Recent zbMATH articles in MSC 70https://zbmath.org/atom/cc/702022-11-17T18:59:28.764376ZWerkzeugExploring continued fractions. From the integers to solar eclipseshttps://zbmath.org/1496.110092022-11-17T18:59:28.764376Z"Simoson, Andrew J."https://zbmath.org/authors/?q=ai:simoson.andrew-jThis is a leisurely introduction to continued fractions and their applications. Most of the material can be read by bright highschool students; only occasionally a matrix or an integral shows up. Applications range from periodic movements in the solar system (the Saros cycle for eclipses of the sun) over music and nim-like games to mathematics itself (Farey sequences, harmonic series, Fibonacci numbers, Pythagorean triples and many more); in particular the book is recommended as a rich source of applications of continued fractions.
Historical claims must be taken with a grain of salt; in particular, the section on Babylonian mathematics and the tablet Plimpton 322 suffers from several deficits. First, the rendition of the sexagesimal numbers is horrible, and the mixture of Arabic and Babylonian numerals misleading. The footnote on p. 174 seems to suggest that the cut-and-paste method can be found on clay tablets. Addressing a Babylonian scribe as ``he or she'' is not historical. Finally, the trigonometric ``application'' of Plimpton 322 is pure speculation -- there's no trace of such calculations on any of the clay tablets known today.
In a similar vein, the claim (p. 340) that dropping small black holes through Earth is a source of energy is not due to Hawking, who suggested using the Hawking radiation of a mini black hole, which requires preventing it from falling through Earth.
Reviewer: Franz Lemmermeyer (Jagstzell)Constrained systems, generalized Hamilton-Jacobi actions, and quantizationhttps://zbmath.org/1496.140152022-11-17T18:59:28.764376Z"Cattaneo, Alberto S."https://zbmath.org/authors/?q=ai:cattaneo.alberto-sergio"Mnev, Pavel"https://zbmath.org/authors/?q=ai:mnev.pavel"Wernli, Konstantin"https://zbmath.org/authors/?q=ai:wernli.konstantinThis paper considers the situation of 1-dimensional field theories from the viewpoint of perturbative gauge theories on manifolds with boundary, hence where the system has certain constraints. In particular, it considers properties of the Hamilton-Jacobi action within the perturbative quantization setting of the BV-BFV formalism, which is a gauge formlism for manifolds with boundary (compatible with cutting-gluing) developed recently by the first two authors together with \textit{N. Reshetikhin} in [Commun. Math. Phys. 332, No. 2, 535--603 (2014; Zbl 1302.81141); Commun. Math. Phys. 357, No. 2, 631--730 (2018; Zbl 1390.81381)]. Since they are considering the case of 1-dimensional source manifolds in this paper, the BFV formalism is applied to the endpoints (which is, in this case, the boundary of the 1-dimensional source). An interesting result of this paper is included in the explicit computation of examples, namely that the toy model for nonabelian Chern-Simons theory and the toy model for 7D Chern-Simons theory endowed with nonlinear Hitchin Polarization do not have quantum corrections in the physical part. Furthermore, they provide a concise collection of background material for the sake of completeness and better understanding.
Reviewer: Nima Moshayedi (Zürich)Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systemshttps://zbmath.org/1496.160452022-11-17T18:59:28.764376Z"Fairon, Maxime"https://zbmath.org/authors/?q=ai:fairon.maximeThis paper is a contribution to the theory of non-commutative Poisson structures, with applications to integrable systems. The main theoretical results concern double (quasi)Poisson structures, as introduced in [\textit{M. Van den Bergh}, Trans. Am. Math. Soc. 360, No. 11, 5711--5769 (2008; Zbl 1157.53046)].
Fusion for algebras generalizes fusion for quiver algebras corresponding to identification of vertices; Van den Bergh established that the behaviour of non-commutative Poisson structures under fusion is of significant interest.
For double Poisson structures, the author first proves that iterated fusions are independent of the choices involved and likewise for Hamiltonian algebras (i.e., in presence of a moment map).
The double quasi-Poisson case is much more delicate, since the passage of such a structure to the fusion algebra involves a correction fusion term, analysed in special cases by Van den Bergh and in full generality in [\textit{M. Fairon}, Algebr. Represent. Theory 24, No. 4, 911--958 (2021; Zbl 1480.16049)].
The main algebraic result (announced in [Zbl 1480.16049]) is a double quasi-Poisson analogue of the above, together with a version for quasi-Hamiltonian algebras (i.e., in presence of a multiplicative moment map).
The results are illustrated by examples constructed from quivers (following Van den Bergh) which give, respectively, a Hamiltonian double Poisson structure and a quasi-Hamiltonian structure. The above theorems imply that, up to isomorphism, these structures only depend upon the underlying graph of the quiver.
These results are applied to give a very conceptual explanation of action-angle duality for several examples of classical integrable systems, notably generalizations of the Calogero-Moser system and of the Ruijsenaars-Schneider systems. The associated phase spaces are constructed as quiver varieties, with Poisson structure induced by a NC-Poisson structure in the sense of [\textit{W. Crawley-Boevey}, J. Algebra 325, No. 1, 205--215 (2011; Zbl 1255.17012)]. The author exhibits action-angle coordinates, building upon [\textit{O. Chalykh} and \textit{M. Fairon}, J. Geom. Phys. 121, 413--437 (2017; Zbl 1418.70026)] and [\textit{O. Chalykh} and \textit{A. Silantyev}, J. Math. Phys. 58, No. 7, 071702, 31 p. (2017; Zbl 1370.37126)]. The action-angle duality corresponds to the reversal of arrows of the quiver.
Reviewer: Geoffrey Powell (Angers)\(\mathfrak{L}\)-prolongations of graded Lie algebrashttps://zbmath.org/1496.170222022-11-17T18:59:28.764376Z"Marini, Stefano"https://zbmath.org/authors/?q=ai:marini.stefano"Medori, Costantino"https://zbmath.org/authors/?q=ai:medori.costantino"Nacinovich, Mauro"https://zbmath.org/authors/?q=ai:nacinovich.mauroAuthors' abstract: In this paper we translate the necessary and sufficient conditions of Tanaka's theorem on the finiteness of effective prolongations of a fundamental graded Lie algebras into computationally effective criteria, involving the rank of some matrices that can be explicitly constructed. Our results would apply to geometries, which are defined by assigning a structure algebra on the contact distribution.
Reviewer: V. V. Gorbatsevich (Moskva)Limit theorems for Jacobi ensembles with large parametershttps://zbmath.org/1496.330102022-11-17T18:59:28.764376Z"Hermann, Kilian"https://zbmath.org/authors/?q=ai:hermann.kilian"Voit, Michael"https://zbmath.org/authors/?q=ai:voit.michaelSummary: Consider \(\beta\)-Jacobi ensembles on the alcoves
\[
A:=\{ x\in\mathbb{R}^N \mid -1\leq x_1\leq \cdots\leq x_N\leq 1\}
\]
with parameters \(k_1,k_2,k_3\geq 0\). In the freezing case \((k_1,k_2,k_3)=\kappa\cdot (a,b,1)\) with \(a,b>0\) fixed and \(\kappa\to\infty\), we derive a central limit theorem. The drift and covariance matrix of the limit are expressed via the zeros of classical Jacobi polynomials. We also determine the eigenvalues and eigenvectors of the covariance matrices. Our results are related to corresponding limits for \(\beta\)-Hermite and Laguerre ensembles for \(\beta\to\infty\).Existence and stability of periodic oscillations of a smooth and discontinuous oscillatorhttps://zbmath.org/1496.340922022-11-17T18:59:28.764376Z"Liang, Zaitao"https://zbmath.org/authors/?q=ai:liang.zaitao"Yang, Yanjuan"https://zbmath.org/authors/?q=ai:yang.yanjuanSummary: In this paper, we study the existence, multiplicity and Lyapunov stability of periodic oscillations of a SD oscillator which exhibits both discontinuous and smooth dynamics depending on the value of the smoothness parameter \(\alpha\). Both linear stability and nonlinear stability results are obtained. The proof is based on some stability criteria of second order differential equations combined with the quantitative information obtained by the method of upper and lower solutions. Moreover, some numerical simulations are provided to illustrate the results.Dynamical phenomena connected with stability loss of equilibria and periodic trajectorieshttps://zbmath.org/1496.370262022-11-17T18:59:28.764376Z"Neishtadt, Anatolii I."https://zbmath.org/authors/?q=ai:neishtadt.anatolii-i"Treschev, Dmitry V."https://zbmath.org/authors/?q=ai:treshchev.dmitrij-vComplex periodic bursting structures in the Rayleigh-van der Pol-Duffing oscillatorhttps://zbmath.org/1496.370452022-11-17T18:59:28.764376Z"Ma, Xindong"https://zbmath.org/authors/?q=ai:ma.xindong"Bi, Qinsheng"https://zbmath.org/authors/?q=ai:bi.qinsheng"Wang, Lifeng"https://zbmath.org/authors/?q=ai:wang.lifengSummary: In the present paper, complex bursting patterns caused by the coupling effect of different frequency scales in the Rayleigh-van der Pol-Duffing oscillator (RVDPDO) driven by the external excitation term are presented theoretically. Seven different kinds of bursting, i.e., bursting of compound ``Homoclinic/Homoclinic'' mode via ``Homoclinic/Homoclinic'' hysteresis loop, bursting of compound ``fold/Homoclinic-Homoclinic/Hopf'' mode via ``fold/Homoclinic'' hysteresis loop, bursting of compound ``fold/Homoclinic-Hopf/Hopf'' mode via ``fold/Homoclinic'' hysteresis loop, bursting of ``fold/Homoclinic'' mode via ``fold/Homoclinic'' hysteresis loop, bursting of ``fold/Hopf'' mode via ``fold/fold'' hysteresis loop, bursting of ``Hopf/Hopf'' mode via ``fold/fold'' hysteresis loop and bursting of ``fold/fold'' mode