Recent zbMATH articles in MSC 70F https://www.zbmath.org/atom/cc/70F 2022-06-24T15:10:38.853281Z Werkzeug The role of pseudo-hypersurfaces in non-holonomic motion https://www.zbmath.org/1485.14083 2022-06-24T15:10:38.853281Z "Delphenich, David" https://www.zbmath.org/authors/?q=ai:delphenich.david The aim of this paper is to generalize the geometry of hypersurfaces to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint. They are applied to the example of a charge moving in an electromagnetic field, and the Lorentz equation of motion is shown to represent a geodesic that is constrained to lie in a pseudo-hypersurface that is defined by the potential $$1$$-form. This paper is organized as follows : Section 1 is an introduction to the subject. Section 2 deals with the geometry of hypersurfaces. The treatment here is a generalization of the classical geometry of surfaces, but a specialization of the more modern treatment. Section 3 is devoted to the geometry of pseudo-hypersurfaces. Many of the geometric constructions that were just made for hypersurfaces are based upon tangent and cotangent objects, which can exist independently of whether the hypersurface is represented as an embedded submanifold. Hence, one must consider its definition as an envelope, not a locus, and not assume that the envelope is completely integrable. In Section 4 the author studies kinematics in pseudo-hypersurfaces. Section 5 deals with an example concerning a charge moving in an electromagnetic field. In Section 6, the author discusses some aspects from what was developed in this study, the scope of the applications of pseudohypersurfaces to physics is essentially identical to the scope of application of the theory of Pfaff equation to physics, which the author has previously discussed [\textit{S. Schroll} and \textit{H. Treffinger}, A $\tau$-tilting approach to the first Brauer-Thrall conjecture'', Preprint, \url{arXiv:1210.4976}]. Hence, there are still many other physical applications of pseudo-hypersurfaces to explore. Section 7 is devoted to conclusions about the results obtained. Reviewer: Ahmed Lesfari (El Jadida) Sliding dynamics on codimension-2 discontinuity surfaces https://www.zbmath.org/1485.34069 2022-06-24T15:10:38.853281Z "Antali, Mate" https://www.zbmath.org/authors/?q=ai:antali.mate "Stepan, Gabor" https://www.zbmath.org/authors/?q=ai:stepan.gabor Summary: The properties of codimension-2 discontinuity sufaces of vector fields are presented which can arise from e.g., spatial Coulomb friction. Concepts of sliding region and sliding dynamics are defined for these systems. For the entire collection see [Zbl 1368.00047]. Non-smooth Hopf-type and grazing bifurcations arising from impact/friction contact events https://www.zbmath.org/1485.34117 2022-06-24T15:10:38.853281Z "Mora, Karin" https://www.zbmath.org/authors/?q=ai:mora.karin "Budd, Chris" https://www.zbmath.org/authors/?q=ai:budd.chris-j Summary: A new discontinuity-induced bifurcation, referred to as nonsmooth Hopf-type bifurcation, observed in a nonautonomous impacting hybrid systems in $$\mathbb R^4$$ is presented. The system studied models the bouncing motion, repeated instantaneous impacts with friction, in rotating machines with magnetic bearing support. At the nonsmooth Hopf-type bifurcation point a stable regular equilibrium and two unstable small amplitude 1-impact periodic orbits arise. The existence of this bifurcation scenario depends on a complex relationship between damping, the restitution, and the friction coefficient. For the entire collection see [Zbl 1368.00047]. Emergence of synchronization in Kuramoto model with frustration under general network topology https://www.zbmath.org/1485.34141 2022-06-24T15:10:38.853281Z "Zhu, Tingting" https://www.zbmath.org/authors/?q=ai:zhu.tingting Summary: In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data are confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [\textit{S.-Y. Ha} et al., Math. Models Methods Appl. Sci. 30, No. 9, 1653--1703 (2020; Zbl 1458.34098)] to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and an invariant set confined in quarter circle after some finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization. Existence of partially hyperbolic motions in the $$N$$-body problem https://www.zbmath.org/1485.70009 2022-06-24T15:10:38.853281Z "Burgos, J. M." https://www.zbmath.org/authors/?q=ai:burgos.juan-manuel In this article it is proved a corollary from the results of [\textit{E. Maderna} and \textit{A. Venturelli}, Ann. Math. (2) 192, No. 2, 499--550 (2020; Zbl 1475.70018)]. Theorem 1 states that, by assuming positive energy and starting at any collisionless configuration, in dimension at least two, there is a partially hyperbolic motion. Partially hyperbolic