Recent zbMATH articles in MSC 82https://www.zbmath.org/atom/cc/822021-03-30T15:24:00+00:00WerkzeugThe phase field method for geometric moving interfaces and their numerical approximations.https://www.zbmath.org/1455.352762021-03-30T15:24:00+00:00"Du, Qiang"https://www.zbmath.org/authors/?q=ai:du.qiang"Feng, Xiaobing"https://www.zbmath.org/authors/?q=ai:feng.xiaobingSummary: This chapter surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical methods and their analyses, the chapter presents a holistic overview about the main ideas of phase field modelling, its mathematical foundation, and relationships between the phase field formalism and other mathematical formalisms for geometric moving interface problems, as well as the current state of the art of numerical approximations of various phase field models with an emphasis on discussing the main ideas of numerical analysis techniques. The chapter also reviews recent development on adaptive grid methods and various applications of the phase field modelling and their numerical methods in materials science, fluid mechanics, biology and image science.
For the entire collection see [Zbl 1435.35001].An elementary proof and detailed investigation of the bulk-boundary correspondence in the generic two-band model of Chern insulators.https://www.zbmath.org/1455.820032021-03-30T15:24:00+00:00"Chen, Bo-Hung"https://www.zbmath.org/authors/?q=ai:chen.bo-hung"Chiou, Dah-Wei"https://www.zbmath.org/authors/?q=ai:chiou.dah-weiBayesian static parameter estimation for partially observed diffusions via multilevel Monte Carlo.https://www.zbmath.org/1455.650082021-03-30T15:24:00+00:00"Jasra, Ajay"https://www.zbmath.org/authors/?q=ai:jasra.ajay"Kamatani, Kengo"https://www.zbmath.org/authors/?q=ai:kamatani.kengo"Law, Kody"https://www.zbmath.org/authors/?q=ai:law.kody-j-h"Zhou, Yan"https://www.zbmath.org/authors/?q=ai:zhou.yanThe second term for two-neighbour bootstrap percolation in two dimensions.https://www.zbmath.org/1455.601302021-03-30T15:24:00+00:00"Hartarsky, Ivailo"https://www.zbmath.org/authors/?q=ai:hartarsky.ivailo"Morris, Robert"https://www.zbmath.org/authors/?q=ai:morris.robert-dSummary: In the \(r\)-neighbour bootstrap process on a graph \(G\), vertices are infected (in each time step) if they have at least \(r\) already-infected neighbours. Motivated by its close connections to models from statistical physics, such as the Ising model of ferromagnetism and kinetically constrained spin models of the liquid-glass transition, the most extensively studied case is the two-neighbour bootstrap process on the two-dimensional grid \([n]^2\). Around 15 years ago, in a major breakthrough, \textit{A. E. Holroyd} [Probab. Theory Relat. Fields 125, No. 2, 195--224 (2003; Zbl 1042.60065)] determined the sharp threshold for percolation in this model, and his bounds were subsequently sharpened further by \textit{J. Gravner} and \textit{A. E. Holroyd} [Ann. Appl. Probab. 18, No. 3, 909--928 (2008; Zbl 1141.60062)], and by Gravner, Holroyd, and Morris [\textit{J. Gravner} et al., Probab. Theory Relat. Fields 153, No. 1--2, 1--23 (2012; Zbl 1254.60092)]. In this paper we strengthen the lower bound of Gravner, Holroyd, and Morris [loc. cit.] by proving that the critical probability \(p_c\big ( [n]^2,2 \big )\) for percolation in the two-neighbour model on \([n]^2\) satisfies \[p_c\big ( [n]^2,2 \big ) = \frac{\pi ^2}{18\log n} - \frac{\Theta (1)}{(\log n)^{3/2}}.\]
The proof of this result requires a very precise understanding of the typical growth of a critical droplet and involves a number of technical innovations. We expect these to have other applications, for example, to the study of more general two-dimensional cellular automata and to the \(r\)-neighbour process in higher dimensions.On boundary confinements for the Coulomb gas.https://www.zbmath.org/1455.820092021-03-30T15:24:00+00:00"Ameur, Yacin"https://www.zbmath.org/authors/?q=ai:ameur.yacin"Kang, Nam-Gyu"https://www.zbmath.org/authors/?q=ai:kang.nam-gyu"Seo, Seong-Mi"https://www.zbmath.org/authors/?q=ai:seo.seong-miSummary: We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field -- a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.An operator that relates to semi-meander polynomials via a two-sided \(q\)-Wick formula.https://www.zbmath.org/1455.050082021-03-30T15:24:00+00:00"Nica, Alexandru"https://www.zbmath.org/authors/?q=ai:nica.alexandru"Zhong, Ping"https://www.zbmath.org/authors/?q=ai:zhong.pingSummary: We consider the sequence \((Q_n)_{n=1}^{\infty}\) of semi-meander polynomials which are used in the enumeration of semi-meandric systems (a family of diagrams related to the classical stamp-folding problem). We show that for a fixed \(d\in\mathbb{N},(Q_n(d))_{n=1}^{\infty}\) appears