinning rate of the BH increases, the \textit{equatorial circumference increases} while the \textit{polar circumference decreases}. We show that there exist two classes of geometry separated by \(\xi_\pm =\frac{1}{2}\) in Kerr-Sen BH. In the regime \(\frac{1}{2}<\xi_\pm \leq \frac{1}{\sqrt{2}}\), the Gaussian curvature is negative and there exist \textit{two polar caps} on the surface. While for \(\xi_\pm <\frac{1}{2}\), the Gaussian curvature is positive and the surface will be an oblate deformed sphere. Furthermore, we compute the exact expression of \textit{rotational energy that should be extracted from the BH via Penrose process}. The maximum value of rotational energy which is extractable should occur for \textit{extremal Kerr-Sen BH} i.e. \(\mathcal{ E}_r^+ =\left( \sqrt{2}-1\right) \sqrt{\frac{J}{2}}\).Spins of primordial black holes formed with a soft equation of statehttps://zbmath.org/1528.830842024-03-13T18:33:02.981707Z"Saito, Daiki"https://zbmath.org/authors/?q=ai:saito.daiki"Harada, Tomohiro"https://zbmath.org/authors/?q=ai:harada.tomohiro"Koga, Yasutaka"https://zbmath.org/authors/?q=ai:koga.yasutaka"Yoo, Chul-Moon"https://zbmath.org/authors/?q=ai:yoo.chul-moon(no abstract)Overcharging process around a magnetized black hole: can the backreaction effect of magnetic field restore cosmic censorship conjecture?https://zbmath.org/1528.830872024-03-13T18:33:02.981707Z"Shaymatov, Sanjar"https://zbmath.org/authors/?q=ai:shaymatov.sanjar"Ahmedov, Bobomurat"https://zbmath.org/authors/?q=ai:ahmedov.bobomurat-jSummary: It is well known that the electrically charged Reissner-Nordström black hole could be overcharged. Here, we investigate the process of overcharging of a magnetized Reissner-Nordström black hole that includes effect of the magnetic field generated by own magnetic charge of source on the background geometry. It is found that magnetic field prevents a transition to occur from black hole to naked singularity, thus overcharging cannot be attained which happens due to the fact that the magnetic field reaches its threshold value. It turns out that beyond threshold value the magnetic field can exert large Lorentz force on particles and dominate over the gravitational force, allowing charged particles not to fall into the black hole. One may conclude, there occurs no evidence for violation of cosmic censorship conjecture for a magnetized Reissner-Nordström black hole beyond threshold value of the magnetic field.Spontaneous pair production near magnetized Reissner-Nordström black holeshttps://zbmath.org/1528.830882024-03-13T18:33:02.981707Z"Siahaan, Haryanto M."https://zbmath.org/authors/?q=ai:siahaan.haryanto-mSummary: We investigate the pair production near a (near) extremal magnetized Reissner-Nordstrom black hole. The pair production is shown to exist in the extremal state, which can be interpreted as the Schwinger effect due to the strong field under consideration. To show a correspondence between the growth of the external magnetic field and the scalar absorption, some numerical examples are provided.Thermodynamic properties of Schwarzschild black hole in non-commutative gauge theory of gravityhttps://zbmath.org/1528.830892024-03-13T18:33:02.981707Z"Touati, Abdellah"https://zbmath.org/authors/?q=ai:touati.abdellah"Zaim, Slimane"https://zbmath.org/authors/?q=ai:zaim.slimaneSummary: In this paper, we use the non-commutative (NC) gauge theory of gravity to investigate the thermodynamic properties of a deformed Schwarzschild Black Hole (SBH). Our results present a new scenario of black hole evaporation. As a first step, we describe the Arnowitt-Deser-Misner (ADM) mass, the Hawking temperature, and the entropy of NC SBH. The non-commutativity removes the divergent behavior of temperature, and the result shows a difference in the pole-equator temperature. These corrections also reveal a new fundamental length at the Planck scale order, \(\Theta\sim 10^{- 35}\) m. In the last stage of evaporation, the NC correction exposes a remnant entropy \(S_0^\Theta\) of the NC SBH with a minimal mass \(\hat{m}_0\), where the non-commutativity prevents the black hole from evaporating more than this minimal mass. Then, the description of the heat capacity and the Helmholtz free energy of the deformed black hole shows the effect of the NC gauge theory on the thermodynamic stability and the phase transitions. Finally, we investigate the influence of the black hole pressure on the stability and the phase transition of SBH in NC space-time. In the final stage of this scenario, the remnant black hole is thermodynamically stable. In this study, we find that the NC parameter plays a role similar to the thermodynamic variable. The results show a second-order phase transition of NC SBH.Gravitational waves from eccentric extreme mass-ratio inspirals as probes of scalar fieldshttps://zbmath.org/1528.830922024-03-13T18:33:02.981707Z"Zhang, Chao"https://zbmath.org/authors/?q=ai:zhang.chao.5|zhang.chao.1|zhang.chao|zhang.chao.17|zhang.chao.11|zhang.chao.3|zhang.chao.2|zhang.chao.12"Gong, Yungui"https://zbmath.org/authors/?q=ai:gong.yungui"Liang, Dicong"https://zbmath.org/authors/?q=ai:liang.dicong"Wang, Bin"https://zbmath.org/authors/?q=ai:wang.bin.1(no abstract)Detecting vector charge with extreme mass ratio inspirals onto Kerr black holeshttps://zbmath.org/1528.830932024-03-13T18:33:02.981707Z"Zhang, Chao"https://zbmath.org/authors/?q=ai:zhang.chao.1|zhang.chao.3|zhang.chao.12|zhang.chao.17|zhang.chao.11|zhang.chao|zhang.chao.5|zhang.chao.2"Guo, Hong"https://zbmath.org/authors/?q=ai:guo.hong"Gong, Yungui"https://zbmath.org/authors/?q=ai:gong.yungui"Wang, Bin"https://zbmath.org/authors/?q=ai:wang.bin.1(no abstract)On possible wormhole solutions supported by non-commutative geometry within \(f(\mathcal{R},\mathcal{L}_m)\) gravityhttps://zbmath.org/1528.830952024-03-13T18:33:02.981707Z"Kavya, N. S."https://zbmath.org/authors/?q=ai:kavya.n-s"Venkatesha, V."https://zbmath.org/authors/?q=ai:venkatesha.venkatesha"Mustafa, G."https://zbmath.org/authors/?q=ai:mustafa.ghulam"Sahoo, P. K."https://zbmath.org/authors/?q=ai:sahoo.pradyumn-kumarSummary: Non-commutativity is a key feature of spacetime geometry. The current article explores the traversable wormhole solutions in the framework of \(f(\mathcal{R},\mathcal{L}_m)\) gravity within non-commutative geometry. By using the Gaussian and Lorentzian distributions, we construct tideless wormholes for the nonlinear \(f(\mathcal{R},\mathcal{L}_m)\) model \(f(\mathcal{R},\mathcal{L}_m)=\frac{\mathcal{R}}{2}+\mathcal{L}_m^\alpha\). For both cases, we derive shape functions and discuss the required different properties with satisfying behavior. For the