motions are defined on closed half real lines. They evolve as clusters separating linearly in time such that the distance between any two bodies in a cluster grows like $$t^{2/3}$$, and there is at least two clusters, one of them with more than one body. The theorem is proved by showing the existence of a free time minimizer partially hyperbolic motion of the supercritical Newtonian action. An equivalent version of the theorem in terms of geodesic rays of the Jacobi-Maupertuis metric is also given. Reviewer: Giovanni Rastelli (Vercelli) Five new methods of celestial mechanics https://www.zbmath.org/1485.70010 2022-06-24T15:10:38.853281Z "Bruno, Alexander" https://www.zbmath.org/authors/?q=ai:bruno.alexander-d Summary: The last volume of the book [Les méthodes nouvelles de la mécanique céleste. Tome III. Invariants intégraux. Paris: Gauthier-Villars et Fils (1899; JFM 30.0834.08)] by \textit{H. Poincaré} was published more than 120 years ago. Since then, the following methods have arisen. 1. Method of normal forms, allowing to study regular perturbations near a stationary solution, near a periodic solution and so on. 2. Method of truncated systems, which are found with a help of the Newton polyhedrons, allowing to study singular perturbations. 3. Method of generating families of periodic solutions (regular and singular). 4. Method of generalized problems, allowing bodies with negative masses. 5. Computation of a net of families of periodic solutions as a skeleton'' of a part of the phase space. Was Jupiter born beyond the current orbits of Neptune and Pluto? https://www.zbmath.org/1485.70011 2022-06-24T15:10:38.853281Z "Croswell, Ken" https://www.zbmath.org/authors/?q=ai:croswell.ken (no abstract) Conserved quantities and Hamiltonization of nonholonomic systems https://www.zbmath.org/1485.70012 2022-06-24T15:10:38.853281Z "Balseiro, Paula" https://www.zbmath.org/authors/?q=ai:balseiro.paula "Yapu, Luis P." https://www.zbmath.org/authors/?q=ai:yapu.luis-p In this paper, the hamiltonization of nonholonomic systems is studied. In Section 2, the geometric approach to nonholonomic systems with symmetries is presented. Some notions such as constraint manifold, nonholonomic bracket, nonholonomic vector field, nonholonomic system, action of a Lie group, symmetries, twisted Poisson structures, and their properties are recalled. In Section 3, a nonholonomic system with a proper symmetry is considered. The concept of a gauge transformation is recalled and used to generate a new almost Poisson bivector associated to the considered system. The main result, regarding the gauge transformation and properties of the new bracket, is given by Theorem 3.7. In order to prove this theorem, other preliminary results are obtained. In Section 4, some examples are discussed, namely the snakeboard, the Chaplygin ball, a solid of revolution rolling on a plane, and a homogeneous ball rolling in the interior side of a cylinder. In Section 5, the hamiltonization problem of the mechanical system formed by a homogeneous ball rolling without sliding on a convex surface of revolution is analyzed. Reviewer: Cristian Lăzureanu (Timişoara) Emergence of self-organized multivortex states in flocks of active rollers https://www.zbmath.org/1485.70013 2022-06-24T15:10:38.853281Z "Han, Koohee" https://www.zbmath.org/authors/?q=ai:han.koohee "Kokot, Gašper" https://www.zbmath.org/authors/?q=ai:kokot.gasper "Snezhko, Alexey" https://www.zbmath.org/authors/?q=ai:snezhko.alexey Summary: Active matter, both synthetic and biological, demonstrates complex spatiotemporal self-organization and the emergence of collective behavior. A coherent rotational motion, the vortex phase, is of great interest because of its ability to orchestrate well-organized motion of self-propelled particles over large distances. However, its generation without geometrical confinement has been a challenge. Here, we show by experiments and computational modeling that concentrated magnetic rollers self-organize into multivortex states in an unconfined environment. We find that the neighboring vortices more likely occur with the opposite sense of rotation. Our studies provide insights into the mechanism for the emergence of coherent collective motion on the macroscale from the coupling between microscale rotation and translation of individual active elements. These results may stimulate design strategies for self-assembled dynamic materials and microrobotics. Hamiltonian approach to the soliton-soliton interaction and for a classical solitonic gas https://www.zbmath.org/1485.81030 2022-06-24T15:10:38.853281Z "Quispe-Flores, Luzmila A." https://www.zbmath.org/authors/?q=ai:quispe-flores.luzmila-a "Urzagasti, Deterlino" https://www.zbmath.org/authors/?q=ai:urzagasti.deterlino