as the sequence of moments of a compactly supported probability measure \(\nu_d\) on \(\mathbb{R} \). More generally, we consider a sequence of two-variable polynomials \((\tilde{Q}_n)_{n=1}^{\infty}\) related to a natural concept of ``self-intersecting semi-meandric system,'' where the second variable of \(\tilde{Q}_n\) keeps track of the crossings of such a system; one has, in particular, that \(Q_n(t)=\tilde{Q}_n(t,0)\). We prove that for fixed \(d\in\mathbb{N}\) and \(q\in(-1,1), (\tilde{Q}_n(d,q))_{n=1}^{\infty}\) can be identified as the sequence of moments of a compactly supported probability measure \(\nu_{d;q}\) on \(\mathbb{R} \). The measure \(\nu_{d;q}\) is found as scalar spectral measure for an operator \(T_{d;q}\) constructed by using left and right creation/annihilation operators on the \(q\)-Fock space over \(\mathbb{C}^d\), a deformation of the full Fock space over \(\mathbb{C}^d\) introduced by Bo \(\dot{\text{z}}\) ejko and Speicher. The relevant calculations of moments for \(T_{d;q}\) are made by using a two-sided version of a (previously studied in the one-sided case) ``\(q\)-Wick formula,'' which involves the number of crossings of a pair-partition.Two-parameter entropies in extended parastatistics of nonextensive systems.https://www.zbmath.org/1455.820042021-03-30T15:24:00+00:00"Zaripov, R. G."https://www.zbmath.org/authors/?q=ai:zaripov.rinat-gSummary: General expressions are given for entropies from which one-parameter and two-parameter entropies for quantum nonextensive systems follow in extended parastatistics.Nematic first order phase transition for liquid crystals in the van der Waals-Kac limit.https://www.zbmath.org/1455.820062021-03-30T15:24:00+00:00"Erignoux, Clément"https://www.zbmath.org/authors/?q=ai:erignoux.clement"Giuliani, Alessandro"https://www.zbmath.org/authors/?q=ai:giuliani.alessandroIn this present paper, the authors deal with some mathematical aspects of Onsager's theory of liquid crystals. A model of anisotropic molecules with three-dimensional orientations interacting via a Kac-type interaction is introduced. The authors present two main results. Firstly, the authors give a variational formula for the thermodynamic free energy. The authors consider a system of infinitely thin rods interacting via a pairwise potential and hard-core repulsion. Secondly, the authors prove a simple criterion for the existence of a first-order phase transition for the free energy. In the last section, the authors prove the criterium for the first order \(n\).
Reviewer: Hasan Akin (Gaziantep)Local solutions of the Landau equation with rough, slowly decaying initial data.https://www.zbmath.org/1455.352142021-03-30T15:24:00+00:00"Henderson, Christopher"https://www.zbmath.org/authors/?q=ai:henderson.christopher"Snelson, Stanley"https://www.zbmath.org/authors/?q=ai:snelson.stanley"Tarfulea, Andrei"https://www.zbmath.org/authors/?q=ai:tarfulea.andreiSummary: We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform polynomial decay in the velocity variable, and that satisfies a technical lower bound assumption (but can have vacuum regions). For uniqueness in this weak class, we have to make the additional assumption that the initial data is Hölder continuous. Our hypotheses are much weaker, in terms of regularity and decay, than previous large-data well-posedness results in the literature. We also derive a continuation criterion for our solutions that is, for the case of very soft potentials, an improvement over the previous state of the art.Algorithmic information theory and its statistical mechanical interpretation.https://www.zbmath.org/1455.680762021-03-30T15:24:00+00:00"Tadaki, Kohtaro"https://www.zbmath.org/authors/?q=ai:tadaki.kohtaroThe paper reviews similarities between statistical mechanics and algorithmic information theory (AIT). It includes a presentation of some elements of AIT, formulations in AIT terms of the partition function, free energy, energy and statistical mechanical entropy. A discussion of the interpretation of temperature as partial randomness is given. No new results in either statistical mechanics or in AIT are proved.
Reviewer: Cristian S. Calude (Auckland)Large deviations for Brownian motion in a random potential.https://www.zbmath.org/1455.820072021-03-30T15:24:00+00:00"Boivin, Daniel"https://www.zbmath.org/authors/?q=ai:boivin.daniel"Lê, Thi Thu Hien"https://www.zbmath.org/authors/?q=ai:le.thi-thu-hienThe authors extended the quenched large deviation principle for the speed of the Brownian motion in a random potential to stationary random potentials without imposing a regularity condition of the potential (required in [\textit{S. N. Armstrong} and \textit{H. V. Tran}, Anal. PDE 7, No. 8, 1969--2007 (2014; Zbl 1320.35033)].