required wormhole properties, we develop some new constraints. The influence of the involved model parameter on energy conditions is analyzed graphically which provides a discussion about the nature of exotic matter. Further, we check the physical behavior regarding the stability of wormhole solutions through the TOV equation. An interesting feature regarding the stability of the obtained solutions via the speed of sound parameters within the scope of average pressure is discussed. Finally, we conclude our results.Transitioning from a bounce to \(R^2\) inflationhttps://zbmath.org/1528.830962024-03-13T18:33:02.981707Z"Daniel, Richard"https://zbmath.org/authors/?q=ai:daniel.richard"Campbell, Mariam"https://zbmath.org/authors/?q=ai:campbell.mariam"van de Bruck, Carsten"https://zbmath.org/authors/?q=ai:van-de-bruck.carsten"Dunsby, Peter"https://zbmath.org/authors/?q=ai:dunsby.peter-k-s(no abstract)Traversable wormholes with double layer thin shells in quadratic gravityhttps://zbmath.org/1528.831052024-03-13T18:33:02.981707Z"Rosa, João Luís"https://zbmath.org/authors/?q=ai:rosa.joao-luis"André, Rui"https://zbmath.org/authors/?q=ai:andre.rui"Lemos, José P. S."https://zbmath.org/authors/?q=ai:lemos.jose-p-sSummary: In quadratic gravity, the junction conditions are six in number and permit the appearance of double layer thin shells. Double layers arise typically in theories with dipoles, i.e., two opposite charges, such as electromagnetic theories, and appear exceptionally in gravitational theories, which are theories with a single charge. We explore this property of the existence of double layers in quadratic gravity to find and study traversable wormholes in which the two domains of the wormhole interior region, where the throat is located, are matched to two vacuum domains of the exterior region via the use of two double layer thin shells. The quadratic gravity we use is essentially given by a \(R+\alpha R^2\) Lagrangian, where \(R\) is the Ricci scalar of the spacetime and \(\alpha\) is a coupling constant, plus a matter Lagrangian. The null energy condition, or NEC for short, is tested for the whole wormhole spacetime. The analysis shows that the NEC is satisfied for the stress-energy tensor of the matter in the whole wormhole interior region, notably at the throat, and is satisfied for some of the stress-energy tensor components of the matter at the double layer thin shell, but is not satisfied for some other components, namely, the double layer stress-energy distribution component, at the thin shell. This seems to mean that the NEC is basically impossible, or at least very hard, to be satisfied when double layer thin shells are present. Single layer thin shells are also admitted within the theory, and we present thin shell traversable wormholes, i.e., wormholes without interior, with a single layer thin shell at the throat for which the corresponding stress-energy tensor satisfies the NEC, that are asymmetric, i.e., with two different vacuum domains of the exterior region joined at the wormhole throat.Non-minimal coupling inflation and dark matter under the \(\mathbb{Z}_3\) symmetryhttps://zbmath.org/1528.831072024-03-13T18:33:02.981707Z"Cheng, Wei"https://zbmath.org/authors/?q=ai:cheng.wei"Liu, Xuewen"https://zbmath.org/authors/?q=ai:liu.xuewen"Zhou, Ruiyu"https://zbmath.org/authors/?q=ai:zhou.ruiyu(no abstract)On the constant roll complex scalar field inflationary modelshttps://zbmath.org/1528.831112024-03-13T18:33:02.981707Z"Mohammadi, Ali"https://zbmath.org/authors/?q=ai:mohammadi.ali"Ahmadi, Nahid"https://zbmath.org/authors/?q=ai:ahmadi.nahid"Shokri, Mehdi"https://zbmath.org/authors/?q=ai:shokri.mehdi(no abstract)Inflation and dark matter in the \(Z_5\) modelhttps://zbmath.org/1528.831122024-03-13T18:33:02.981707Z"Qi, XinXin"https://zbmath.org/authors/?q=ai:qi.xinxin"Sun, Hao"https://zbmath.org/authors/?q=ai:sun.hao.5(no abstract)Cosmic microwave background anisotropies generated by cosmic strings with small-scale structurehttps://zbmath.org/1528.831152024-03-13T18:33:02.981707Z"Silva, R. P."https://zbmath.org/authors/?q=ai:da-silva.ricardo-parreira|silva.rafael-paulino"Sousa, L."https://zbmath.org/authors/?q=ai:sousa.lara-g"Rybak, I. Yu."https://zbmath.org/authors/?q=ai:rybak.i-yu(no abstract)Entanglement masquerading in the CMBhttps://zbmath.org/1528.831182024-03-13T18:33:02.981707Z"Adil, Arsalan"https://zbmath.org/authors/?q=ai:adil.arsalan"Albrecht, Andreas"https://zbmath.org/authors/?q=ai:albrecht.andreas-a"Baunach, Rose"https://zbmath.org/authors/?q=ai:baunach.rose"Holman, R."https://zbmath.org/authors/?q=ai:holman.richard|holman.r-a"Ribeiro, Raquel H."https://zbmath.org/authors/?q=ai:ribeiro.raquel-h"Richard, Benoit J."https://zbmath.org/authors/?q=ai:richard.benoit-j(no abstract)Model-independent bubble wall velocities in local thermal equilibriumhttps://zbmath.org/1528.831192024-03-13T18:33:02.981707Z"Ai, Wen-Yuan"https://zbmath.org/authors/?q=ai:ai.wen-yuan"Laurent, Benoit"https://zbmath.org/authors/?q=ai:laurent.benoit"van de Vis, Jorinde"https://zbmath.org/authors/?q=ai:van-de-vis.jorinde(no abstract)Late-time constraints on modified Gauss-Bonnet cosmologyhttps://zbmath.org/1528.831222024-03-13T18:33:02.981707Z"Bajardi, Francesco"https://zbmath.org/authors/?q=ai:bajardi.francesco"D'Agostino, Rocco"https://zbmath.org/authors/?q=ai:dagostino.roccoSummary: In this paper, we consider a gravitational action containing a combination of the Ricci scalar, \(R\), and the topological Gauss-Bonnet term, \(G\). Specifically, we study the cosmological features of a particular class of modified gravity theories selected by symmetry considerations, namely the \(f(R,G)= R^n G^{1-n}\) model. In the context of a spatially flat, homogeneous and isotropic background, we show that the currently observed acceleration of the Universe can be addressed through geometry, hence avoiding \textit{de facto} the shortcomings of the cosmological constant. We thus present a strategy to numerically solve the Friedmann equations in presence of pressureless matter and obtain the redshift behavior of the Hubble expansion rate. Then, to check the viability of the model, we place constraints on the free parameters of the theory by means of a Bayesian Monte Carlo method applied to late-time cosmic observations. Our results show that the \(f(R, G)\) model is capable of mimicking the low-redshift behavior of the standard \(\Lambda\) CDM model. Finally, we investigate the energy conditions and show that, under suitable choices for the values of the cosmographic parameters, they are all violated when considering the mean value of \(n\) obtained from our analysis, as occurs in the case of a