are studied by using the phase diagram, time domain signal analysis, phase portrait superposition analysis and slow-fast analysis. With the help of the Melnikov method, the parameter properties related to the beingness of the Homoclinic and Heteroclinic bifurcations chaos of the periodic excitations are investigated. Then, by acting the external forcing term as a slowly changing state variable, the stability and bifurcation characteristics of the generalized autonomous system are given, which performs a major part in the interpretative principles of different bursting patterns. This paper aims to show the sensitivity of dynamical characteristics of RVDPDO to the variation of parameter \(\mu\) and decide how the choice of the parameters influences the manifold of RVDPDO during the repetitive spiking states. Finally, the validity of the research is tested and verified by the numerical simulations.Dynamic behaviors of a symmetrically coupled period-doubling systemhttps://zbmath.org/1496.370462022-11-17T18:59:28.764376Z"Yu, Zhiheng"https://zbmath.org/authors/?q=ai:yu.zhiheng"Li, Lin"https://zbmath.org/authors/?q=ai:li.lin.1"Zhang, Wenmeng"https://zbmath.org/authors/?q=ai:zhang.wenmengSummary: A system of two coupled mappings demonstrates a variety of nonlinear phenomena such as the inverse state, spatiotemporal intermittence, traveling wave and the synchronization. In this paper, we are concerned with a system of symmetrically coupled quadratic mappings. \textit{B. P. Bezruchko} et al. [Chaos Solitons Fractals 15, No. 4, 695--711 (2003; Zbl 1031.70012)] employed numerical method to study the bifurcation problem of such a system, but did not give a full investigation in theory because of the complicated computation. In this paper, we adopt the \textit{complete discrimination system theory} and \textit{the real root isolation algorithm} to overcome the difficulty. We will give a completed description of the bifurcations in theory for such a system, including the transcritical bifurcation, pitchfork bifurcation, flip bifurcation and the Neimark-Sacker bifurcation.On \(1:3\) resonance under reversible perturbations of conservative cubic Hénon mapshttps://zbmath.org/1496.370492022-11-17T18:59:28.764376Z"Gonchenko, Marina S."https://zbmath.org/authors/?q=ai:gonchenko.marina-s"Kazakov, Alexey O."https://zbmath.org/authors/?q=ai:kazakov.alexey-o"Samylina, Evgeniya A."https://zbmath.org/authors/?q=ai:samylina.evgeniya-a"Shykhmamedov, Aikan"https://zbmath.org/authors/?q=ai:shykhmamedov.aikanSummary: We consider reversible nonconservative perturbations of the conservative cubic Hénon maps \(H_3^{\pm} : \bar{x}=y,\bar{y}=-x+M_1 +M_2 y\pm y^3\) and study their influence on the 1:3 resonance, i.e., bifurcations of fixed points with eigenvalues \(e^{\pm i2\pi /3}\). It follows from [\textit{H. R. Dullin} and \textit{J. D. Meiss}, Physica D 143, No. 1--4, 262--289 (2000; Zbl 0961.37010)] that this resonance is degenerate for \(M_1 =0,M_2 =-1\) when the corresponding fixed point is elliptic. We show that bifurcations of this point under reversible perturbations give rise to four 3-periodic orbits, two of them are symmetric and conservative (saddles in the case of map \(H_3^+\) and elliptic orbits in the case of map \(H_3^-)\), the other two orbits are nonsymmetric and they compose symmetric couples of dissipative orbits (attracting and repelling orbits in the case of map \(H_3^+\) and saddles with the Jacobians less than 1 and greater than 1 in the case of map \(H_3^-)\). We show that these local symmetry-breaking bifurcations can lead to mixed dynamics due to accompanying global reversible bifurcations of symmetric nontransversal homo- and heteroclinic cycles. We also generalize the results of [loc. cit.] to the case of the \(p:q\) resonances with odd \(q\) and show that all of them are also degenerate for the maps \(H_3^{\pm}\) with \(M_1 =0\).The influence of a parameter that controls the asymmetry of a potential energy surface with an entrance channel and two potential wellshttps://zbmath.org/1496.370572022-11-17T18:59:28.764376Z"Agaoglou, Makrina"https://zbmath.org/authors/?q=ai:agaoglou.makrina"Katsanikas, Matthaios"https://zbmath.org/authors/?q=ai:katsanikas.matthaios"Wiggins, Stephen"https://zbmath.org/authors/?q=ai:wiggins.stephenSummary: In this paper we study an asymmetric valley-ridge inflection point (VRI) potential, whose energy surface (PES) features two sequential index-1 saddles (the upper and the lower), with one saddle having higher energy than the other, and two potential wells separated by the lower index-1 saddle. We show how the depth and the flatness of our potential changes as we modify the parameter that controls the asymmetry as well as how the branching ratio (ratio of the trajectories that enter each well) is changing as we modify the same parameter and its correlation with the area of the lobes as they have been formed by the stable and unstable manifolds that have been extracted from the gradient of the LD scalar fields.Zeros of rational functions and solvable nonlinear evolution equationshttps://zbmath.org/1496.370582022-11-17T18:59:28.764376Z"Calogero, Francesco"https://zbmath.org/authors/?q=ai:calogero.francesco-aSummary: Recently a convenient technique to relate the time evolution of the \(N\) zeros of a time-dependent polynomial \(p_N(z; t\) of degree \(N\) in the complex variable \(z\) to the time evolution of its \(N\) coefficients has been exploited to identify large classes of dynamical systems solvable by \textit{algebraic} operations. These models also include \(N\)-body problems that evolve in the complex plane (or, equivalently, in the real Cartesian plane) according to systems of nonlinearly-coupled equations of motion of Newtonian type (``accelerations equal forces''). Many of these models feature remarkable properties: for instance, they are Hamiltonian and integrable and/or multiply periodic or even isochronous (featuring completely periodic solutions with a fixed period largely independent of the initial data), or \textit{asymptotically isochronous} (featuring isochrony only up to corrections vanishing in the remote future). In this paper, an analogous technique is introduced that focuses instead on the time evolution of the \(N\) zeros of an appropriate class of time-dependent rational functions \(R_N(z; t)\), thereby opening large vistas of new dynamical systems solvable by \textit{algebraic} operations and featuring remarkable properties. A few examples are reported.{
\copyright 2018 American Institute of Physics}On the integrability of circulatory systemshttps://zbmath.org/1496.370592022-11-17T18:59:28.764376Z"Kozlov, V. V."https://zbmath.org/authors/?q=ai:kozlov.victor-v|kozlov.vasilii-vasilevich|kozlov.vladimir-vasilievich|kozlov.valerij-vasilievichSummary: This paper discusses conditions for the existence of polynomial (in velocities) first integrals of the equations of motion of mechanical systems in a nonpotential force field (circulatory systems). These integrals are assumed to be single-valued smooth functions on the phase space of the system (on the space of the tangent bundle of a smooth configuration manifold). It is shown that, if the genus of the closed configuration manifold of such a system with two degrees of freedom is greater than unity, then the equations of motion admit no nonconstant single-valued polynomial integrals. Examples are given of circulatory systems with configuration space in the form of a sphere and a torus which have nontrivial polynomial laws of conservation. Some unsolved problems involved in these phenomena are discussed.Integrability by separation of variableshttps://zbmath.org/1496.370602022-11-17T18:59:28.764376Z"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaume"Ramírez, Rafael"https://zbmath.org/authors/?q=ai:ramirez.rafael-oSummary: We study the integrability in the Jacobi sense (integrability by separation of variables), of the Hamiltonian differential systems using the Levi-Civita Theorem. In particular we solve the Stark problem for \(N > 3\).A generalized Poincaré-Birkhoff theoremhttps://zbmath.org/1496.370692022-11-17T18:59:28.764376Z"Moreno, Agustin"https://zbmath.org/authors/?q=ai:moreno.agustin-s"van Koert, Otto"https://zbmath.org/authors/?q=ai:van-koert.ottoSummary: We prove a generalization of the classical Poincaré-Birkhoff theorem for Liouville domains, in arbitrary even dimensions. This is inspired by the existence of global hypersurfaces of section for the spatial case of the restricted three-body problem [\textit{A. Moreno} and \textit{O. van Koert}, Nonlinearity 35, No. 6, 2920--2970 (2022; Zbl 07539293)].Some reversing orbits for a rattleback modelhttps://zbmath.org/1496.370702022-11-17T18:59:28.764376Z"Arioli, Gianni"https://zbmath.org/authors/?q=ai:arioli.gianni"Koch, Hans"https://zbmath.org/authors/?q=ai:koch.hans-friedrichSummary: A physical rattleback is a toy that can exhibit counter-intuitive behavior when spun on a horizontal plate. Most notably, it can spontaneously reverse its direction of rotation. Using a standard mathematical model of the rattleback, we prove the existence of reversing motion, reversing motion combined with rolling, and orbits that exhibit such behavior repeatedly.Contact Hamiltonian and Lagrangian systems with nonholonomic constraintshttps://zbmath.org/1496.370712022-11-17T18:59:28.764376Z"de León, Manuel"https://zbmath.org/authors/?q=ai:de-leon.manuel"Jiménez, Víctor M."https://zbmath.org/authors/?q=ai:jimenez.victor-manuel"Lainz, Manuel"https://zbmath.org/authors/?q=ai:lainz.manuelThis paper aims at using contact and Jacobi geometry to develop the natural geometric framework for studying the dynamics of mechanical systems that are subject to both nonholonomic constraints and Rayleigh dissipation.