Reviewer: Utkir A. Rozikov (Tashkent)On the derivation of the mean field equation of the Gibbs distribution function for equilibrium vortices in an external field.https://www.zbmath.org/1455.760102021-03-30T15:24:00+00:00"Ohtsuka, Hiroshi"https://www.zbmath.org/authors/?q=ai:ohtsuka.hiroshiSummary: Motivated by several experimental facts, we are interested in the linear response of equilibrium vortices. In order to study the phenomenon, here we investigate the mean field limit of equilibrium vortices perturbed by an external field and derive the mean field equation of the Gibbs distribution function. Similar limits for classical point particles with bounded interactions were studied by [\textit{J. Messer} and \textit{H. Spohn}, ``Statistical mechanics of the isothermal Lane-Emden equation'', J. Statist. Phys. 29, 561--578 (1982)] and later the results were extended to the system of vortices, which interact via the singular logarithmic potential, by \textit{E. Caglioti} et al. [Commun. Math. Phys. 143, No. 3, 501--525 (1992; Zbl 0745.76001)] and \textit{M. K. H. Kiessling} [Commun. Pure Appl. Math. 46, No. 1, 27--56 (1993; Zbl 0811.76002)] . In this paper, we start with the review of these results in some detail and extend their arguments to the case for vortices perturbed by an external field.Global solutions to the Boltzmann equation without angular cutoff and the Landau equation with Coulomb potential.https://www.zbmath.org/1455.351662021-03-30T15:24:00+00:00"Duan, Renjun"https://www.zbmath.org/authors/?q=ai:duan.renjun"Liu, Shuangqian"https://www.zbmath.org/authors/?q=ai:liu.shuangqian"Sakamoto, Shota"https://www.zbmath.org/authors/?q=ai:sakamoto.shota"Strain, Robert M."https://www.zbmath.org/authors/?q=ai:strain.robert-mSummary: This report succinctly summarizes results proved in the authors' recent work [``Global mild solutions of the Landau and non-cutoff Boltzmann equations'', \url{arXiv:1904.12086}] where the unique existence of solutions to the Boltzmann equation without angular cut-off and the Landau equation with Coulomb potential are studied in a perturbation framework. A major feature is the use of the Wiener space \(A(\Omega)\), which can be expected to play a similar role to \(L^\infty\). Compared to the \(L^2\)-based solution spaces that were employed for prior known results, this function space enables us to establish a new global existence theory. One further feature is that, not only an initial value problem, but also an initial boundary value problem whose boundary conditions can be regarded as physical boundaries in some simple situation, are considered for both equations. In addition to unique existence, large-time behavior of the solutions and propagation of spatial regularity are also proved. In the end of report, key ideas of the proof will be explained in a concise way.One-sided reflected Brownian motions and the KPZ fixed point.https://www.zbmath.org/1455.601312021-03-30T15:24:00+00:00"Nica, Mihai"https://www.zbmath.org/authors/?q=ai:nica.mihai|nica.mihai.2"Quastel, Jeremy"https://www.zbmath.org/authors/?q=ai:quastel.jeremy"Remenik, Daniel"https://www.zbmath.org/authors/?q=ai:remenik.danielSummary: We consider the system of one-sided reflected Brownian motions that is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling-invariant Markov process defined in [\textit{K. Matetski} et al., ``The KPZ fixed point'', Preprint, \url{arXiv: 1701.00018}] and believed to govern the long-time, large-scale fluctuations for all models in the KPZ universality class. Brownian last-passage percolation was shown recently in [\textit{D. Dauvergne} et al., ``The directed landscape'', Preprint, \url{arXiv: 1812.00309}] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.Nano/microscale heat transfer. 2nd updated and expanded edition.https://www.zbmath.org/1455.800032021-03-30T15:24:00+00:00"Zhang, Zhuomin M."https://www.zbmath.org/authors/?q=ai:zhang.zhuomin-mHeat transfer at nanoscale has been a prominent issue for a multitude nanotechnology application, such as energy, materials, biomedicine, and consumer products. Computer Science researchers are also looking to nanotechnology for more efficient ways to transfer data on a chip at low power with minimal energy loss and have found a solution in nano-photonics in transmitting optical signals. The basic thermophysical properties are quite different at nano scale. The continuum assumption has no longer been valid for the system having characteristic length comparable to mean free path.
This book covers a wide range of the topics on the subject. With a brief introduction setting the objective of the book in Chapter 1, an overview of macroscopic thermal sciences is presented in Chapter 2. The fundamentals of statistical thermodynamics, quantum mechanics are discussed in Chapter 3. Three major statistics, namely, the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac are explained. The kinetic theory of gases is introduced in Chapter 4 with reference to a microscopic description of the transport coefficients, such as viscosity, diffusivity and thermal conductivity. Chapter 5 presents the lattice vibrations (i.e., phonons) in solids and discussed the dimensionality and the quantum size effects on the lattice size effect on the lattice specific heat. The classical size effects on electrical and thermal conductivities are presented using both geometric arguments and the Boltzmann transport equation.
Advanced topics on the electron and phonon scattering, size effects, quantum conductance, electronic band theory, tunneling, non-equilibrium heat conduction and analysis of solid state devices such as thermoelectric refrigeration and optoelectronics are introduced in Chapter 6. The underlying physics of the p-n junction is discussed in this chapter with applications such as photovoltaic cells, thermo-photovoltaic, LEDs, luminescent refrigeration and semiconductor lasers. Chapter 7 is focused on the transient and non- equilibrium heat conduction applicable at micro and nano-scale. The equation of Phonon radiative transfer is introduced and its solution techniques are presented. Also heat conduction across layered structures, thermal boundary layer and atomistic Green's function are presented.