dark fluid.Holographic space-time, Newton's law, and the dynamics of horizonshttps://zbmath.org/1528.831232024-03-13T18:33:02.981707Z"Banks, Tom"https://zbmath.org/authors/?q=ai:banks.thomas"Fischler, Willy"https://zbmath.org/authors/?q=ai:fischler.willySummary: We revisit the construction of models of quantum gravity in \(d\) dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton's law. The scattering amplitudes in these models describe scattering of jets of particles, and also include amplitudes for the production of highly meta-stable states with all the parametric properties of black holes. These models have emergent energy, momentum and angular conservation laws, despite being based on time dependent Hamiltonians. The scattering amplitudes in which no intermediate black holes are produced have a time-ordered Feynman diagram space-time structure: local interaction vertices connected by propagation of free particles (really Sterman-Weinberg jets of particles). However, there are also amplitudes where jets collide to form large meta-stable objects, with all the scaling properties of black holes: energy, entropy and temperature, as well as the characteristic time scale for the decay of perturbations. We generalize the conjecture of Sekino and Susskind, to claim that all of these models are fast scramblers. The rationale for this claim is that the interactions are invariant under fuzzy subgroups of the group of volume preserving diffeomorphisms, so that they are highly non-local on the holographic screen. We review how this formalism resolves the Firewall Paradox.Coupling quintessence kinetics to electromagnetismhttps://zbmath.org/1528.831252024-03-13T18:33:02.981707Z"Barros, Bruno J."https://zbmath.org/authors/?q=ai:barros.bruno-jose-s"da Fonseca, Vitor"https://zbmath.org/authors/?q=ai:da-fonseca.vitor(no abstract)Cosmological constant and Szekeres-Szafron metrichttps://zbmath.org/1528.831262024-03-13T18:33:02.981707Z"Bordbar, Mohammad Rahim"https://zbmath.org/authors/?q=ai:bordbar.mohammad-rahim"Amirmojahedi, Mojtaba"https://zbmath.org/authors/?q=ai:amirmojahedi.mojtabaSummary: The present paper is devoted to analyzing light deflection caused by the presence of a cosmological constant in a space-time described by the Szekeres-Szafron metric. We use the orbital equation for light to calculate the deflection angle in gravitational lensing in the equatorial plane of the Szekeres-Szafron metric. The present study confirms that the cosmological constant has an effect on gravitational lensing.Revisiting Vainshtein screening for fast \(N\)-body simulationshttps://zbmath.org/1528.831282024-03-13T18:33:02.981707Z"Brando, Guilherme"https://zbmath.org/authors/?q=ai:brando.guilherme"Koyama, Kazuya"https://zbmath.org/authors/?q=ai:koyama.kazuya"Winther, Hans A."https://zbmath.org/authors/?q=ai:winther.hans-a(no abstract)On adiabatic subtraction in an inflating universehttps://zbmath.org/1528.831312024-03-13T18:33:02.981707Z"Corbà, Sofia P."https://zbmath.org/authors/?q=ai:corba.sofia-p"Sorbo, Lorenzo"https://zbmath.org/authors/?q=ai:sorbo.lorenzo(no abstract)An update on adiabatic modes in cosmology and \(\delta N\) formalismhttps://zbmath.org/1528.831322024-03-13T18:33:02.981707Z"Cruces, Diego"https://zbmath.org/authors/?q=ai:cruces.diego"Germani, Cristiano"https://zbmath.org/authors/?q=ai:germani.cristiano"Palomares, Adrian"https://zbmath.org/authors/?q=ai:palomares.adrian(no abstract)A diffeomorphism invariant family of metric-affine actions for loop cosmologieshttps://zbmath.org/1528.831332024-03-13T18:33:02.981707Z"Delhom, Adrià"https://zbmath.org/authors/?q=ai:delhom.adria"Olmo, Gonzalo J."https://zbmath.org/authors/?q=ai:olmo.gonzalo-j"Singh, Parampreet"https://zbmath.org/authors/?q=ai:singh.parampreet(no abstract)Hidden freedom in the mode expansion on static spacetimeshttps://zbmath.org/1528.831342024-03-13T18:33:02.981707Z"de Souza Campos, Lissa"https://zbmath.org/authors/?q=ai:de-souza-campos.lissa"Dappiaggi, Claudio"https://zbmath.org/authors/?q=ai:dappiaggi.claudio"Sinibaldi, Luca"https://zbmath.org/authors/?q=ai:sinibaldi.lucaSummary: We review the construction of ground states focusing on a real scalar field whose dynamics is ruled by the Klein-Gordon equation on a large class of static spacetimes. As in the analysis of the classical equations of motion, when enough isometries are present, via a mode expansion the construction of two-point correlation functions boils down to solving a second order, ordinary differential equation on an interval of the real line. Using the language of Sturm-Liouville theory, most compelling is the scenario when one endpoint of such interval is classified as a limit circle, as it often happens when one is working on globally hyperbolic spacetimes with a timelike boundary. In this case, beyond initial data, one needs to specify a boundary condition both to have a well-defined classical dynamics and to select a corresponding ground state. Here, we take into account boundary conditions of Robin type by using well-known results from Sturm-Liouville theory, but we go beyond the existing literature by exploring an unnoticed freedom that emerges from the intrinsic arbitrariness of secondary solutions at a limit circle endpoint. Accordingly, we show that infinitely many one-parameter families of sensible dynamics are admissible. In other words, we emphasize that physical constraints guaranteeing the construction of ground states do not, in general, fix one such state unambiguously. In addition, we provide, in full detail, an example on \((1+1)\)-half Minkowski spacetime to spell out the rationale in a specific scenario where analytic formulae can be obtained.Updating constraints on phantom crossing \(f(T)\) gravityhttps://zbmath.org/1528.831352024-03-13T18:33:02.981707Z"dos Santos, F. B. M."https://zbmath.org/authors/?q=ai:dos-santos.f-b-m(no abstract)Constraints on the non-minimally coupled Witten-O'Raifeartaigh inflationhttps://zbmath.org/1528.831362024-03-13T18:33:02.981707Z"dos Santos, F. B. M."https://zbmath.org/authors/?q=ai:dos-santos.f-b-m"Silva, R."https://zbmath.org/authors/?q=ai:silva.raimundo-jun"Alcaniz, J. S."https://zbmath.org/authors/?q=ai:alcaniz.jailson-s(no abstract)Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedomhttps://zbmath.org/1528.831382024-03-13T18:33:02.981707Z"Fanizza, G."https://zbmath.org/authors/?q=ai:fanizza.giuseppe"Marozzi, G."https://zbmath.org/authors/?q=ai:marozzi.giovanni"Medeiros, M."https://zbmath.org/authors/?q=ai:medeiros.marcelo-c|medeiros.marcello-a-f|medeiros.marcio(no abstract)Gauge/frame invariant variables for the numerical relativity study of cosmological