Summary: The known stationary solutions of the parametrically driven and damped nonlinear Schrödinger equation (PDDNLS) have been used to calculate the interaction potential and the interaction law of pairs of solitons from a strictly theoretical point of view. In agreement with the numerical simulations reported in the literature, our results reveal that the phase difference between solitons plays an important role in their dynamics (this can be either zero or $$\pi$$), and that the two-soliton interaction is very weak and exponential type. Finally, the model was applied to a solitonic gas to find its thermodynamics and numerical simulations were also performed to study the dynamics of this gas. Quantum phases of two-component bosons in the extended Bose-Hubbard model https://www.zbmath.org/1485.81071 2022-06-24T15:10:38.853281Z "Zhang, Dian-Cheng" https://www.zbmath.org/authors/?q=ai:zhang.diancheng "Feng, Shi-Ping" https://www.zbmath.org/authors/?q=ai:feng.shiping "Yang, Shi-Jie" https://www.zbmath.org/authors/?q=ai:yang.shijie Summary: Quantum phases of two-component bosons in a 2D square lattice are studied within the extended Bose-Hubbard model. By using the inhomogeneous Gutzwiller mean-field method, we identified the density-wave as well as supersolid phases which have different average particles fillings in each component. Phases separation occurs in some parameter regimes, including on-site and nearest neighbor interactions within one component or between two components. Reconstruction of primordial power spectrum of curvature perturbation from the merger rate of primordial black hole binaries https://www.zbmath.org/1485.83014 2022-06-24T15:10:38.853281Z "Kimura, Rampei" https://www.zbmath.org/authors/?q=ai:kimura.rampei "Suyama, Teruaki" https://www.zbmath.org/authors/?q=ai:suyama.teruaki "Yamaguchi, Masahide" https://www.zbmath.org/authors/?q=ai:yamaguchi.masahide "Zhang, Ying-li" https://www.zbmath.org/authors/?q=ai:zhang.ying-li|zhang.yingli Eliminating the LIGO bounds on primordial black hole dark matter https://www.zbmath.org/1485.83064 2022-06-24T15:10:38.853281Z "Bœhm, Céline" https://www.zbmath.org/authors/?q=ai:boehm.celine "Kobakhidze, Archil" https://www.zbmath.org/authors/?q=ai:kobakhidze.archil-b "A. J. O'Hare, Ciaran" https://www.zbmath.org/authors/?q=ai:a-j-ohare.ciaran "S. C. Picker, Zachary" https://www.zbmath.org/authors/?q=ai:s-c-picker.zachary "Sakellariadou, Mairi" https://www.zbmath.org/authors/?q=ai:sakellariadou.mairi Estimating the final spin of binary black holes merger in STU supergravity https://www.zbmath.org/1485.83082 2022-06-24T15:10:38.853281Z "Li, Shou-Long" https://www.zbmath.org/authors/?q=ai:li.shoulong "Tan, Wen-Di" https://www.zbmath.org/authors/?q=ai:tan.wen-di "Wu, Puxun" https://www.zbmath.org/authors/?q=ai:wu.puxun "Yu, Hongwei" https://www.zbmath.org/authors/?q=ai:yu.hongwei Summary: In this paper, we adopt the so-called Buonanno-Kidder-Lehner (BKL) recipe to estimate the final spin of a rotating binary black hole merger in STU supergravity. According to the BKL recipe, the final spin can be viewed as the sum of the individual spins plus the orbital angular momentum of the binary system which could be approximated as the angular momentum of a test particle orbiting at the innermost stable circular orbit around the final black hole. Unlike previous works, we consider the contribution of the orbital angular momentum of the binary system to the final spin by requiring the test particle to preserve the scaling symmetry in the Lagrangian of supergravity. We find some subtle differences between two cases corresponding to whether the symmetry is taken into account or not. In the equal initial spin configuration, when the initial black holes are non-spinning, the final spin of the merger is always larger than that in the case in which the symmetry is not imposed although the general behaviors are similar. The difference increases firstly and then decreases as the initial mass ratio approaches unity. Besides, as the initial spins exceed a threshold, the final spin is always smaller than that in the case where the scaling symmetry is not considered. The difference decreases constantly as the equal initial mass limit is approached. All these features exist in the merger of a binary STU black hole with different charge configurations. We also study the final spin's difference between different charge configurations and different initial spin configurations. Fractional order PD control of friction-induced vibrations in a continuous system https://www.zbmath.org/1485.93188 2022-06-24T15:10:38.853281Z "Kokane, Tejas" https://www.zbmath.org/authors/?q=ai:kokane.tejas "Saha, Ashesh" https://www.zbmath.org/authors/?q=ai:saha.ashesh Summary: Fractional-order PD ($$\mathrm{PD}^\lambda$$) control of friction-induced vibrations in a beam-mass model is analysed in this paper. Mathematical modelling of the system with a piezo-patch actuator bonded to the beam surface is presented. Linear stability analysis is performed to determine the stability boundary corresponding to the Hopf bifurcation points. The nature of bifurcation is found to be supercritical from the non-linear analysis by the method of averaging. The role of fractional-order on the effectiveness of the controller in quenching friction-induced vibrations is thoroughly investigated. The efficacy of the controller with varying size and locations of the piezo-patch is also studied. Modelling and simulation of self-regulating pneumatic valves https://www.zbmath.org/1485.93415 2022-06-24T15:10:38.853281Z "Pollok, Alexander" https://www.zbmath.org/authors/?q=ai:pollok.alexander "Casella, Francesco" https://www.zbmath.org/authors/?q=ai:casella.francesco Summary: In conventional aircraft energy systems, self-regulating pneumatic valves (SRPVs) are used to control the pressure and mass flow of the bleed air. The dynamic behaviour of these valves is complex and dependent on several physical phenomena. In some cases, limit cycles can occur, deteriorating performance. This article presents a complex multi-physical model of SRPVs implemented in Modelica. First, the working principle is explained, and common challenges in control-system design-problems related to these valves are illustrated. Then, a Modelica-model is presented in detail, taking into account several physical domains. It is shown, how limit cycle oscillations occurring in aircraft energy systems can be reproduced with this model. The sensitivity of the model regarding both solver options and physical parameters is investigated. On the geometric construction of a stabilizing time-invariant state feedback controller for the nonholonomic integrator https://www.zbmath.org/1485.93462 2022-06-24T15:10:38.853281Z "Zeng, Shen" https://www.zbmath.org/authors/?q=ai:zeng.shen The classical Brockett integrator is revisited. This is the first example of a nonlinear control system that is fully controllable but for which no stabilizing continuous time-invariant state feedback exists [\textit{R. W. Brockett}, Prog. Math. 27, 181--191 (1983; Zbl 0528.93051)]. A natural and elementary geometric construction is used to construct a stabilizing time-invariant state feedback law. This feedback is smooth almost everywhere except for discontinuities along the $$z$$-axis and non-differentiability on the $$xy$$-plane. The corresponding closed-loop trajectories exhibit uniform exponential convergence to the origin. To illustrate the proposed approach, the closed-loop state trajectory is calculated for the initial state $$(0, 0, 1)$$. Reviewer: Mikhail I. Krastanov (Sofia) Privacy-preserving dynamic average consensus via state decomposition: case study on multi-robot formation control https://www.zbmath.org/1485.93548 2022-06-24T15:10:38.853281Z "Zhang, Kaixiang" https://www.zbmath.org/authors/?q=ai:zhang.kaixiang "Li, Zhaojian" https://www.zbmath.org/authors/?q=ai:li.zhaojian "Wang, Yongqiang" https://www.zbmath.org/authors/?q=ai:wang.yongqiang "Louati, Ali" https://www.zbmath.org/authors/?q=ai:louati.ali "Chen, Jian" https://www.zbmath.org/authors/?q=ai:chen.jian Summary: Dynamic average consensus is a decentralized control/estimation framework where a group of agents cooperatively track the average of local time-varying reference signals. In this paper, we develop a novel state decomposition-based privacy preservation scheme to protect the privacy of agents when sharing information with neighboring agents. Specifically, we first show that an external eavesdropper can successfully wiretap the reference signals of all agents in a conventional dynamic average consensus algorithm. To protect privacy against the eavesdropper, a state decomposition scheme is developed where the original state of each agent is decomposed into two sub-states: one succeeds the role of the original state in inter-node interactions, while the other sub-state only communicates with the first one and is invisible to other neighboring agents. Rigorous analyses are performed to show that (1) the proposed privacy scheme preserves the convergence of the average consensus; and (2) the privacy of the agents is protected such that an eavesdropper cannot discover the private reference signals with guaranteed accuracy. The developed privacy-preserving dynamic average consensus framework is then applied to the formation control of multiple non-holonomic mobile robots, in which the efficacy of the scheme is demonstrated. Numerical simulation is provided to illustrate the effectiveness of the proposed approach.