Nanoscale thermal radiation and radiative properties of nanomaterials, radiation temperature and entropy, surface electromagnetic waves and near-field radiation for energy conversion devices are discussed in Chapters 8--10. With a brief introduction of radiation thermometry expressions for radiation pressure and photon entropy are derived. In these chapters, discussions are also presented on the radiative properties of semi transparent materials, windows, multilayers, periodic gratings, rough surfaces, as well as evanescent waves, surface polarities, photon tunneling, and near field radiative heat transfer.
Each chapter of the book provides a number of examples as well as exercises to help readers to understand the topics. Some useful mathematical formulae are available in Appendix B for the benefit of the readers of the book. The book also cites a number of research papers at the end of each chapter to help researchers to explore the subject further.
The book is well written and covers many important topics on nano heat transfer. It will serve as a text book for the graduate students and a reference book for the researchers and technologists. It will find an important place in the libraries of the universities and the scientific laboratories.
Reviewer: K. N. Shukla (Gurgaon)Surface physics. Foundations and methods.https://www.zbmath.org/1455.740022021-03-30T15:24:00+00:00"Fauster, Thomas"https://www.zbmath.org/authors/?q=ai:fauster.thomas"Hammer, Lutz"https://www.zbmath.org/authors/?q=ai:hammer.lutz"Heinz, Klaus"https://www.zbmath.org/authors/?q=ai:heinz.klaus"Schneider, M. Alexander"https://www.zbmath.org/authors/?q=ai:schneider.m-alexanderPublisher's description: Oberflächen von Festkörpern sind heute aus der Grundlagenforschung von Physik, Chemie und Materialwissenschaften nicht mehr wegzudenken und spielen in zahlreichen Anwendungen eine immer bedeutendere Rolle.
Das vorliegende Lehrbuch gibt eine Einführung in die moderne experimentelle Oberflächenphysik. Aufgrund langjähriger Lehrerfahrung gelingt es den Autoren, oberflächenspezifische Eigenschaften und Prozesse in leicht verständlicher Form zu erarbeiten und ein mikroskopisches Verständnis der Phänomene an der Oberfläche zu vermitteln.
Das Werk besticht durch sein klares, didaktisches Konzept und ist sowohl als begleitende als auch vertiefende Lektüre zur Vorlesung geeignet. Icons am Seitenrand kennzeichnen Vertiefungsthemen, Zusammenfassungen und weiterführende Literaturangaben am Ende der Kapitel.Derivation of the Maxwell-Schrödinger equations from the Pauli-Fierz Hamiltonian.https://www.zbmath.org/1455.352102021-03-30T15:24:00+00:00"Leopold, Nikolai"https://www.zbmath.org/authors/?q=ai:leopold.nikolai"Pickl, Peter"https://www.zbmath.org/authors/?q=ai:pickl.peterThe Pauli-Fierz Hamiltonian describes a quantum system of identical, non-relativistic particles which are coupled to a quantized electromagnetic field. The authors study the time evolution of this system in a mean-field limit, where the number of particles \(N\) becomes large and the coupling to the radiation field is scaled by \(N^{-1/2}\). At time zero, it is assumed that there is a Bose-Einstein condensate. As \(N\to\infty\), the authors show that the time evolution preserves the condensate and that it can be approximated by the Maxwell-Schrödinger system. In order to obtain these results, it is assumed that the repulsive interaction potential is positive, real, and even, such that the Pauli-Fierz Hamiltonian is self-adjoint on its domain. It is also assumed that there is enough regularity on solutions of the Maxwell-Schrödinger system.
Reviewer: Eric Stachura (Marietta)New coupling conditions for isentropic flow on networks.https://www.zbmath.org/1455.351932021-03-30T15:24:00+00:00"Holle, Yannick"https://www.zbmath.org/authors/?q=ai:holle.yannick"Herty, Michael"https://www.zbmath.org/authors/?q=ai:herty.michael-matthias"Westdickenberg, Michael"https://www.zbmath.org/authors/?q=ai:westdickenberg.michaelSummary: We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model by imposing a condition on energy dissipation. Existence and uniqueness of solutions to the generalized Riemann and Cauchy problem are proven. The result for the generalized Riemann problem is globally in state space. Furthermore, non-increasing energy at the junction and a maximum principle are proven. A numerical example is given in which the new conditions are the only known conditions leading to the physically correct wave types. The approach generalizes to full gas dynamics.Theory of thermodynamic measurements of quantum systems far from equilibrium.https://www.zbmath.org/1455.820022021-03-30T15:24:00+00:00"Shastry, Abhay"https://www.zbmath.org/authors/?q=ai:shastry.abhayThe publication provides a very clearly written account of research work in the field of nonequilibrium quantum thermodynamics, performed by the author during his PhD. The first chapter sets the stage and mentions the relevant framework, namely the formalism of nonequilibrium Green's functions for fermions. The following ones deal with distinct but related aspects of measurements on quantum system in stationary nonequilibrium states. In Chapter 2 the author shows that while separate measurements of temperature or voltage in a nonequilibrium system are ill-posed, due to Peltier and Seebeck effects respectively, in the limit of a noninvasive thermoelectric probe their simultaneous measurement is well defined for any fermion system in the steady state, arbitrarily far from equilibrium. The result is obtained leveraging on the the second law of thermodynamics, and it provides, as an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory. Building on this result, in Chapter 4 an experimental method to measure the local temperature of an electron system is proposed, which could enable improvements to the spatial resolution of thermometry. Chapter 3 addresses the related issue of the lowest possible temperature that can be measured in a nonequilibrium system. The final chapter is devoted to an analysis of the quantum entropy for a system of non-interacting fermions in the steady state, expressed in terms of so-called scattering states, which exactly diagonalize the Hamiltonian. The concavity property of the entropy expression is shown to lead to a natural hierarchy of inequalities for entropies measured by a local observer having access to different partial informations on the system. The various chapters are mostly self-consistent and for each considered topic a realistic model system is treated for which numerical results are worked out and discussed in detail.