spacetimeshttps://zbmath.org/1528.831432024-03-13T18:33:02.981707Z"Ijjas, Anna"https://zbmath.org/authors/?q=ai:ijjas.anna(no abstract)Viable vector coherent oscillation dark matterhttps://zbmath.org/1528.831442024-03-13T18:33:02.981707Z"Kitajima, Naoya"https://zbmath.org/authors/?q=ai:kitajima.naoya"Nakayama, Kazunori"https://zbmath.org/authors/?q=ai:nakayama.kazunori(no abstract)Stable cosmological solutions in Horndeski theoryhttps://zbmath.org/1528.831502024-03-13T18:33:02.981707Z"Mironov, S."https://zbmath.org/authors/?q=ai:mironov.sergei-vladimirovich|mironov.sergei-grigorevich|mironov.s-a|mironov.s-f|mironov.sergey-v"Shtennikova, A."https://zbmath.org/authors/?q=ai:shtennikova.a(no abstract)Infrared (in)sensitivity of relativistic effects in cosmological observable statisticshttps://zbmath.org/1528.831512024-03-13T18:33:02.981707Z"Mitsou, Ermis"https://zbmath.org/authors/?q=ai:mitsou.ermis"Yoo, Jaiyul"https://zbmath.org/authors/?q=ai:yoo.jaiyul"Magi, Matteo"https://zbmath.org/authors/?q=ai:magi.matteoSummary: The relativistic effects in cosmological observables contain critical information about the initial conditions and gravity on large scales. Compared to the matter density fluctuation, some of these relativistic contributions scale with negative powers of comoving wave number, implying a growing sensitivity to infrared modes. However, this can be inconsistent with the equivalence principle and can also lead to infrared divergences in the observable \(N\)-point statistics. Recent perturbative calculations have shown that this infrared sensitivity is indeed spurious due to subtle cancellations in the cosmological observables that have been missed in the bulk of the literature. Here we demonstrate that the cosmological observable statistics are infrared-insensitive in a general and fully non-linear way, assuming diffeomorphism invariance and adiabatic fluctuations on large scales.A non-singular bouncing cosmology in \(f(R,T)\) gravityhttps://zbmath.org/1528.831632024-03-13T18:33:02.981707Z"Singh, J. K."https://zbmath.org/authors/?q=ai:singh.j-k"Shaily"https://zbmath.org/authors/?q=ai:shaily."Singh, Akanksha"https://zbmath.org/authors/?q=ai:singh.akanksha"Beesham, Aroonkumar"https://zbmath.org/authors/?q=ai:beesham.aroonkumar"Shabani, Hamid"https://zbmath.org/authors/?q=ai:shabani.hamidSummary: We investigate a bounce realization in the framework of higher order curvature in \(f(R,T)\) modified theory of gravity. We perform a detailed analysis of the cosmological parameters to explain the contraction phase, the bounce phase, and the expansion phase. Furthermore, we observe a violation of the null energy condition, instability of the model, and a singularity upon deceleration at the bouncing point, which are the supporting results for a bouncing cosmology. The equation of state parameter exhibits a ghost condensate behavior of the model near the bouncing point. Additionally, we discuss the stability of the model using linear perturbations in the Hubble parameter as well as the energy density.Consistent cosmological structure formation on all scales in relativistic extensions of MONDhttps://zbmath.org/1528.831662024-03-13T18:33:02.981707Z"Thomas, D. B."https://zbmath.org/authors/?q=ai:thomas.daniel-b"Mozaffari, A."https://zbmath.org/authors/?q=ai:mozaffari.ali|mozaffari.ahmad"Zlosnik, T."https://zbmath.org/authors/?q=ai:zlosnik.tom-g(no abstract)Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisitedhttps://zbmath.org/1528.831712024-03-13T18:33:02.981707Z"Wang, Dong-Gang"https://zbmath.org/authors/?q=ai:wang.dong-gang"Pimentel, Guilherme L."https://zbmath.org/authors/?q=ai:pimentel.guilherme-l"Achúcarro, Ana"https://zbmath.org/authors/?q=ai:achucarro.anaSummary: Primordial non-Gaussianities from multi-field inflation are a leading target for cosmological observations, because of the possible large correlations generated between long and short distances. These signatures are captured by the local shape of the scalar bispectrum. In this paper, we revisit the nonlinearities of the conversion process from additional light scalars into curvature perturbations during inflation. We provide analytic templates for correlation functions valid at any kinematical configuration, using the cosmological bootstrap as a main computational tool. Our results include the possibility of large breaking of boost symmetry, in the form of small speeds of sound for both the inflaton and the mediators. We consider correlators coming from the tree-level exchange of a massless scalar field. By introducing a late-time cutoff, we identify that the symmetry constraints on the correlators are modified. This leads to anomalous conformal Ward identities, and consequently the bootstrap differential equations acquire a source term that depends on this cutoff. The solutions to the differential equations are scalar seed functions that incorporate these late-time growth effects. Applying weight-shifting operators to auxiliary ``seed'' functions, we obtain a systematic classification of shapes of non-Gaussianity coming from massless exchange. For theories with de Sitter symmetry, we compare the resulting shapes with the ones obtained via the \(\delta N\) formalism, identifying missing contributions away from the squeezed limit. For boost-breaking scenarios, we derive a novel class of shape functions with phenomenologically distinct features in scale-invariant theories. Specifically, the new shape provides a simple extension of equilateral non-Gaussianity: the signal peaks at a geometric configuration controlled by the ratio of the sound speeds of the mediator and the inflaton.Localization of U(1) gauge field by non-minimal coupling with gravity in braneworldshttps://zbmath.org/1528.831742024-03-13T18:33:02.981707Z"Zhao, Zhen-Hua"https://zbmath.org/authors/?q=ai:zhao.zhenhua"Xie, Qun-Ying"https://zbmath.org/authors/?q=ai:xie.qun-ying"Fu, Chun-E."https://zbmath.org/authors/?q=ai:fu.chun-e"Zhou, Xiang-Nan"https://zbmath.org/authors/?q=ai:zhou.xiangnan(no abstract)Anisotropic compact stars with karmarkar condition in energy-momentum squared gravityhttps://zbmath.org/1528.850082024-03-13T18:33:02.981707Z"Sharif, M."https://zbmath.org/authors/?q=ai:sharif.muhammad"Gul, M. Zeeshan"https://zbmath.org/authors/?q=ai:gul.m-zeeshanSummary: The main objective of this paper is to examine the viability and stability of anisotropic compact stellar objects adopting the Karmarkar condition in energy-momentum squared gravity. For this purpose, we take a static spherical metric in the inner and Schwarzschild spacetime in the outer region of the stars. The values of unknown parameters are found by the observational values of mass and radius