A \textit{nonholonomic mechanical system} is a mechanical system subject to \textit{nonholonomic constraints}, i.e., constraints (on the position and velocities) that do not derive from constraints only on the positions. Examples include mechanical systems that have rolling contact (like a ball rolling without slipping on a plane) or some kind of sliding contact (like a rigid body sliding on a plane). In the Lagrangian formalism, a mechanical system is described by a \textit{Lagrangian function} \(L\colon TQ\to\mathbb{R},\ (q,\dot q)\mapsto L(q,\dot q)\), where the smooth manifold \(Q\) denotes the \textit{configuration space} of the system. Then a nonholonomic constraint is given by a submanifold \(\mathcal{D}\subset TQ\) such that \(\tau_Q(\mathcal{D})=Q\), where \(\tau_Q\colon TQ\to Q\) denotes the bundle map. In the following, one only considers nonholonomic constraints that are linear in the velocities, i.e., \(\mathcal{D}\subset TQ\) is a vector subbundle.
If the mechanical system is conservative, i.e., \(L=K_g-V\), where \(V\in C^\infty(Q)\) and \(K_g\) is the kinetic energy of some pseudo-Riemannian metric \(g\) on \(Q\), then the Lagrangian \(L\) is regular, i.e., the associated Legendre transform \(\mathbb{F}L:TQ\to T^\ast Q\) is a local diffeomorphism. In this case, the natural geometric description of their dynamics is provided in terms of Hamiltonian systems on symplectic manifolds (see, e.g., [\textit{R. Abraham} and \textit{J. E. Marsden}, Foundations of mechanics. 2nd ed., rev., enl., and reset. With the assistance of Tudor Ratiu and Richard Cushman. Reading, Massachusetts: The Benjamin/Cummings Publishing Company, Inc (1978; Zbl 0393.70001)] and references therein). Indeed, the unconstrained dynamics is obtained as the projection on \(Q\) of the flow of the Euler-Lagrange vector field \(\Gamma_L\), i.e., the Hamiltonian vector field of the system \((TQ,\omega_L,E_L)\), where \(E_L=\Delta(L)-L\) is the energy, with \(\Delta\) the Euler vector field on \(TQ\), and \(\omega_L=(\mathbb{F}L)^\ast\omega_{\text{can}}\) is the pull-back along \(\mathbb{F}L\) of the canonical symplectic form on \(T^\ast Q\). This \(\Gamma_L\) is a SODE (second-order differential equation) on \(TQ\) and its flow is obtained integrating the standard Euler-Lagrange equations. This description of the dynamics is consistent with the one arising from D'Alembert principle.
If the conservative mechanical system is additionally subject to nonholonomic constraints, then its dynamics can be still described in terms of Hamiltonian systems on symplectic manifolds (see, e.g., [\textit{C.-M. Marle}, Rep. Math. Phys. 42, No. 1--2, 211--229 (1998; Zbl 0931.37023)] and references therein). Indeed, its dynamics is the projection on \(Q\) of the flow of a nonholonomic Euler-Lagrange vector field \(\Gamma_L^\mathcal{D}\). The latter is still a SODE on \(TQ\) and is obtained from \(\Gamma_L\) by projection with respect to a certain decomposition of \((TTQ)|_\mathcal{D}\). This description of the nonholonomic dynamics is consistent with the one arising from Chetaev version of D'Alembert principle. Moreover, this nonholonomic dynamics is almost-Poisson but not Poisson. Indeed, there is a bracket \(\{-,-\}\) on \(C^\infty(\mathcal{D})\) that satisfies the Leibniz rule in each entry and, together with the energy \(E_L\) on \(TQ\), controls the time evolution of the observables, but in generally it fails to satisfy the Jacobi identity.
The authors start from the observation that there are other kinds of nonholonomic mechanical systems that do not fit in the previous framework. As a first example, one can consider a nonholonomic mechanical system that is also subject to Rayleigh dissipation and so non-conservative. Additional examples come from thermodynamics. These mechanical systems can be described by a Lagrangian function \(L\colon TQ\times\mathbb{R}\to\mathbb{R},\ (q,\dot q,z)\mapsto L(q,\dot q,z):=L_z(q,\dot q),\) where the smooth manifold \(Q\) is the configuration space and the parameter \(z\) on \(\mathbb{R}\) denotes friction (or a thermal variable in thermodynamics).
If the Lagrangian \(L\) is regular, in the sense that, for any \(z\in\mathbb{R}\), the associated Legendre transform \(\mathbb{F}L_z:TQ\to T^\ast Q\) is a local diffeomorphism, the natural geometric framework of their dynamics is provided by the theory of Hamiltonian systems on contact manifolds (cf., e.g., [\textit{M. de León} and \textit{M. Lainz Valcázar}, J. Math. Phys. 60, No. 10, 102902, 18 p. (2019; Zbl 1427.70039)] and references therein). Indeed, the unconstrained dynamics is obtained as the projection on \(Q\) of the flow of the Euler-Lagrange vector field \(\Gamma_L\), i.e., the Hamiltonian vector field of the system \((TQ\times\mathbb{R},\eta_L,E_L)\), where \(E_L=\Delta(L)-L\) is the energy, with \(\Delta\) the Euler vector field on \(TQ\), and \(\eta_L=(\mathbb{F}L\times\operatorname{id}_\mathbb{R})^\ast\eta_{\text{can}}\) is the pull-back along \(\mathbb{F}L\times\operatorname{id}_\mathbb{R}\) of the canonical contact form on \(T^\ast Q\times\mathbb{R}\). In the current setting, this \(\Gamma_L\) is still an SODE on \(TQ\times\mathbb{R}\) (in the sense recalled in Definition~5) and its flow is obtained integrating the so-called Herglotz equations. Indeed, this description of the dynamics is consistent with the one arising from the Herglotz variational principle (as recalled in Section~4).
In this paper the authors show that the theory of Hamiltonian systems on contact manifolds can be adapted to provide a geometric interpretation of the dynamics of mechanical systems that are subject to both dissipation and nonholonomic constraints. Section~5 defines a version of the Herglotz principle in presence of nonholonomic constraints: essentially, one restricts the variations so that they satisfy the constraints. Then the dynamics is described by the extremals of this Herglotz principle with constraints and they are given by the solutions of the so-called constrained Herglotz equations (see Theorem~5). Actually, this description admits a geometric description similar to the one obtained when there are no constraints. Indeed, Theorem 6 shows that, if the Lagrangian \(L\colon TQ\times\mathbb{R}\to\mathbb{R}\) is regular (i.e., \(F_z\colon TQ\to\mathbb{R}\) is regular, for any \(z\in\mathbb{R}\), as recalled above), the solutions of the constrained Herglotz equations are the projections on \(Q\) of the integral curves of the nonholonomic Euler-Lagrange vector field \(\Gamma_L^\mathcal{D}\). The latter is still a SODE on \(TQ\times\mathbb{R}\) (see Definition~5) and is obtained from \(\Gamma_L\) by projection with respect to a certain decomposition of \(T(TQ\times\mathbb{R})\) along \(\mathcal{D}\).
The authors also prove that the time evolution of these mechanical systems subject to both dissipation and nonholonomic constraints is governed by an almost-Jacobi bracket (see Definition 7). Indeed, in Section 6, they first construct a nonholonomic bracket from functions on \(TQ\times\mathbb{R}\) to functions on \(\mathcal{D}\times\mathbb{R}\) (see Equation 100), then they prove that this nonholonomic bracket (together with the Energy \(E_L\)) controls the time evolution of the observables (see Theorem 12) and it is an almost Jacobi bracket (see Proposition 6). Further, it turns out that this nonholonomic bracket is actually a Jacobi structure (i.e., it satisfies the Jacobi identity) if and only if the constraint \(\mathcal{D}\subset TQ\) is an involutive vector subbundle (see Theorem 13).
Finally, in Example 2, the authors illustrate their results applying them to a particular example given by a model of the Chaplygin's sleight subject to Rayleigh dissipation.