Reviewer: Bassano Vacchini (Milano)Magneto-optical/ferromagnetic-material computation: Bäcklund transformations, bilinear forms and \(N\) solitons for a generalized \((3+1)\)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system.https://www.zbmath.org/1455.352482021-03-30T15:24:00+00:00"Gao, Xin-Yi"https://www.zbmath.org/authors/?q=ai:gao.xin-yi"Guo, Yong-Jiang"https://www.zbmath.org/authors/?q=ai:guo.yongjiang"Shan, Wen-Rui"https://www.zbmath.org/authors/?q=ai:shan.wenrui"Yuan, Yu-Qiang"https://www.zbmath.org/authors/?q=ai:yuan.yu-qiang"Zhang, Chen-Rong"https://www.zbmath.org/authors/?q=ai:zhang.chen-rong"Chen, Su-Su"https://www.zbmath.org/authors/?q=ai:chen.su-suThe authors study a generalized \((3+1)\)-dimensional modified Kadomtsev-Petviashvili system for electromagnetic waves in a ferromagnetic material. In particular, the authors derive variable coefficient dependent Auto-Bäcklund transformations for this system; from this, soliton examples are obtained. The authors also derive associated bilinear forms with the Hirota method and obtain two branches of \(N\)-solitonic solutions for the system.
Reviewer: Eric Stachura (Marietta)Point-to-line polymers and orthogonal Whittaker functions.https://www.zbmath.org/1455.601282021-03-30T15:24:00+00:00"Bisi, Elia"https://www.zbmath.org/authors/?q=ai:bisi.elia"Zygouras, Nikos"https://www.zbmath.org/authors/?q=ai:zygouras.nikolaosSummary: We study a one-dimensional directed polymer model in an inverse-gamma random environment, known as the \textit{log-gamma polymer}, in three different geometries: point-to-line, point-to-half-line and when the polymer is restricted to a half-space with end point lying free on the corresponding half-line. Via the use of \textit{A. N. Kirillov}'s geometric Robinson-Schensted-Knuth correspondence [in: Physics and combinatorics. Proceedings of the Nagoya 2000 2nd international workshop, Nagoya, Japan, August 21--26, 2000. Singapore: World Scientific. 82--150 (2001; Zbl 0989.05127)], we compute the Laplace transform of the partition functions in the above geometries in terms of orthogonal Whittaker functions, thus obtaining new connections between the ubiquitous class of Whittaker functions and exactly solvable probabilistic models. In the case of the first two geometries we also provide multiple contour integral formulae for the corresponding Laplace transforms. Passing to the zero-temperature limit, we obtain new formulae for the corresponding last passage percolation problems with exponential weights.Traveling chimera states in continuous media.https://www.zbmath.org/1455.740102021-03-30T15:24:00+00:00"Alvarez-Socorro, Alejandro J."https://www.zbmath.org/authors/?q=ai:alvarez-socorro.alejandro-j"Clerc, M. G."https://www.zbmath.org/authors/?q=ai:clerc.marcel-g"Verschueren, N."https://www.zbmath.org/authors/?q=ai:verschueren.nicolasSummary: Coupled oscillators exhibit intriguing dynamical states characterized by the coexistence of coherent and incoherent domains known as chimera states. Similar behaviors have been observed in coupled systems and continuous media. Here we investigate the transition from motionless to traveling chimera states in continuous media. Based on a prototype model for pattern formation, we observe coexistence between motionless and traveling chimera states. The spatial disparity of chimera states allows us to reveal the motion mechanism. The propagation of chimera states is described by their median and centroidal point. The mobility of these states depends on the size of the incoherent domain. The bifurcation diagram of traveling chimeras is elucidated.A nonlinear hyperbolic model for radiative transfer equation in slab geometry.https://www.zbmath.org/1455.352472021-03-30T15:24:00+00:00"Fan, Yuwei"https://www.zbmath.org/authors/?q=ai:fan.yuwei"Li, Ruo"https://www.zbmath.org/authors/?q=ai:li.ruo"Zheng, Lingchao"https://www.zbmath.org/authors/?q=ai:zheng.lingchaoThe authors study the problem of non-linear radiative transfer in slab geometry by an improved moment model for a globally hyperbolic system. The derived procedure yields a numerical scheme for solving the corresponding non-linear radiative transfer equation, which was applied to several numerical examples such as the two-beam problem, Gaussian source problem, Su-Olson problem, and anti-diffusive radiation flow.