of the considered compact stars. We consider a particular model of this theory to investigate the behavior of energy density, pressure components, anisotropy, equation of state parameters and energy bounds in the inner region of the proposed stellar objects. The equilibrium state of the stellar models is examined via the Tolman-Oppenheimer-Volkoff equation and their stability is analyzed by causality condition, Herrera cracking approach and adiabatic index. We find that Karmarkar solutions in this modified theory are physically viable and stable for anisotropic stellar objects.Quantum mechanical calculations of synchro-curvature radiations: maser possibilityhttps://zbmath.org/1528.850092024-03-13T18:33:02.981707Z"Tomoda, Hiroko"https://zbmath.org/authors/?q=ai:tomoda.hiroko"Yamada, Shoichi"https://zbmath.org/authors/?q=ai:yamada.shoichiSummary: We calculate the radiative transition rates for synchro-curvature radiation to explore the possibility of maser in the environment that may occur in the magnetosphere of neutron stars (NSs). Unlike previous studies, we employ relativistic quantum mechanics, solving the Dirac equation for an electron in helical magnetic fields. Following \textit{G. Voisin} et al. [Phys. Rev. D (3) 95, No. 8, Article ID 085002, 16 p. (2017, \url{doi:10.1103/PhysRevD.95.085002}); Phys. Rev. D (3) 95, No. 10, Article ID 105008, 17 p. (2017; \url{doi:10.1103/PhysRevD.95.105008})], we utilize adiabatic spinor rotations, under the assumption that the curvature of magnetic-field lines is much larger than the Larmor radius, to obtain the wave functions of an electron. We classify the electron states either by the spin operator projected on the magnetic field or by the helicity operator. To demonstrate that there is a regime where the true absorption rate becomes negative, we numerically evaluate the obtained formulae for some parameter values that may be encountered in the outer gaps of different types of NSs. We show that there is indeed a range of parameters for the negative true absorption rate to occur. We will also study the dependence on those parameters systematically and discuss the classical limit of our formulae. We finally give a crude estimate of the amplification factor in the same environment.Learning-based super-twisting sliding-mode control for space circumnavigation mission with suboptimal reaching under input constraintshttps://zbmath.org/1528.930222024-03-13T18:33:02.981707Z"Dong, Hanlin"https://zbmath.org/authors/?q=ai:dong.hanlin"Yang, Xuebo"https://zbmath.org/authors/?q=ai:yang.xueboSummary: The problem of attitude-orbit synchronous finite-time control for the space circumnavigation (SCN) mission with input constraints is investigated in this research article. A novel terminal sliding-mode (TSM) manifold with nonsingular first derivative is developed to ensure that the sliding-mode reduced-order system is practical finite-time stable. Then, the learning-based adaptive dynamic programming (ADP) technique is adopted to design a super-twisting sliding-mode control scheme, so that the proposed TSM is suboptimal reached. Especially, benefited from the introduction of two nonlinear performance indexes, the proposed sliding-mode control strategy satisfies the saturation constraint of the propulsion system, and the weight update rate of the actor-critic (AC) network will not be too large, even if the initial value of the system is too large. Finally, the simulation results show that both attitude and orbital tracking errors in the SCN mission are forced to converge to a small neighborhood containing the origin synchronously under input saturation constraints.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Nonuniform piecewise membership function approximation methods based robust tracking control design of T-S fuzzy systemshttps://zbmath.org/1528.930462024-03-13T18:33:02.981707Z"Xie, Wen-Bo"https://zbmath.org/authors/?q=ai:xie.wenbo"Xu, Bo-Lin"https://zbmath.org/authors/?q=ai:xu.bolin"Peng, Chen"https://zbmath.org/authors/?q=ai:peng.chen"Zhang, Jian"https://zbmath.org/authors/?q=ai:zhang.jian.2Summary: For the stability analysis issue of a T-S fuzzy system, improved piecewise membership functions dependent approach is proposed to reduce conservatism. Based on a least-square method, the nonlinear membership functions are approximated by a series of decoupled polynomial functions. Then the piecewise vertices are chosen by a newly proposed derivative-integral nonuniform division approach. For the robust tracking control task, a series of convex robust stable conditions are obtained. Finally, a mass-spring-damper (MSD) simulation example is adopted to illustrate the effectiveness of the designed method.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Dynamic surface control with a nonlinear disturbance observer for multi-degree of freedom underactuated mechanical systemshttps://zbmath.org/1528.930682024-03-13T18:33:02.981707Z"Ding, Feng"https://zbmath.org/authors/?q=ai:ding.feng.1"Huang, Jian"https://zbmath.org/authors/?q=ai:huang.jian.4"Xu, WenXia"https://zbmath.org/authors/?q=ai:xu.wenxia"Yang, Chenguang"https://zbmath.org/authors/?q=ai:yang.chenguang"Sun, Chong"https://zbmath.org/authors/?q=ai:sun.chong"Ai, Yong"https://zbmath.org/authors/?q=ai:ai.yongSummary: Underactuated systems are extensively utilized in practice while attracting a huge deal of attention in theoretical studies. There are few robust control strategies for general underactuated systems because of the variety of their dynamic models. A dynamic surface control strategy with a nonlinear disturbance observer is proposed in this study, to stabilize multi-degree of freedom underactuated systems. In such systems the number of underactuated degrees of freedom is not higher compared to the actuated ones. A disturbance observer is utilized to dispose of the uncertain disturbance and cross terms in dynamic model which may cause failure to the controller. Then, a dynamic surface control strategy is presented which is not sensitive to the diversity of dynamic models. The stability of whole system is proven by Lyapunov-based method. The control law is successfully applied to nonlinear underactuated systems in benchmark cascade form such as two-translational oscillator with rotational actuator, crane, wheeled inverted pendulum. The effectiveness of proposed controllers are illustrated by MATLAB simulation results. Finally, comparative studies are presented to verify the superiority of the proposed method.