Reviewer: Alfonso Giuseppe Tortorella (Porto)Persistence of invariant tori in infinite-dimensional Hamiltonian systemshttps://zbmath.org/1496.370762022-11-17T18:59:28.764376Z"Huang, Peng"https://zbmath.org/authors/?q=ai:huang.pengSummary: In this paper, we consider the persistence of invariant tori in infinite-dimensional Hamiltonian systems
\[
H=\langle\omega, I\rangle +P(\theta, I, \omega),
\]
where \(\theta \in \mathbb{T}^\Lambda\), \(I\in \mathbb{R}^\Lambda\), the frequency \(\omega=(\cdots, \omega_\lambda, \cdots)_{\lambda\in\Lambda}\) is regarded as parameters varying freely over some subset \(\ell^\infty(\Lambda, \mathbb{R})\) of the parameter space \(\mathbb{R}^\Lambda\), \(\omega = (\cdots, \omega_\lambda, \cdots)_{\lambda\in\Lambda}\) is a bilateral infinite sequence of rationally independent frequency, in other words, any finite segments of \(\omega = (\cdots, \omega_\lambda, \cdots)_{\lambda\in\Lambda}\) are rationally independent.Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcinghttps://zbmath.org/1496.370772022-11-17T18:59:28.764376Z"Rui, Jie"https://zbmath.org/authors/?q=ai:rui.jie"Wang, Yi"https://zbmath.org/authors/?q=ai:wang.yi.9|wang.yi.8|wang.yi.4|wang.yi.5|wang.yi.6|wang.yi.1|wang.yi.7|wang.yi.2|wang.yi.3Summary: In this paper, we focus on the class of almost-periodically forced higher-dimensional beam equations
\[
u_{tt}+(-\Delta +\mu)^2u+\psi (\omega t)u=0,\quad \mu >0, t \in \mathbb{R}, x\in \mathbb{R}^d,
\] subject to periodic boundary conditions, where \(\psi (\omega t)\) is real analytic and almost-periodic in \(t\). We show the existence of almost-periodic solutions for this equation under some suitable hypotheses. In the proof, we improve the KAM iteration to deal with the infinite-dimensional frequency \(\omega =(\omega_1,\omega_2,\ldots)\).Hamiltonian and Lagrangian systems in contact geometryhttps://zbmath.org/1496.530032022-11-17T18:59:28.764376Z"Souto Pérez, Silvia"https://zbmath.org/authors/?q=ai:souto-perez.silvia(no abstract)Stochastic averaging principle for two-time-scale jump-diffusion SDEs under the non-Lipschitz coefficientshttps://zbmath.org/1496.600672022-11-17T18:59:28.764376Z"Xu, Jie"https://zbmath.org/authors/?q=ai:xu.jie"Liu, Jicheng"https://zbmath.org/authors/?q=ai:liu.jichengSummary: In this paper, we shall prove a stochastic averaging principle for two-time-scale jump-diffusion SDEs under the non-Lipschitz coefficients.Constructing equivalence-preserving Dirac variational integrators with forceshttps://zbmath.org/1496.650382022-11-17T18:59:28.764376Z"Parks, Helen"https://zbmath.org/authors/?q=ai:parks.helen-f"Leok, Melvin"https://zbmath.org/authors/?q=ai:leok.melvinSummary: The dynamical motion of mechanical systems possesses underlying geometric structures and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single mechanical system, structure preservation can be achieved by adopting the variational integrator construction [\textit{J. E. Marsden} and \textit{M. West}, Acta Numerica 10, 357--514 (2001; Zbl 1123.37327)]. This construction has been generalized to more complex systems involving forces or constraints as well as to the setting of Dirac mechanics [the second author and \textit{T. Ohsawa}, Found. Comput. Math. 11, No. 5, 529--562 (2011; Zbl 1231.70016)]. Forced Lagrange-Dirac systems are described by a Lagrangian and an external force pair, and two pairs of Lagrangians and external forces are said to be equivalent if they yield the same equations of motion. However, the variational discretization of a forced Lagrange-Dirac system discretizes the Lagrangian and forces separately, and will generally depend on the choice of representation. In this paper, we derive a class of Dirac variational integrators with forces that yield well-defined numerical methods that are independent of the choice of representation. We present a numerical simulation to demonstrate how such equivalence-preserving discretizations avoid spurious solutions that otherwise arise from poorly chosen representations.Efficient flexible boundary conditions for long dislocationshttps://zbmath.org/1496.652332022-11-17T18:59:28.764376Z"Hodapp, M."https://zbmath.org/authors/?q=ai:hodapp.maxSummary: We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix (\(\mathscr{H}\)-matrix) representation of the periodic Green matrix, reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms. In addition, our implementation is supported by various other tools from numerical analysis, such as a residual-based transformation of the boundary conditions to accelerate the convergence. We assess the method for a comprehensive set of examples, relevant for predicting mechanical properties, such as yield strength or ductility, including dislocation bow-out, dislocation-precipitate interaction, and dislocation cross-slip. The main result of our analysis is that the FBC method is robust, easy-to-use, and up to two orders of magnitude more efficient than the current state-of-the-art method for this class of problems, the periodic array of dislocations (PAD) method, in terms of the required number of per-atom force computations when both methods give similar accuracy. This opens new prospects for large-scale atomistic simulations -- without having to worry about spurious image effects that plague classical boundary conditions.Differential-algebraic equations and beyond: from smooth to nonsmooth constrained dynamical systemshttps://zbmath.org/1496.700012022-11-17T18:59:28.764376Z"Kleinert, Jan"https://zbmath.org/authors/?q=ai:kleinert.jan"Simeon, Bernd"https://zbmath.org/authors/?q=ai:simeon.berndSummary: In the 1970s of the last century, the progress in powerful simulation software for mechanical multibody systems and for electrical circuits led to a new class of models that is characterized by differential equations and algebraic constraints. These Differential-Algebraic Equations (DAEs) became soon a hot topic, and the methodology that has emerged since then represents now a general field in applied and computational mathematics, with various new applications in science and engineering. Taking a historical approach, the present article introduces a summarizing view at DAEs, with emphasis on numerical aspects and without aiming for completeness. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.
For the entire collection see [Zbl 1483.65008].Modular time integration of coupled problems in system dynamicshttps://zbmath.org/1496.700022022-11-17T18:59:28.764376Z"Arnold, Martin"https://zbmath.org/authors/?q=ai:arnold.martinSummary: In industrial design processes, the system dynamics of complex engineering structures is modelled by a network approach that results in differential-algebraic model equations. For this problem class, well-established modular simulation techniques like multi-rate or multi-method approaches, co-simulation or waveform relaxation may suffer from exponential instability. With a novel framework for the stability and convergence analysis of modular time integration methods for differential-algebraic systems the sources of numerical instability could be identified and eliminated. Stabilized modular methods have been developed for such diverse fields of application like multibody system dynamics and circuit simulation. This mathematical research has strongly influenced the design of an industrial interface standard for co-simulation in system dynamics.
For the entire collection see [Zbl 1483.65008].Dynamics of a system of coupled inverted pendula with vertical forcinghttps://zbmath.org/1496.700032022-11-17T18:59:28.764376Z"Bhadra, Nivedita"https://zbmath.org/authors/?q=ai:bhadra.nivedita"Banerjee, Soumitro"https://zbmath.org/authors/?q=ai:banerjee.soumitroSummary: Dynamical stabilization of an inverted pendulum through vertical movement of the pivot is a well-known counter intuitive phenomenon in classical mechanics. This system is also known as Kapitza pendulum and the stability can be explained with the aid of effective potential. We explore the effect of many body interaction for such a system. Our numerical analysis shows that interaction between pendula generally degrades the dynamical stability of each pendulum. This effect is more pronounced in nearest neighbour coupling than all-to-all coupling and stability improves with the increase of the system size. We report development of beats and clustering in network of coupled pendula.From the swarm robotics to material deformationshttps://zbmath.org/1496.700042022-11-17T18:59:28.764376Z"D'Avanzo, Paolo"https://zbmath.org/authors/?q=ai:davanzo.paolo"Rapisarda, Alessio Ciro"https://zbmath.org/authors/?q=ai:rapisarda.alessio-ciro"Sirletti, Salvatore Samuele"https://zbmath.org/authors/?q=ai:sirletti.salvatore-samueleSummary: In this chapter a discrete 2D kinematic system model is presented. Its aim is to reproduce the behavior of several 2D continuum systems. We started from studies on swarm robotics; in these papers, simple interaction laws among the elements of the swarm are used to manage its behavior. We have employed them to simulate materials deformation. This model seems to be promising because it is able to qualitatively reproduce standard deformations and a lot of exotic phenomena that other methods in literature can't reproduce. Furthermore, it has a low computational cost and it is parallelizable, allowing us to take profit of CUDA\({}_{\circledR}\) architecture. Some numerical simulations are provided and discussed using two different kinds of lattices and changing some model's parameters.
For the entire collection see [Zbl 1478.74002].Symbolic methods for studying the equilibrium orientations of a system of two connected bodies in a circular orbithttps://zbmath.org/1496.700052022-11-17T18:59:28.764376Z"Gutnik, S. A."https://zbmath.org/authors/?q=ai:gutnik.sergey-a"Sarychev, V. A."https://zbmath.org/authors/?q=ai:sarychev.vasily-aSummary: This paper investigates the dynamics of a system of two bodies connected by a spherical hinge that moves along a circular orbit under the action of gravitational torque. A computer algebra method based on the resultant approach is applied to reduce the satellite's stationary motion system of algebraic equations to a single algebraic equation in one variable, which determines the equilibrium configurations of the two-body system in the plane orthogonal to the orbital plane. Classification of domains with equal numbers of equilibrium solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. Bifurcation curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria for the two-body system are obtained symbolically. Depending on the parameters of the problem, the number of equilibria is found by analyzing the real roots of the algebraic equations. Using the proposed approach, it is shown that the satellite-stabilizer system can have up to 44 equilibrium orientations in a circular orbit.On the stability of the triangular equilibrium points in the photogravitational R3BP with an oblate infinitesimal and triaxial primaries for the binary lalande 21258 systemhttps://zbmath.org/1496.700062022-11-17T18:59:28.764376Z"Gyegwe, Jessica Mrumun"https://zbmath.org/authors/?q=ai:gyegwe.jessica-mrumun"Vincent, Aguda Ekele"https://zbmath.org/authors/?q=ai:vincent.aguda-ekele"Perdiou, Angela E."https://zbmath.org/authors/?q=ai:perdiou.angela-eSummary: In the framework of the planar circular restricted three-body problem (R3BP), we explore the effects of oblateness of the infinitesimal mass body as well as radiation pressure and triaxiality of the two primaries on the position and stability of the triangular equilibrium points (TEPs). It is found that all the involved parameters affect the positions and stability of these points. Specifically, it has been shown that TEPs are stable for \(0 < \mu < \mu_c\) and unstable for \(\mu_c \leqslant \mu \leqslant 1/2\), where \(\mu_c\) denotes the critical mass parameter which depends on system's parameters. In addition, all the parameters of the bigger primary, except that of triaxiality, have destabilizing tendencies resulting in a decrease in the size of the region of stability. Finally, we justify the relevance of the model in astronomy by applying it to the binary Lalande 21258 system for which the equilibrium points have been seen to be unstable.