Reviewer: Vladimir Čadež (Beograd)Two-dimensional grain boundary networks: stochastic particle models and kinetic limits.https://www.zbmath.org/1455.740112021-03-30T15:24:00+00:00"Klobusicky, Joe"https://www.zbmath.org/authors/?q=ai:klobusicky.joe"Menon, Govind"https://www.zbmath.org/authors/?q=ai:menon.govind-k"Pego, Robert L."https://www.zbmath.org/authors/?q=ai:pego.robert-lSummary: We study kinetic theories for isotropic, two-dimensional grain boundary networks which evolve by curvature flow. The number densities \(f_s (x, t)\) for \(s\)-sided grains, \(s =1, 2, \ldots\), of area \(x\) at time \(t\), are modeled by kinetic equations of the form \(\partial_t f_s + v_s \partial_x f_s =j_s\). The velocity \(v_s\) is given by the Mullins-von Neumann rule and the flux \(j_s\) is determined by the topological transitions caused by the vanishing of grains and their edges. The foundations of such kinetic models are examined through simpler particle models for the evolution of grain size, as well as purely topological models for the evolution of trivalent maps. These models are used to characterize the parameter space for the flux \(j_s\). Several kinetic models in the literature, as well as a new kinetic model, are simulated and compared with direct numerical simulations of mean curvature flow on a network. The existence and uniqueness of mild solutions to the kinetic equations with continuous initial data is established.Advantages of the fast reactor with an advanced active zone in comparison with the BREST-300 reactor project.https://www.zbmath.org/1455.820112021-03-30T15:24:00+00:00"Gol'din, V. Ya."https://www.zbmath.org/authors/?q=ai:goldin.vladimir-ya"Pestryakova, G. A."https://www.zbmath.org/authors/?q=ai:pestryakova.g-aSummary: Advantages of fast U-Pu reactor of new generation with complete plutonium breeding with an advanced active zone in comparison with the BREST-300 reactor project are shown.Scalar field model applied to the lamellar to the inverse hexagonal phase transition in lipid systems.https://www.zbmath.org/1455.370742021-03-30T15:24:00+00:00"Mendanha, Sebastião A."https://www.zbmath.org/authors/?q=ai:mendanha.sebastiao-a"Cardoso, Wesley B."https://www.zbmath.org/authors/?q=ai:cardoso.wesley-b"Avelar, Ardiley T."https://www.zbmath.org/authors/?q=ai:avelar.ardiley-t"Bazeia, Dionisio"https://www.zbmath.org/authors/?q=ai:bazeia.dionisioSummary: In this paper we use a phenomenological field theory model to study the first-order phase transition from the lamellar phase to the inverse hexagonal phase in specific lipid bilayers. The model is described by a real scalar field with potential that supports both symmetric and asymmetric phase conformations. We adapt the coordinate and parameters of the model to describe the phase transition, and we show that the model is capable of correctly inferring the fraction of the inverse hexagonal phase in the phase transition, suggesting an alternative way to be couple to experimental techniques generally required for \(H_{II}\)-phase characterization.Reshaping of Dirac cones in topological insulators and graphene.https://www.zbmath.org/1455.820012021-03-30T15:24:00+00:00"Fernández, Álvaro Díaz"https://www.zbmath.org/authors/?q=ai:fernandez.alvaro-diazPublisher's description: Dirac cones are ubiquitous to non-trivial quantum matter and are expected to boost and reshape the field of modern electronics. Particularly relevant examples where these cones arise are topological insulators and graphene. From a fundamental perspective, this thesis proposes schemes towards modifying basic properties of these cones in the aforementioned materials. The thesis begins with a brief historical introduction which is followed by an extensive chapter that endows the reader with the basic tools of symmetry and topology needed to understand the remaining text. The subsequent four chapters are devoted to the reshaping of Dirac cones by external fields and delta doping. At all times, the ideas discussed in the second chapter are always a guiding principle to understand the phenomena discussed in those four chapters. As a result, the thesis is cohesive and represents a major advance in our understanding of the physics of Dirac materials.Unconditionally stable numerical simulations of a new generalized reduced resistive magnetohydrodynamics model.https://www.zbmath.org/1455.762092021-03-30T15:24:00+00:00"Malapaka, Shiva Kumar"https://www.zbmath.org/authors/?q=ai:malapaka.shiva-kumar"Després, Bruno"https://www.zbmath.org/authors/?q=ai:despres.bruno"Sart, Rémy"https://www.zbmath.org/authors/?q=ai:sart.remySummary: Reduced-resistive magnetohydrodynamics (MHD) models are used in understanding different phenomenon in various domains, for example, astrophysics to model magnetotail or for solar arcades [\textit{J. M. Finn} and \textit{P. N. Guzdar}, ``Loss of equilibrium and reconnection in tearing of two dimensional equilibrias'', AIP Phys. Fluids B 5, 2870--2876 (1993; \url{doi:10.1063/1.860674})], modeling plasma confinements in reverse field pinch [\textit{H. R. Strauss}, Phys. Fluids 28, 2786--2792 (1985; Zbl 0572.76117)] and tokamaks [\textit{H. R. Strauss}, ``Reduced MHD in nearly potential magnetic fields'', J. Plasma Phys. 57, No. 1, 83--87 (1997; \url{doi:10.1017/S0022377896005296}); \textit{J. P. Freidberg}, Plasma physics and fusion energy. Cambridge: Cambridge University Press (2008; \url{doi:10.1017/CBO9780511755705})]. In this context, recently, a new generalized reduced-resistive MHD model, which can make use of an arbitrary density profile was proposed [\textit{B. Després} and \textit{R. Sart}, ESAIM, Math. Model. Numer. Anal. 46, No. 5, 1081--1106 (2012; Zbl 1267.76034)]. We in this work show that this proposed