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Constrained control for rigid spacecrafthttps://zbmath.org/1528.930712024-03-13T18:33:02.981707Z"Lyu, Bailiang"https://zbmath.org/authors/?q=ai:lyu.bailiang"Yue, Xiaokui"https://zbmath.org/authors/?q=ai:yue.xiaokui"Liu, Chuang"https://zbmath.org/authors/?q=ai:liu.chuang.1Summary: This article develops a multi-observer-based fault-tolerant disturbance-rejection control strategy to solve the attitude stabilization problem of spacecraft subject to multisource complex disturbances, for example, external disturbance, measurement error, actuator fault, input constraint. First, two intermediate variables are introduced for multi-observer design, so that the synergistic estimations of attitude information, actuator fault and external disturbance are obtained simultaneously. Then, a fault-tolerant disturbance-rejection control strategy is proposed based on the estimations, and an augmented closed-loop system is derived. Afterwards, Lyapunov stability analysis is performed to prove the quadratic stability and robust \(H_{\infty}\) performance, and corresponding conditions in terms of linear matrix inequalities (LMIs) is proved, where the input constraint is satisfied as well. Finally, numerical simulations of a spacecraft attitude control system are performed which demonstrate the effectiveness and superiority of the proposed multi-observer-based control strategy.
{{\copyright} 2022 John Wiley \& Sons Ltd.}State observers for the time discretization of a class of impulsive mechanical systemshttps://zbmath.org/1528.930732024-03-13T18:33:02.981707Z"Preiswerk, Pascal V."https://zbmath.org/authors/?q=ai:preiswerk.pascal-v"Leine, Remco I."https://zbmath.org/authors/?q=ai:leine.remco-iSummary: In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the original continuous-time system by a discrete linear complementarity system (LCS) through the use of the Schatzman-Paoli scheme. From there, we derive a deadbeat observer in the form of a linear complementarity problem. Sufficient conditions guaranteeing the uniqueness of its solution then serve as observability conditions. In addition, the discrete adaptation of an existing passivity-based observer design for LCSs can be applied. A key point in using a time discretization is that the discretization acts as a regularization, that is, the impacts take place over multiple time steps (here two time steps). This makes it possible to render the estimation error dynamics asymptotically stable. Furthermore, the so-called peaking phenomenon appears as singularity within the time discretization approach, posing a challenge for robust observer design.
{{\copyright} 2022 The Authors. \textit{International Journal of Robust and Nonlinear Control} published by John Wiley \& Sons Ltd.}Adaptive friction compensation for a class of mechanical systems based on LuGre modelhttps://zbmath.org/1528.930962024-03-13T18:33:02.981707Z"Chen, Pengnian"https://zbmath.org/authors/?q=ai:chen.pengnian"Liu, Xiangbin"https://zbmath.org/authors/?q=ai:liu.xiangbin"Yan, Qiuzhen"https://zbmath.org/authors/?q=ai:yan.qiuzhenSummary: This paper deals with the problem of friction compensation for a class of uncertain mechanical systems based on LuGre model. The objective is to develop control laws such that the position variable of the system tracks a periodic desired signal or a constant desired signal. Since the friction behavior of the system with periodic desired signals is largely different from that of the system with constant desired signals, two different adaptive control methods are presented for the two cases, respectively. For the case of periodic desired signals, an adaptive repetitive learning control method is presented, and for the case of constant desired signals, an adaptive dynamic state feedback control method is presented. Both the control laws can guarantee that all the signals in the closed loop system are bounded and the tracking errors converge to zero. Several numerical simulations are carried out to show effectiveness of the proposed control algorithms.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Adaptive fault-tolerant robust control based on radial basis function neural network for a class of mechanical systems with input constraintshttps://zbmath.org/1528.930982024-03-13T18:33:02.981707Z"Gao, Shiqi"https://zbmath.org/authors/?q=ai:gao.shiqi"Liu, Jinkun"https://zbmath.org/authors/?q=ai:liu.jinkunSummary: In this paper, a robust adaptive fault-tolerant control (FTC) strategy based on hyperbolic tangent function is proposed for a class of mechanical systems with unknown disturbance and unknown nonlinear friction model. The robust adaptive FTC algorithm proposed in this paper can maintain the system performance even after partial failure occurs in the actuator. Different from the traditional fault-tolerant control algorithms, the proposed algorithm uses the hyperbolic tangent function and a projection algorithm to limit the control input within a known upper bound. In addition, radial basis function neural network is used to approximate the unknown continuous nonlinear function that contains the friction model in the mechanical system. The control target of the system is realized; and the asymptotic stability of the closed-loop system is proved via the Lyapunov direct method. Finally, the numerical simulation results also demonstrate the effectiveness of the designed controller.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Dynamics of slender single-link flexible robotic manipulator based on Timoshenko beam theoryhttps://zbmath.org/1528.931632024-03-13T18:33:02.981707Z"Rao, Priya"https://zbmath.org/authors/?q=ai:rao.priya"Chakraverty, S."https://zbmath.org/authors/?q=ai:chakraverty.snehashish"Roy, Debanik"https://zbmath.org/authors/?q=ai:roy.debanikSummary: It is well known that irrespective of the joint signature, namely serial or articulated, a single-link manipulator has a great application in the field of robotics. For the study of dynamics of single-link manipulators, the conjugate problem is studied based on Timoshenko beam theory. Governing differential equations and the boundary conditions are usually considered as exact and the formulation leads to an eigenvalue problem where the elements of the matrices are in exact form. In view of the above, this chapter investigates the said problem in particular for a single-link semi-compliant flexible robotic manipulator. After the successful modelling of the single-link manipulator, with Timoshenko beam theory, the model has been compared with the existing calculation of an undamped Euler-Bernoulli cantilever beam as well, taking tip mass to be zero. The study extends further by taking tip mass to be non-zero and the results are compared with mass-loaded clamped-free Timoshenko beam. These comparisons are found to be in good agreement.