For the entire collection see [Zbl 1485.65002].Existence and stability of equilibrium points under the influence of Poynting-Robertson and Stokes drags in the restricted three-body problemhttps://zbmath.org/1496.700072022-11-17T18:59:28.764376Z"Vincent, Aguda Ekele"https://zbmath.org/authors/?q=ai:vincent.aguda-ekele"Perdiou, Angela E."https://zbmath.org/authors/?q=ai:perdiou.angela-eSummary: In the framework of the circular restricted three-body problem, the dynamical effects of Stokes and Poynting-Robertson (P-R) drag forces on the existence, location, and stability of equilibrium points are investigated. It is found that under constant effects of P-R and/or Stokes drags, collinear equilibrium points cease to exist, but there are in the absence of the perturbing forces. The problem admits five non-collinear equilibrium points, and it is seen that the perturbing forces have significant effects on their positions. The linear stability of the equilibrium points is also studied in certain cases, and it is found that the stability of some of these points significantly depends on the perturbing forces. More precisely, the motion of the infinitesimal body near the non-collinear equilibrium points is unstable under the effect of both kinds of perturbing forces except from the equilibria \(L_4\) and \(L_5\) for which is stable only for Stokes drag effect, namely, the remaining parameter that corresponds to P-R drag is fixed to zero. We may conclude, therefore, that the P-R effect destroys stability of the equilibrium points.
For the entire collection see [Zbl 1483.00042].On the equilibria of the restricted four-body problem with triaxial rigid primaries - I. Oblate bodieshttps://zbmath.org/1496.700082022-11-17T18:59:28.764376Z"Muhammad, Shah"https://zbmath.org/authors/?q=ai:muhammad.shah"Duraihem, Faisal Zaid"https://zbmath.org/authors/?q=ai:duraihem.faisal-zaid"Zotos, Euaggelos E."https://zbmath.org/authors/?q=ai:zotos.euaggelos-eSummary: The equilateral restricted four-body problem, with triaxial rigid oblate bodies, is investigated. Using numerical methods we examine how the linear stability and the positions of the coplanar libration points are affected by the triaxility parameters of the primaries. In each case, we perform a rigorous and systematic analysis for determining the influence of the triaxility parameters \(\sigma_1\) and \(\sigma_2\) on the dynamics of the system. Our computations suggest the strong influence of these parameters by revealing additional cases, regarding the total number of equilibria, thus improving the findings of previous related works.The effect of radiation pressure on the basins of convergence in the restricted four-body problemhttps://zbmath.org/1496.700092022-11-17T18:59:28.764376Z"Suraj, Md Sanam"https://zbmath.org/authors/?q=ai:suraj.md-sanam"Aggarwal, Rajiv"https://zbmath.org/authors/?q=ai:aggarwal.rajiv"Asique, Md Chand"https://zbmath.org/authors/?q=ai:asique.md-chand"Mittal, Amit"https://zbmath.org/authors/?q=ai:mittal.amitSummary: The present problem deals with the effect of the radiation pressure on the topology of the basins of convergence in the restricted problem of four bodies in two different configurations: (I) the equilateral four-body configuration (II) the collinear four-body problem. We have illustrated the basins of convergence linked to the in-plane as well as out-of-plane libration points by applying the Newton-Raphson multivariate iterative scheme, in both the configurations. Additionally, the basin entropy is illustrated to estimate the degree of fractality of the basins of convergence.Discontinuous dynamical behaviors in a 2-DOF friction collision system with asymmetric dampinghttps://zbmath.org/1496.700102022-11-17T18:59:28.764376Z"Cao, Jing"https://zbmath.org/authors/?q=ai:cao.jing"Fan, Jinjun"https://zbmath.org/authors/?q=ai:fan.jinjunSummary: By using the flow switchability theory in discontinuous dynamical systems, this paper deals with the discontinuous dynamical behaviors of a two degrees of freedom system with asymmetric damping, where considering that friction and impact coexist and the static and dynamic friction coefficients are different. Because of the particularity of friction force, the flow barriers on the velocity boundary that affect the leaving flow are considered in this paper. Based on discontinuity that is caused by the sudden change of friction force or the collision between two objects, the phase space of motion for the object is divided into several different domains and boundaries; and with the help of the analysis of vector fields and G-functions on the corresponding discontinuous boundaries or in domains, the analytical conditions for all possible motions are obtained, which is used to determine the switching of motion state in this system. Finally, numerical simulations are presented to better understand the analytical conditions of the stick, grazing, impact, stuck and periodic motions.On the gradient flow formulation of the Lohe matrix model with high-order polynomial couplingshttps://zbmath.org/1496.700112022-11-17T18:59:28.764376Z"Ha, Seung-Yeal"https://zbmath.org/authors/?q=ai:ha.seung-yeal"Park, Hansol"https://zbmath.org/authors/?q=ai:park.hansolSummary: We present a first-order aggregation model for a homogeneous Lohe matrix ensemble with higher order couplings via a gradient flow approach. For homogeneous free flow with the same Hamiltonian, it is well known that the Lohe matrix model with cubic couplings can be recast as a gradient system with a potential which is a squared Frobenius norm of of averaged state. In this paper, we further derive a generalized Lohe matrix model with higher-order couplings via gradient flow approach for a polynomial potential. For the proposed model, we also provide a sufficient framework in terms of coupling strengths and initial data leading to the emergent dynamics of a homogeneous ensemble.From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theoryhttps://zbmath.org/1496.700122022-11-17T18:59:28.764376Z"Kirillov, Oleg N."https://zbmath.org/authors/?q=ai:kirillov.oleg-n"Verhulst, Ferdinand"https://zbmath.org/authors/?q=ai:verhulst.ferdinandSummary: Four classical systems, the Kelvin gyrostat, the Maclaurin spheroids, the Brouwer rotating saddle, and the Ziegler pendulum have directly inspired development of the theory of Pontryagin and Krein spaces with indefinite metric and singularity theory as independent mathematical topics, not to mention stability theory and nonlinear dynamics. From industrial applications in shipbuilding, turbomachinery, and artillery to fundamental problems of astrophysics, such as asteroseismology and gravitational radiation -- that is the range of phenomena involving the Krein collision of eigenvalues, dissipation-induced instabilities, and spectral and geometric singularities on the neutral stability surfaces, such as the famous Whitney's umbrella.
For the entire collection see [Zbl 1483.65008].Propagation of chaos for a stochastic particle system modelling epidemicshttps://zbmath.org/1496.700132022-11-17T18:59:28.764376Z"Ciallella, Alessandro"https://zbmath.org/authors/?q=ai:ciallella.alessandro"Pulvirenti, Mario"https://zbmath.org/authors/?q=ai:pulvirenti.mario"Simonella, Sergio"https://zbmath.org/authors/?q=ai:simonella.sergioSummary: We consider a simple stochastic \(N\)-particle system, already studied by the same authors in [Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 32, No. 2, 295--315 (2021; Zbl 07420114)], representing different populations of agents. Each agent has a label describing his state of health. We show rigorously that, in the limit \(N \rightarrow \infty\) propagation of chaos holds, leading to a set of kinetic equations which are a spatially inhomogeneous version of the classical SIR model. We improve a similar result obtained in [loc. cit.] by using here a different coupling technique, which makes the analysis simpler, more natural and transparent.
For the entire collection see [Zbl 1487.74006].Approximated dynamics of chatter in turning processeshttps://zbmath.org/1496.740722022-11-17T18:59:28.764376Z"Beri, Bence"https://zbmath.org/authors/?q=ai:beri.bence"Stepan, Gabor"https://zbmath.org/authors/?q=ai:stepan.gaborSummary: The nonlinear behaviour of the turning process is analysed, which is described by a one degree-of-freedom dynamical system. The model takes the form of a delay differential equation that is non-smooth when the cutting tool leaves contact with the surface. The delay equation is approximated by means of a power series with respect to the delay to reveal the geometric structure of the relevant dynamics in a low dimensional phase space. The bifurcation diagram of the non-smooth system is calculated and compared to the existing theoretical and experimental results of the literature.
For the entire collection see [Zbl 1464.70003].Helicopter pilot biomechanics by multibody analysishttps://zbmath.org/1496.741022022-11-17T18:59:28.764376Z"Masarati, Pierangelo"https://zbmath.org/authors/?q=ai:masarati.pierangelo"Zanoni, Andrea"https://zbmath.org/authors/?q=ai:zanoni.andrea"Muscarello, Vincenzo"https://zbmath.org/authors/?q=ai:muscarello.vincenzo"Paolini, Rita"https://zbmath.org/authors/?q=ai:paolini.rita"Quaranta, Giuseppe"https://zbmath.org/authors/?q=ai:quaranta.giuseppeSummary: Helicopter handling qualities can be affected by the voluntary and involuntary interaction between the vehicle dynamics and the human body biomechanics. To investigate the possible couplings, a first-principles approach has been taken: biomechanical multibody models of the pilot upper limbs and spine have been developed along with generation procedures that can be used to represent human bodies of broadly varying anthropometric parameters. The models have been used both for the identification of the linearized behavior about arbitrary steady conditions and for full nonlinear analysis of helicopter transient maneuvers, through direct and inverse dynamics analyses.
For the entire collection see [Zbl 1464.70003].Compliant actuation for wearable roboticshttps://zbmath.org/1496.741032022-11-17T18:59:28.764376Z"Verstraten, Tom"https://zbmath.org/authors/?q=ai:verstraten.tom"Lefeber, Dirk"https://zbmath.org/authors/?q=ai:lefeber.dirkSummary: The requirements of wearable robots such as robotic prostheses and exoskeletons differ considerably from those of traditional robots. These requirements are usually met well by compliant actuators, i.e., actuators which feature an elastic element. In this chapter, we explain how compliant actuators can solve the formidable actuation challenges inherent to wearable robots, with particular attention for their ability to improve energy efficiency.