theoretical model can be realized numerically as well, and that it is very robust if the equation set is written in a very particular form using the properties of FEM. To illustrate these points, we pick the current hole configuration [\textit{T. Fujita} et al., ``Plasma equilibrium and confinement in a tokamak with nearly zero central current density in JT-60U'', Phys. Rev. Lett. 87, No. 11, Article ID 245001, 4 p. (2001; \url{doi:10.1103/PhysRevLett.87.245001}); \textit{N. C. Hawkes} et al., ``Observation of zero current density in the core of JET discharges with lower hybrid heating and current drive'', ibid. 87, No. 11, Article ID 115001, 4 p. (2001; \url{doi:10.1103/PhysRevLett.87.115001})], which was modeled using reduced-resistive MHD and remodel it using different combinations of current sources and density profiles. Our model can be implemented with reasonable computational resources at the price of solving a well-posed global linear system and it is unconditionally stable. These features are also demonstrated as a part of our numerical experiments.The energy of dilute Bose gases.https://www.zbmath.org/1455.810502021-03-30T15:24:00+00:00"Fournais, Søren"https://www.zbmath.org/authors/?q=ai:fournais.soren"Solovej, Jan Philip"https://www.zbmath.org/authors/?q=ai:solovej.jan-philipThe authors study a non-relativistic, interacting Bose gas in three dimensions. The bosons are assumed to interact via a non-negative, two-body potential that is spherically symmetric and of class \(\mathrm{L}^1(\mathbb R^3)\) with compact support. This includes a large family of relevant interaction potentials but not the hard core case. The authors prove a two-term lower bound for the thermodynamic limit of the ground-state energy density in the dilute limit. This crucial step completes, together with an upper bound that was previously proved under slightly different assumptions for the interaction potential, a rigorous proof of the Lee-Huang-Yang formula, which was a long standing conjecture in mathematical physics.
Reviewer: Maximilian Pechmann (Knoxville)Implicit-explicit multistep methods for hyperbolic systems with multiscale relaxation.https://www.zbmath.org/1455.651262021-03-30T15:24:00+00:00"Albi, Giacomo"https://www.zbmath.org/authors/?q=ai:albi.giacomo"Dimarco, Giacomo"https://www.zbmath.org/authors/?q=ai:dimarco.giacomo"Pareschi, Lorenzo"https://www.zbmath.org/authors/?q=ai:pareschi.lorenzoIn current paper, the authors consider the development of high-order space and time numerical methods based
on implicit-explicit multistep time integrators for hyperbolic systems with relaxation. More specifically, they consider hyperbolic balance laws in which the convection and the source term may have very different time and space scales. As a consequence, the nature of the asymptotic limit changes
completely, passing from a hyperbolic to a parabolic system. From the computational point of view, standard numerical methods designed for the fluid-dynamic scaling of hyperbolic systems with relaxation present several drawbacks and typically lose efficiency in describing the parabolic limit regime. In this work, in the context of implicit-explicit linear multistep methods we construct high-order space-time discretizations which are able to handle all the different scales and to capture the correct asymptotic behavior, independently from its nature, without time step restrictions imposed by the fast scales. Several numerical examples confirm the theoretical analysis.
Reviewer: Qifeng Zhang (Hangzhou)Critical states embedded in the continuum.https://www.zbmath.org/1455.810272021-03-30T15:24:00+00:00"Koirala, M."https://www.zbmath.org/authors/?q=ai:koirala.m"Yamilov, A."https://www.zbmath.org/authors/?q=ai:yamilov.a"Basiri, A."https://www.zbmath.org/authors/?q=ai:basiri.abdolali"Bromberg, Y."https://www.zbmath.org/authors/?q=ai:bromberg.y"Cao, H."https://www.zbmath.org/authors/?q=ai:cao.he|cao.hongping|cao.haifang|cao.hongyi|cao.huiyi|cao.hongrui|cao.huijun|cao.hongjun|cao.haixin|cao.huabin|cao.haixing|cao.huajun|cao.hai|cao.haixia|cao.haijun|cao.hui|cao.huiqin|cao.huaihuo|cao.huanxin|cao.haofeng|cao.haitao|cao.hongen|cao.huai-dong|cao.huichao|cao.hongyan|cao.hongbao|cao.huaigu|cao.hu|cao.huangjin|cao.hongqing|cao.huarong|cao.haiyan|cao.hao|cao.hongju|cao.haitao.1|cao.hailong|cao.huiping|cao.huaixin|cao.huizhong|cao.huanhuan|cao.hanqiang|cao.hong|cao.han|cao.hongxia|cao.haotao|cao.huahua|cao.hongduo|cao.huirong|cao.hongzhe|cao.huan|cao.hailin|cao.hongxing|cao.hongyuan|cao.hefei|cao.hengyi|cao.hongbo|cao.honggen|cao.huayang|cao.huijuan|cao.hailu|cao.hua|cao.huaxin|cao.huai|cao.handing|cao.hanwen|cao.hang|cao.hongmei|cao.huiying|cao.huiyun|cao.huichuan|cao.huiliang|cao.huhua|cao.haisong"Kottos, T."https://www.zbmath.org/authors/?q=ai:kottos.tsampikosThermodynamic limit for directed polymers and stationary solutions of the Burgers equation.https://www.zbmath.org/1455.601342021-03-30T15:24:00+00:00"Bakhtin, Yuri"https://www.zbmath.org/authors/?q=ai:bakhtin.yuri-yu"Li, Liying"https://www.zbmath.org/authors/?q=ai:li.liyingSummary: The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the infinite-volume limit for every fixed asymptotic slope, concentration inequalities for free energy implying a bound on its fluctuation exponent, and straightness estimates implying a bound on the transversal fluctuation exponent. The culmination of this program is almost sure existence and uniqueness of polymer measures on one-sided infinite paths with given endpoint and slope, and interpretation of these infinite-volume Gibbs measures as thermodynamic limits. Moreover, we prove that marginals of polymer measures with the same slope and different endpoints are asymptotic to each other.