For the entire collection see [Zbl 1523.37002].Generalization of the Rutherford formula and synthesis of trajectories with gravity assist maneuvershttps://zbmath.org/1528.931672024-03-13T18:33:02.981707Z"Golubev, Yu. F."https://zbmath.org/authors/?q=ai:golubev.yu-f"Grushevskii, A. V."https://zbmath.org/authors/?q=ai:grushevskii.a-v"Koryanov, V. V."https://zbmath.org/authors/?q=ai:koryanov.v-v"Tuchin, A. G."https://zbmath.org/authors/?q=ai:tuchin.a-g"Tuchin, D. A."https://zbmath.org/authors/?q=ai:tuchin.d-aSummary: This article studies the development of new effective methods for designing spacecraft (SC) trajectories for missions using the generalization of the Rutherford formula for the scattering of charged particles proposed by the authors for the case of gravitational scattering. For controlled gravity assist maneuvers of SC, a rule is formulated that makes it possible to purposefully create beams of trajectories with specified properties as a result of a gravity assist maneuver. Modifications of this rule are presented that make it possible to implement efficient and reliable beam recurrent procedures for searching for the ballistic scenarios of interplanetary flights. Of particular importance is the synthesis of sequences of gravity assist maneuvers that provide the given change in the asymptotic velocity of the SC relative to the target planet.Time-optimal turning of a spring pendulumhttps://zbmath.org/1528.931682024-03-13T18:33:02.981707Z"Kayumov, O. R."https://zbmath.org/authors/?q=ai:kayumov.o-rSummary: We consider the problem of the time-optimal turning of a system with two degrees of freedom in the form of a material point on a spring oscillating along a rigid weightless rod that rotates in a horizontal plane. The external control moment is applied to the axis of rotation of the rod and is limited in absolute value; and there is no friction. The problem of the fastest turning of the rod through the given angle from a state of rest with oscillation damping is solved. A feature of a nonlinear system is that its linearized model (in the vicinity of the state of rest) is not controllable.Optimal control of the reorientation of a spacecraft in the given time with a quadratic performance criterion related to the control and phase variableshttps://zbmath.org/1528.931692024-03-13T18:33:02.981707Z"Levskii, M. V."https://zbmath.org/authors/?q=ai:levskii.m-vSummary: The problem of the dynamic optimal turn of a spacecraft (SC) from an arbitrary initial to the required final angular position is considered and solved. The time required for the turn is fixed. To optimize the rotation control program, a combined quality criterion is used, the minimized functional characterizes the energy costs and combines the costs of control forces and the rotation energy integral in the given proportion. The problem is solved analytically. The construction of the optimal turn control is based on quaternion models and the maximum principle of L.S. Pontryagin. The optimality conditions are written in analytical form, and the properties of the optimal motion are studied. Formalized equations and calculation expressions are given to determine the optimal turning program. The control law is formulated as an explicit dependence of the control variables on the phase coordinates. Analytical equations and relations are written out for finding the optimal motion of the SC. The key relationships are given that determine the optimal values of the parameters of the rotation control algorithm. A constructive scheme for solving the boundary value problem of the maximum principle for arbitrary turning conditions is also described. For an axisymmetric SC, a complete solution of the reorientation problem in a closed form is given. An example and results of the mathematical modeling of the SC's motion dynamics under the optimal control are given, demonstrating the practical feasibility of the developed method for controlling the spatial orientation of an SC.Analytical quasi-optimal algorithm for the programmed control of the angular motion of a spacecrafthttps://zbmath.org/1528.931712024-03-13T18:33:02.981707Z"Molodenkov, A. V."https://zbmath.org/authors/?q=ai:molodenkov.aleksei-vladimirovich"Sapunkov, I. G."https://zbmath.org/authors/?q=ai:sapunkov.i-gSummary: The problem of the optimal program control of the angular motion of a spacecraft (SC) as a rigid body with a quadratic functional of the energy spent on the maneuver of the SC and a fixed time of the transition process is investigated. The dynamic configuration of the SC and the boundary conditions are arbitrary and the control vector function is not limited. In the Poinsot concept, using the Pontryagin maximum principle, a quasi-optimal analytical solution of the problem is obtained, which is developed into an algorithm. Confirming numerical examples are given, showing the proximity of the quasi-optimal solution to the optimal solution of the problem.Modeling and vertical torsional coupling vibration control of the rolling mill with full state constraintshttps://zbmath.org/1528.931722024-03-13T18:33:02.981707Z"Qian, Cheng"https://zbmath.org/authors/?q=ai:qian.cheng"Xu, Jiajun"https://zbmath.org/authors/?q=ai:xu.jiajun"Hua, Changchun"https://zbmath.org/authors/?q=ai:hua.changchun"Park, Kyoung-Su"https://zbmath.org/authors/?q=ai:park.kyoung-suSummary: This article establishes a mechanical-electrical-hydraulic vertical torsional coupling vibration mathematical model, and investigates its vibration suppression control strategy with time varying full state constraints for the rolling mill vertical torsional coupling vibration system. Firstly, the mechanical-electrical-hydraulic vertical torsional coupling vibration nonlinear model is developed using dynamic theory, which takes into account nonlinear damping, nonlinear rolling force and the coupling relationship between the vertical vibration system and the torsional vibration system. Then, nonlinear constraint transformation functions and coordinate transformations are implemented to remove the feasibility condition in handling the full state constraints problem, and neural networks are used to approximate unknown nonlinear functions. Furthermore, the vibration suppression control algorithm of the mechanical-electrical-hydraulic vertical torsional coupling system is designed with the specific sequence backstepping method and dynamic surface control technique, which can resolve the problem of nesting in the controller design process. Finally, the effective of the proposed method on vibration suppression is verified by the simulation.