For the entire collection see [Zbl 1470.93004].Automatic generation of statistical volume elements using multibody dynamics and an erosion-based homogenization methodhttps://zbmath.org/1496.741192022-11-17T18:59:28.764376Z"Couture, A."https://zbmath.org/authors/?q=ai:couture.a"François, V."https://zbmath.org/authors/?q=ai:francois.vincent"Cuillière, Jean-Christophe"https://zbmath.org/authors/?q=ai:cuilliere.jean-christophe"Pilvin, Ph."https://zbmath.org/authors/?q=ai:pilvin.philippeSummary: Modeling particle based heterogeneous materials using statistical volume elements (SVE) for predicting its mechanical behavior can be tedious when the particles are densely packed or elongated. Positioning particles without creating overlaps and avoiding meshing problems are two obstacles frequently mentioned. To counter these obstacles, a new modeling methodology based on multibody dynamics (MBD) and on an erosion-based homogenization method is proposed. The CAD model of a SVE is first generated and particles causing meshing problems are excluded. Meshing and finite element analysis are automatically carried out and a subsequent erosion-based homogenization method is used to retrieve the macroscopic behavior of the SVE. To illustrate the potential of this new method, results obtained with a random sequential adsorption algorithm on non-eroded SVEs are compared with results obtained from the same SVEs submitted to our erosion method. These results are then compared with results obtained using the new MBD based approach.Phase lag predicts nonlinear response maxima in liquid-sloshing experimentshttps://zbmath.org/1496.760262022-11-17T18:59:28.764376Z"Bäuerlein, Bastian"https://zbmath.org/authors/?q=ai:bauerlein.bastian"Avila, Kerstin"https://zbmath.org/authors/?q=ai:avila.kerstinSummary: Mass-spring models are essential for the description of sloshing resonances in engineering. By experimentally measuring the liquid's centre of mass in a horizontally oscillated rectangular tank, we show that low-amplitude sloshing obeys the Duffing equation. A bending of the response curve in analogy to a softening spring is observed, with growing hysteresis as the driving amplitude increases. At large amplitudes, complex wave patterns emerge (including wave breaking and run up at the tank walls), competition between flow states is observed and the dynamics departs progressively from Duffing. We also provide a quantitative comparison of wave shapes and response curves to the predictions of a multimodal model based on potential flow theory [\textit{O. M. Faltinsen} and \textit{A. N. Timokha}, Sloshing. Cambridge: Cambridge University Press (2009)] and show that it systematically overestimates the sloshing amplitudes and the hysteresis. We find that the phase lag between the liquid's centre of mass and the forcing is the key predictor of the nonlinear response maxima. The phase lag reflects precisely the onset of deviations from Duffing dynamics and -- most importantly -- at resonance the sloshing motion always lags the driving by \(90^{\circ } \) (independently of the wave pattern). This confirms the theoretical \(90^{\circ }\)-phase-lag criterion [\textit{M. Cenedese} and \textit{G. Haller}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190494, 26 p. (2020; Zbl 1439.70030)].Stokesian motion of a spherical particle near a right corner made by tangentially moving wallshttps://zbmath.org/1496.760432022-11-17T18:59:28.764376Z"Romanò, Francesco"https://zbmath.org/authors/?q=ai:romano.francesco"des Boscs, Pierre-Emmanuel"https://zbmath.org/authors/?q=ai:des-boscs.pierre-emmanuel"Kuhlmann, Hendrik C."https://zbmath.org/authors/?q=ai:kuhlmann.hendrik-cSummary: The slow motion of a small buoyant sphere near a right dihedral corner made by tangentially sliding walls is investigated. Under creeping-flow conditions the force and torque on the sphere can be decomposed into eleven elementary types of motion involving simple particle translations, particle rotations and wall movements. Force and torque balances are employed to find the velocity and rotation of the particle as functions of its location. Depending on the ratio of the wall velocities and the gravitational settling velocity of the sphere, different dynamical regimes are identified. In particular, a non-trivial line attractor/repeller for the particle motion exists at a location detached from both the walls. The existence, location and stability of the corresponding two-dimensional fixed point are studied depending on the wall velocities and the buoyancy force. The impact of the line attractors/repellers on the motion of small particles in cavities and its relevance for corner cleaning applications are discussed.Nambu dynamics and hydrodynamics of granular materialhttps://zbmath.org/1496.761532022-11-17T18:59:28.764376Z"Sugamoto, Akio"https://zbmath.org/authors/?q=ai:sugamoto.akio"Bamba, Kazuharu"https://zbmath.org/authors/?q=ai:bamba.kazuharu"Kawamura, Tetuya"https://zbmath.org/authors/?q=ai:kawamura.tetuya"Kuwana, Anna"https://zbmath.org/authors/?q=ai:kuwana.anna"Nagata, Yusaku"https://zbmath.org/authors/?q=ai:nagata.yusaku"Saitou, Mayumi"https://zbmath.org/authors/?q=ai:saitou.mayumiSummary: On the basis of the intimate relation between Nambu dynamics and hydrodynamics, hydrodynamics on a non-commutative space (obtained by the quantization of space), proposed by Nambu in his last work, is formulated as hydrodynamics of granular material. In Sect. 2, the quantization of space is done using a Moyal product, and the hydrodynamic simulation is performed for the thus-obtained 2D fluid, which flows inside a channel with an obstacle. The obtained results differ between two cases in which the size of a fluid particle is zero and finite. The difference seems to come from the behavior of vortices generated by an obstacle. In Sect. 3, considering a vortex as a string, two models are examined; one is the hybrid model in which vortices interact with each other by exchanging Kalb-Ramond fields (a generalization of stream functions), and the other is the more general string field theory in which the Kalb-Ramond field is one of the excitation modes of string oscillations. In the string field theory, an Altarelli-Parisi-type evolution equation is introduced. This is expected to describe the response of the distribution function of a vortex inside turbulence, when the energy scale is changed. The behavior of viscosity differs in string theory compared with particle theory, so that the Landau theory of fluids to introduce viscosity may be modified. In conclusion, hydrodynamics and string theory are almost identical theories. It should be noted, however, that the string theory needed to reproduce a given hydrodynamics is not the usual string theory.Physics from symmetryhttps://zbmath.org/1496.810112022-11-17T18:59:28.764376Z"Schwichtenberg, Jakob"https://zbmath.org/authors/?q=ai:schwichtenberg.jakobPublisher's description: This is a textbook that derives the fundamental theories of physics from symmetry.
It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.
As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.
See the review of the first edition in [Zbl 1330.81005].Modulated wave and modulation instability gain brought by the cross-phase modulation in birefringent fibers having anti-cubic nonlinearityhttps://zbmath.org/1496.810472022-11-17T18:59:28.764376Z"Abbagari, Souleymanou"https://zbmath.org/authors/?q=ai:abbagari.souleymanou"Saliou, Youssoufa"https://zbmath.org/authors/?q=ai:saliou.youssoufa"Houwe, Alphonse"https://zbmath.org/authors/?q=ai:houwe.alphonse"Akinyemi, Lanre"https://zbmath.org/authors/?q=ai:akinyemi.lanre"Inc, Mustafa"https://zbmath.org/authors/?q=ai:inc.mustafa"Bouetou, Thomas B."https://zbmath.org/authors/?q=ai:bouetou-bouetou.thomasSummary: In this paper, we investigate the modulated wave and W-shaped profile in birefringent fibers having the anti-cubic nonlinearity terms. We use the traveling wave hypothesis to show out the velocity of the soliton and the constraint relation on the anti-cubic nonlinear terms. We use the Jacobi elliptic function solutions to point out two types of combined solutions. After some assumption on the modulus of the Jacobi elliptic function, we have shown out the combined bright-bright soliton and dark-dark soliton-like solutions. We use the linearizing algorithm to analyze the modulation instability (MI) growth rate. We have shown that the anti-cubic nonlinear terms and cross-phase modulation (XPM) can increase MI bands and the amplitude of the MI growth rate. To corroborate the prediction made on analytical results, we use the numerical investigation to show the propagation of the modulated wave and W-shaped profile in terms of cell index. We exhibited through the numerical results that the modulated wave can conserve high energy during its propagation in birefringent fibers. The obtained results will certainly open new perspectives in optical fibers during the transmission of huge data.Bound state solutions and thermodynamic properties of modified exponential screened plus Yukawa potentialhttps://zbmath.org/1496.810482022-11-17T18:59:28.764376Z"Antia, Akaninyene D."https://zbmath.org/authors/?q=ai:antia.akaninyene-d"Okon, Ituen B."https://zbmath.org/authors/?q=ai:okon.ituen-b"Isonguyo, Cecilia N."https://zbmath.org/authors/?q=ai:isonguyo.cecilia-n"Akankpo, Akaninyene O."https://zbmath.org/authors/?q=ai:akankpo.akaninyene-o"Eyo, Nsemeke E."https://zbmath.org/authors/?q=ai:eyo.nsemeke-eSummary: In this research paper, the approximate bound state solutions and thermodynamic properties of Schrödinger equation with modified exponential screened plus Yukawa potential (MESPYP) were obtained with the help Greene-Aldrich approximation to evaluate the centrifugal term. The Nikiforov-Uvarov (NU) method was used to obtain the analytical solutions. The numerical bound state solutions of five selected diatomic molecules, namely mercury hydride (HgH), zinc hydride (ZnH), cadmium hydride (CdH), hydrogen