The second goal of the paper is to develop ergodic theory of the Burgers equation with positive viscosity and random kick forcing on the real line without any compactness assumptions. Namely, we prove a one force -- one solution principle, using the infinite-volume polymer measures to construct a family of stationary global solutions for this system, and proving that each of those solutions is a one-point pullback attractor on the initial conditions with the same spatial average. This provides a natural extension of the same program realized for the inviscid Burgers equation with the help of action minimizers that can be viewed as zero temperature limits of polymer measures.Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential.https://www.zbmath.org/1455.820102021-03-30T15:24:00+00:00"Kachmar, Ayman"https://www.zbmath.org/authors/?q=ai:kachmar.ayman"Pan, Xing-Bin"https://www.zbmath.org/authors/?q=ai:pan.xingbinThe paper under review is concerned with the study of the transition from normal to superconducting solutions
within the Ginzburg-Landau system with Aharonov-Bohm magnetic potential. A central result of this paper establishes oscillatory patterns which are consistent with the
Little-Parks effect. Next, the authors study the same problem but for a
regularization of the Aharonov-Bohm potential. In this framework, the authors prove that the transition between superconducting and
normal solutions is not monotone.
Reviewer: Vicenţiu D. Rădulescu (Craiova)Tightness of Liouville first passage percolation for \(\gamma \in (0,2)\).https://www.zbmath.org/1455.820082021-03-30T15:24:00+00:00"Ding, Jian"https://www.zbmath.org/authors/?q=ai:ding.jian"Dubédat, Julien"https://www.zbmath.org/authors/?q=ai:dubedat.julien"Dunlap, Alexander"https://www.zbmath.org/authors/?q=ai:dunlap.alexander"Falconet, Hugo"https://www.zbmath.org/authors/?q=ai:falconet.hugoSummary: We study Liouville first passage percolation metrics associated to a Gaussian free field \(h\) mollified by the two-dimensional heat kernel \(p_t\) in the bulk, and related star-scale invariant metrics. For \(\gamma \in (0, 2)\) and \(\xi = \frac{\gamma}{d_{\gamma}}\), where \(d_{\gamma}\) is the Liouville quantum gravity dimension defined in Ding and Gwynne (Commun. Math. Phys. 374:1877-1934, 2020), we show that renormalized metrics \((\lambda_t^{-1} e^{ \xi p_t * h} ds)_{t \in (0, 1)}\) are tight with respect to the uniform topology. We also show that subsequential limits are bi-Hölder with respect to the Euclidean metric, obtain tail estimates for side-to-side distances, and derive error bounds for the normalizing constants \(\lambda_t\).Decomposition matrices for the square lattices of the Lie groups \(SU(2)\times SU(2)\).https://www.zbmath.org/1455.820052021-03-30T15:24:00+00:00"Bodner, M."https://www.zbmath.org/authors/?q=ai:bodner.mark"Grabowiecka, Z."https://www.zbmath.org/authors/?q=ai:grabowiecka.zofia"Patera, J."https://www.zbmath.org/authors/?q=ai:patera.jiri"Szajewska, M."https://www.zbmath.org/authors/?q=ai:szajewska.marzenaIn the present paper, the authors obtain a method for the
decomposition of data functions sampled on a finite fragment of
rectangular lattice based on the semisimple Lie group \(\mathrm{S}U(2)\times \mathrm{SU}(2)\). The authors consider the Weyl groups \(A_1\) and \(A_1 \times
A_1\). The characters of the irreducible representations of the Lie group
\(A_1 \times A_1\) are investigated. Two methods for splitting the
data are described. The Fourier decomposition of functions on the
fundamental region \(F_{M,M'}\) is studied, where
\(F_{M,M'}=\{(\frac{s_1}{M}(1,0),\frac{s_1'}{M'}(0,1)):
M=s_0+s_1,M'=s_{0}'+s_1'\in \mathbb{Z}^{\geq 0}\}\).
Reviewer: Hasan Akin (Gaziantep)