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Stabilization of programmed motions of constrained mechanical systemshttps://zbmath.org/1528.931742024-03-13T18:33:02.981707Z"Golubev, A. E."https://zbmath.org/authors/?q=ai:golubev.a-eSummary: The problem of the stabilization of programmed trajectories of mechanical systems, taking the constraints on the values of generalized coordinates, velocities, and accelerations into account, is considered. The control is built using the backstepping method in combination with the use of logarithmic Lyapunov barrier functions. The stabilizing feedbacks obtained in this study, in contrast to similar known results, do not lead to an unlimited increase in the values of the control variables when the state variables of the system approach the boundary values. As an example, the problem of constructing and stabilizing the trajectory of the spatial motion of an underwater vehicle is considered.Orbital synchronization of homogeneous mechanical systems with one degree of underactuationhttps://zbmath.org/1528.931842024-03-13T18:33:02.981707Z"Herrera, Leonardo"https://zbmath.org/authors/?q=ai:herrera.leonardo"Rodríguez-Liñán, María del Carmen"https://zbmath.org/authors/?q=ai:rodriguez-linan.maria-del-carmen"Meza-Sánchez, Marlen"https://zbmath.org/authors/?q=ai:meza-sanchez.marlen"Clemente, Eddie"https://zbmath.org/authors/?q=ai:clemente.eddieSummary: A methodology for asymptotic orbital synchronization of a set of homogeneous mechanical systems with one degree of underactuation is proposed. A reference model generating a reference orbit is first constructed under the virtual holonomic constraints approach. Then, the \(\mathcal{H}_\infty\) synthesis is designed to, first, estimate the state vector of the homogeneous systems, provided that only position measurements are available, and second, to drive the state of the systems to that of the reference model. Due to the \(\mathcal{H}_\infty\) synthesis properties, the homogeneous systems converge asymptotically to the reference orbit when there are no disturbances affecting the systems nor the measurements. When disturbances are present, robustness is guaranteed provided that the \(\mathcal{L}_2\) gain of the closed-loop systems remains lower than an attenuation level \(\gamma\). Numerical results for a set of underactuated cart-pendulums corroborate the proposed methodology.
{{\copyright} 2022 John Wiley \& Sons Ltd.}A more exhaustive study on the finite-time and exponential tracking continuous control for constrained-input mechanical systems: improved design and experimentshttps://zbmath.org/1528.932032024-03-13T18:33:02.981707Z"Zavala-Río, Arturo"https://zbmath.org/authors/?q=ai:zavala-rio.arturo"Zamora-Gómez, Griselda I."https://zbmath.org/authors/?q=ai:zamora-gomez.griselda-ivone"Sanchez, Tonametl"https://zbmath.org/authors/?q=ai:sanchez.tonametl"Reyes-Cortes, Fernando"https://zbmath.org/authors/?q=ai:reyes-cortes.fernando"López-Araujo, Daniela J."https://zbmath.org/authors/?q=ai:lopez-araujo.daniela-juanitaSummary: A more exhaustive study on the finite-time/exponential tracking continuous control for mechanical systems with input constraints is developed. The resulting control scheme is characterized by the inclusion of position-error and velocity-error correction terms which are suitably shaped to achieve the concerned types of convergence. Such a shaping is carried out through control parameters that act as exponential weights on the gained position and velocity errors. As an innovative aspect of the proposal, such exponential weights are not restricted to satisfy a fixed equivalence relation among them but rather a wider comparative one. This gives rise to a wider spectrum of finite-time convergent closed-loop trajectories and gives an optional type of (unconventional) exponential convergence (in addition to the conventional one), which enlarges the controller potential for performance adjustment. This is further potentiated through a more generalized saturating structure on the error correction terms, that includes the usual saturating-proportional saturating-derivative type one as a particular case. The improved design is supported through a more general analysis based on more general strict Lyapunov functions, stating more solid analytical bases for possible design extensions on the accomplishment of other (more complex) control objectives. The study is further supported through experimental tests on a 3-degree-of-freedom robot manipulator.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Normalized passivity control for robust tuning in real-time hybrid testshttps://zbmath.org/1528.932202024-03-13T18:33:02.981707Z"Peiris, Lokukankanamge Dushyantha Hashan"https://zbmath.org/authors/?q=ai:peiris.lokukankanamge-dushyantha-hashan"Plummer, Andrew R."https://zbmath.org/authors/?q=ai:plummer.andrew-r"du Bois, Jonathan L."https://zbmath.org/authors/?q=ai:dubois.jonathan-lSummary: Real-time hybrid testing involves the separation of a system into an experimental component and a numerically simulated substructure which are coupled and run together. The coupling between substructures is achieved using actuators and force sensors which comprise the transfer system. Close synchronization is required between substructures for reliable hybrid testing. However, actuator lag may cause tracking errors and instability in hybrid tests. Existing lag compensation schemes require identification of the coupled dynamics of the transfer system and experimental component and can be sensitive to changes in these components. Passivity control is a technique intended to maintain stability without the need for system identification or assumptions about the actuators or test specimens. Yet, the tuning of existing passivity controllers is sensitive to both the system being tested and the amplitude and frequency range excited. This paper presents a new, normalized passivity controller which behaves well across a much broader range of operating conditions once tuned for a single-test scenario. The proposed approach uses a virtual damping element on the numerical substructure to dissipate spurious power injected by the actuator into the system, based on the ratio of net power output to mean power throughput. The scheme has been shown to result in identical performance for a linear hybrid test with a range of step excitations from 0.5\,mm up to 500\,mm. The proposed method can be used to improve test stability and fidelity in isolation or alongside other compensation schemes to further improve performance.
{{\copyright} 2022 The Authors. \textit{International Journal of Robust and Nonlinear Control} published by John Wiley \& Sons Ltd.}