bromide (HBr) and hydrogen fluoride (HF) molecules were also obtained. We obtained the energy eigenvalues for these molecules using the resulting energy eigenequation and total unnormalized wave function expressed in terms of associated Jacobi polynomial. The resulting energy eigenequation was presented in a closed form and applied to study partition function (Z) and other thermodynamic properties of the system such as vibrational mean energy (U), vibrational specific heat capacity (C), vibrational entropy (S) and vibrational free energy (F). The numerical bound state solutions were obtained from the resulting energy eigenequation for some orbital angular quantum number. The results obtained from the thermodynamic properties are in excellent agreement with the existing literature. All numerical computations were carried out using spectroscopic constants of the selected diatomic molecules with the help of MATLAB 10.0 version. The numerical bound state solutions obtained increases with an increase in quantum state.On the number of eigenvalues of the lattice model operator in one-dimensional casehttps://zbmath.org/1496.810562022-11-17T18:59:28.764376Z"Bozorov, I. N."https://zbmath.org/authors/?q=ai:bozorov.i-n"Khurramov, A. M."https://zbmath.org/authors/?q=ai:khurramov.abdumazhid-molikovichSummary: It is considered a model operator \(h_{\mu}(k),k\in\mathbb{T}\equiv(-\pi,\pi]\), corresponding to the Hamiltonian of systems of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function that describes the transfer of a particle from one site to another interacting by a some short-range attraction potential \(v_{\mu}, \mu=(\mu_0,\mu_1,\mu_2,\mu_3)\in\mathbb{R}^4_+ \). The number of eigenvalues of the operator \(h_{\mu}(k),k\in\mathbb{T}\) depending on the energy of the particle interaction vector \(\mu\in\mathbb{R}^4_+\) and the total quasi-momentum \(k\in\mathbb{T}\) is studied.Aharonov-Bohm effect of induced gauge fields and geometric phase factors in Suter experimenthttps://zbmath.org/1496.810652022-11-17T18:59:28.764376Z"Lv, Xiao-Xi"https://zbmath.org/authors/?q=ai:lv.xiao-xi"Yu, Zhao-Xian"https://zbmath.org/authors/?q=ai:yu.zhaoxianSummary: Combined with the concept of induced gauge field, the Aharonov-Bohm effect of induced gauge field is analyzed. The relationship between gauge potential and Berry phase factor, gauge potential and Aharonov-Anandan phase factor in Suter experiment is given.Explosive synchronization induced by environmental couplinghttps://zbmath.org/1496.810742022-11-17T18:59:28.764376Z"Ramesan, Gayathri"https://zbmath.org/authors/?q=ai:ramesan.gayathri"Shajan, Emilda"https://zbmath.org/authors/?q=ai:shajan.emilda"Shrimali, Manish Dev"https://zbmath.org/authors/?q=ai:shrimali.manish-devSummary: The occurrence of explosive synchronization transition in a system of limit-cycle oscillators in the presence of two types of coupling; direct mean field diffusive and indirect environmental couplings, both operating simultaneously, is reported. The dynamics of coupled nonlinear Van der Pol and Rayleigh oscillators are studied in detail as a function of the distribution of intrinsic parameters of the oscillators. This explosive synchronization transition depends on the strength of indirect coupling and is irreversible giving rise to a characteristic hysteresis region. The different routes to synchronization observed in these coupled oscillators are studied in detail with the help of effective frequency and time series analysis. We have investigated the efficiency of the proposed scheme in various other topologies such as random, scale-free, and two-community networks as well.Hamiltonian and Lagrangian BRST quantization in Riemann manifold. IIhttps://zbmath.org/1496.810762022-11-17T18:59:28.764376Z"Pandey, Vipul Kumar"https://zbmath.org/authors/?q=ai:pandey.vipul-kumarSummary: We have previously developed the BRST quantization on the hypersurface \(V_{N - 1}\) embedded in \(N\)-dimensional Euclidean space \(R_N\) in both Hamiltonian and Lagrangian formulation. We generalize the formalism in the case of \(L\)-dimensional manifold \(V_L\) embedded in \(R_N\) with \(1\leq L<N\). The result is essentially the same as the previous one. We have also verified the results obtained here using a simple example of particle motion on a torus knot.
For Part I, see [\textit{V. K. Pandey}, Adv. High Energy Phys. 2022, Article ID 2158485, 12 p. (2022; Zbl 1485.81045)].Transport properties of a 3-dimensional holographic effective theory with gauge-axion couplinghttps://zbmath.org/1496.810872022-11-17T18:59:28.764376Z"Li, Yi-Lin"https://zbmath.org/authors/?q=ai:li.yilin"Wang, Xi-Jing"https://zbmath.org/authors/?q=ai:wang.xi-jing"Fu, Guoyang"https://zbmath.org/authors/?q=ai:fu.guoyang"Wu, Jian-Pin"https://zbmath.org/authors/?q=ai:wu.jian-pinSummary: In this paper, we implement a 3-dimensional holographic effective theory with gauge-axion coupling. The analytical black hole solution is worked out. We investigate the Direct current (DC) thermoelectric conductivities. A novel property is that DC electric conductivity for vanishing gauge-axion coupling is temperature dependent. It is different from that of 4-dimensional axion model whose DC electric conductivity is temperature independent. In addition, the gauge-axion coupling induces a metal insulator transition (MIT) at zero temperature. The properties of other DC thermoelectric conductivities are also discussed. Moreover we find that the Wiedemann-Franz (WF) law is violated in our model.The asymptotic approach to the continuum of lattice QCD spectral observableshttps://zbmath.org/1496.810952022-11-17T18:59:28.764376Z"Husung, Nikolai"https://zbmath.org/authors/?q=ai:husung.nikolai"Marquard, Peter"https://zbmath.org/authors/?q=ai:marquard.peter"Sommer, Rainer"https://zbmath.org/authors/?q=ai:sommer.rainerSummary: We consider spectral quantities in lattice QCD and determine the asymptotic behaviour of their discretization errors. Wilson fermion with \(\mathrm{O}(a)\)-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height \(M_5 = 1 + \mathrm{O}(g_0^2)\) have the same, approximate, form of the asymptotic cutoff effects: \(Ka^2 [\bar{g}^2(a^{-1})]^{0.760}\). A domain wall height \(M_5 = 1.8\), as often used, introduces large mass-dependent \(K^\prime(m) a^2 [\bar{g}^2(a^{-1})]^{0.518}\) effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [\textit{B. Sheikholeslami} and \textit{R. Wohlert}, ``Improved continuum limit lattice action for QCD with Wilson fermions'', Nucl. Phys., B 259, No. 4, 572--596 (1985; \url{doi:10.1016/0550-3213(85)90002-1})] is included. For their mass-dependent cutoff effects we have information on the exponents \(\hat{\Gamma}_i\) of \(\bar{g}^2(a^{-1})\) but not for the pre-factors. For staggered fermions there is only partial information on the exponents.
We propose that tree-level \(\mathrm{O}(a^2)\) improvement, which is easy to do [\textit{M. Alford}, \textit{T. R. Klassen} and \textit{G. P. Lepage}, ``Improving lattice quark actions'', Nucl. Phys., B 496, No. 1--2, 377--407 (1997; \url{doi:10.1016/S0550-3213(97)00249-6})], should be used in the future -- both for the fermion and the gauge action. It improves the asymptotic behaviour in all cases.Emergence of non-linear electrodynamic theories from \(T\bar{T}\)-like deformationshttps://zbmath.org/1496.810962022-11-17T18:59:28.764376Z"Babaei-Aghbolagh, H."https://zbmath.org/authors/?q=ai:babaei-aghbolagh.h"Velni, Komeil Babaei"https://zbmath.org/authors/?q=ai:velni.komeil-babaei"Yekta, Davood Mahdavian"https://zbmath.org/authors/?q=ai:yekta.davood-mahdavian"Mohammadzadeh, H."https://zbmath.org/authors/?q=ai:mohammadzadeh.hamid|mohammadzadeh.hosein|mohammadzadeh.hosseinSummary: In this letter, we investigate the deformation of the ModMax theory, as a unique Lagrangian of non-linear electrodynamics preserving both conformal and electromagnetic-duality invariance, under \(T\bar{T}\)-like flows. We will show that the deformed theory is the generalized non-linear Born-Infeld electrodynamics. Being inspired by the invariance under the flow equation for Born-Infeld theories, we propose another \(T\bar{T}\)-like operator generating the ModMax and generalized Born-Infeld non-linear electrodynamic theories from the usual Maxwell and Born-Infeld theories, respectively.Finite electrodynamics from T-dualityhttps://zbmath.org/1496.810972022-11-17T18:59:28.764376Z"Gaete, Patricio"https://zbmath.org/authors/?q=ai:gaete.patricio"Nicolini, Piero"https://zbmath.org/authors/?q=ai:nicolini.pieroSummary: In this paper, we present the repercussions of Padmanabhan's propagator in electrodynamics. This corresponds to implement T-duality effects in a U(1) gauge theory. By formulating a nonlocal action consistent with the above hypothesis, we derive the profile of static potentials between electric charges via a path integral approach. Interestingly, the Coulomb potential results regularized by a length scale proportional to the parameter \((\alpha^\prime)^{1/2}\). Accordingly, fields are vanishing at the origin. We also discuss an array of experimental testbeds to expose the above results. It is interesting to observe that T-duality generates an effect of dimensional fractalization, that resembles similar phenomena in fractional electromagnetism. Finally, our results have also been derived with a gauge-invariant method, as a necessary check of consistency for any non-Maxwellian theory.Longitudinal structure function \(F_L\) at low \(Q^2\) and low \(x\) with model for higher twist: an updatehttps://zbmath.org/1496.811002022-11-17T18:59:28.764376Z"Badełek, Barbara"https://zbmath.org/authors/?q=ai:badelek.barbara"Staśto, Anna M."https://zbmath.org/authors/?q=ai:stasto.anna-mSummary: A reanalysis of the model for the longitudinal structure function \(F_L(x, Q^2)\) at low \(x\) and low \(Q^2\) was undertaken, in view of the advent of the EIC. The model is based on the photon-gluon fusion mechanism suitably extrapolated to the region of low \(Q^2\). It includes the kinematic constraint \(F_L \sim Q^4\) as \(Q^2 \to 0\) and higher twist contribution which vanishes as \(Q^2 \to \infty \). Revised model was critically updated and compared to the presently available data.Quantum Hall effect and geometric phase factor in strong magnetic fieldshttps://zbmath.org/1496.811112022-11-17T18:59:28.764376Z"Lv, Xiao-Xi"https://zbmath.org/authors/?q=ai:lv.xiao-xi"Yu, Zhao-Xian"https://zbmath.org/authors/?q=ai:yu.zhaoxian"Liu, Ye-Hou"https://zbmath.org/authors/?q=ai:liu.yehouSummary: The concept of Berry phase factor in adiabatic processes is extended to degenerate systems. The relationship between quantum Hall effect and Berry phase factor is studied under symmetric gauge conditions, and the relationship between quantum Hall conductivity and Berry phase factor is derived, the theoretical analysis is consistent with the experimental results of Klitzing, [\textit{D. C. Tsui}, \textit{H. L. Stormer}, and \textit{A. C. Gossard}, ``Two-dimensional magnetotransport in the extreme quantum limit'', Phys. Rev. Lett. 48, No. 22, 1559--1562 (1982; \url{doi:10.1103/PhysRevLett.48.1559})].Ground-state cooling of the mechanical resonator in an optomechanical cavity with two-level atomic ensemblehttps://zbmath.org/1496.811152022-11-17T18:59:28.764376Z"Liu, Ni"https://zbmath.org/authors/?q=ai:liu.ni"Chang, Rui"https://zbmath.org/authors/?q=ai:chang.rui"Zhang, Suying"https://zbmath.org/authors/?q=ai:zhang.suying"Liang, J.-Q."https://zbmath.org/authors/?q=ai:liang.jiuqingSummary: We first propose the ground-state cooling of a mechanical resonator (MR) via a electromagnetically-induced-transparency (EIT)-like cooling mechanism in an optomechanical cavity with two-level atomic ensemble. By tuning optimal parameters in stable region, we meet that the cooling process of the MR corresponds to the maximum value of the optical fluctuation spectrum, while the heating process of the MR corresponds to the minimum value of the optical fluctuation spectrum. Without the original resolved sideband condition, the MR could be cooled to its ground state by manipulating the atom-field coupling strength only satisfying the decay rate is smaller than the MR's frequency, which can be observed by the cooling rate and the mean phonon number. Meanwhile, the action of the atomic ensemble in the ground-state cooling of the MR is equal to the one of the auxiliary cavity in a double-cavity optomechanical system. In addition, the influence of other parameters on the cooling of the MR is also discussed. In the experiment and theory, the optomechanical cavity with two-level atomic ensemble is easier to implement and manipulate than the related double-cavity optomechanical system.Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: analytical analyses of steady state evolving from initial statehttps://zbmath.org/1496.820182022-11-17T18:59:28.764376Z"Wang, Yu-Qing"https://zbmath.org/authors/?q=ai:wang.yuqing"Wang, Chao-Fan"https://zbmath.org/authors/?q=ai:wang.chao-fan"Wang, Hao-Tian"https://zbmath.org/authors/?q=ai:wang.haotian"Du, Min-Xuan"https://zbmath.org/authors/?q=ai:du.min-xuan"Wang, Bing-Hong"https://zbmath.org/authors/?q=ai:wang.binghongSummary: Being a vital two-dimensional multibody interacting particle system in nonlinear science and complex systems, exclusion network fuses totally asymmetric simple exclusion process into underlying complex network dynamics. This study constructs equiprobable exclusion network with heterogeneous interactions by introducing randomly generated interaction rates on each random path. Nodes are equivalent to subnetworks modelled by periodic TASEPs. Analytical solutions of typical order parameters are obtained by exploring dynamical transitions among configuration probabilities validated by meticulous balance theory. Physical mechanisms of underlying exclusion network dynamics are revealed by discussing TASEP with boundaries and Langmuir kinetics. New analytical method named as isoline analyses on mechanisms of spatial correlation and spatiotemporal evolution is proposed. Phase boundaries between initial state and steady state are analytically solved, which have a high agreement with simulations. Fruitful mechanisms of system transiting from initial phase to steady phases are discovered. It will have theoretical and practical value of deeply understanding evolution laws of cluster dynamics of self-driven particles and exploring non-equilibrium phase transitions in active systems.Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-timeshttps://zbmath.org/1496.830022022-11-17T18:59:28.764376Z"Gottschalk, Hanno"https://zbmath.org/authors/?q=ai:gottschalk.hanno"Rothe, Nicolai R."https://zbmath.org/authors/?q=ai:rothe.nicolai-r"Siemssen, Daniel"https://zbmath.org/authors/?q=ai:siemssen.danielClassical double copy at null infinityhttps://zbmath.org/1496.830052022-11-17T18:59:28.764376Z"Adamo, Tim"https://zbmath.org/authors/?q=ai:adamo.tim"Kol, Uri"https://zbmath.org/authors/?q=ai:kol.uriTwo-component scalar and fermionic dark matter candidates in a generic \(U(1)_X\) modelhttps://zbmath.org/1496.830182022-11-17T18:59:28.764376Z"Das, Arindam"https://zbmath.org/authors/?q=ai:das.arindam"Gola, Shivam"https://zbmath.org/authors/?q=ai:gola.shivam"Mandal, Sanjoy"https://zbmath.org/authors/?q=ai:mandal.sanjoy"Sinha, Nita"https://zbmath.org/authors/?q=ai:sinha.nitaSummary: We consider a \(U(1)_X \otimes \mathbb{Z}_2 \otimes \mathbb{Z}_2^\prime\) extension of the Standard Model (SM), where the \(U(1)_X\) charge of an SM field is given by a linear combination of its hypercharge and \(B-L\) number. Apart from the SM particle content, the model contains three right-handed neutrinos (RHNs) \(N_R^i\) and two scalars \(\Phi\), \(\chi\), all singlets under the SM gauge group but charged under \(U(1)_X\) gauge group. Two of these additional fields, fermion \(N_R^3\) is odd under \(\mathbb{Z}_2\) and scalar \(\chi\) is odd under \(\mathbb{Z}_2^\prime\) symmetry. Thus both \(\chi\) and \(N_R^3\) contribute to the observed dark matter relic density, leading to two-component dark matter candidates. We study in detail its dark matter properties such as relic density and direct detection taking into account the constraints coming from collider studies. We find that in our model, there can be possible annihilation of one Dark Matter (DM) into the other, which may potentially alter the relic density in a significant way.Scotogenic \(A_5 \rightarrow A_4\) Dirac neutrinos with freeze-in dark matterhttps://zbmath.org/1496.830192022-11-17T18:59:28.764376Z"Ma, Ernest"https://zbmath.org/authors/?q=ai:ma.ernestSummary: Radiative Dirac neutrino masses and their mixing are linked to dark matter through the non-Abelian discrete symmetry \(A_5\) of the 4-dimensional pentatope, softly broken to \(A_4\) of the 3-dimensional tetrahedron. This unifying understanding of neutrino family structure from dark matter is made possible through the interplay of gauge symmetry, renormalizable Lagrangian field theory, and softly broken discrete symmetries. Dark neutral fermions are produced through Higgs decay.An effective model for the quantum Schwarzschild black holehttps://zbmath.org/1496.830202022-11-17T18:59:28.764376Z"Alonso-Bardaji, Asier"https://zbmath.org/authors/?q=ai:alonso-bardaji.asier"Brizuela, David"https://zbmath.org/authors/?q=ai:brizuela.david"Vera, Raül"https://zbmath.org/authors/?q=ai:vera.raulSummary: We present an effective theory to describe the quantization of spherically symmetric vacuum motivated by loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation and a linear combination of constraints of general relativity, such that the modified constraint algebra closes. The system is then provided with a fully covariant and unambiguous geometric description, independent of the gauge choice on the phase space. The resulting spacetime corresponds to a singularity-free (black-hole/white-hole) interior and two asymptotically flat exterior regions of equal mass. The interior region contains a minimal smooth spacelike surface that replaces the Schwarzschild singularity. We find the global causal structure and the maximal analytical extension. Both Minkowski and Schwarzschild spacetimes are directly recovered as particular limits of the model.Applications of the close-limit approximation: horizonless compact objects and scalar fieldshttps://zbmath.org/1496.830212022-11-17T18:59:28.764376Z"Annulli, Lorenzo"https://zbmath.org/authors/?q=ai:annulli.lorenzo"Cardoso, Vitor"https://zbmath.org/authors/?q=ai:cardoso.vitor"Gualtieri, Leonardo"https://zbmath.org/authors/?q=ai:gualtieri.leonardoAspects of three-dimensional higher curvatures gravitieshttps://zbmath.org/1496.830252022-11-17T18:59:28.764376Z"Bueno, Pablo"https://zbmath.org/authors/?q=ai:bueno.pablo"Cano, Pablo A."https://zbmath.org/authors/?q=ai:cano.pablo-a"Llorens, Quim"https://zbmath.org/authors/?q=ai:llorens.quim"Moreno, Javier"https://zbmath.org/authors/?q=ai:moreno.javier"van der Velde, Guido"https://zbmath.org/authors/?q=ai:van-der-velde.guidoAdS-dS stationary rotating black hole exact solution within Einstein-nonlinear electrodynamicshttps://zbmath.org/1496.830282022-11-17T18:59:28.764376Z"García-Díaz, Alberto A."https://zbmath.org/authors/?q=ai:garcia-diaz.alberto-aSummary: In this report the exact rotating charged black hole solution to the Einstein-nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic charges, cosmological constant \(\Lambda\), and three parameters due to the nonlinear electrodynamics: \(\beta\) is associated to the potential vectors \(A_\mu\) and \(^\star P_\mu\), and two constants, \(F_0\) and \(G_0\), due to the presence of the invariants \(F\) and \(G\) in the Lagrangian \(L(F(x^\mu),G(x^\mu))\). This solution is of Petrov type D, characterized by the Weyl tensor eigenvalue \(\Psi_2\), the traceless Ricci tensor eigenvalue \(S=2\Phi_{(11)}\), and the scalar curvature \(R\); it allows for event horizons, exhibits a ring singularity and fulfils the energy conditions. Its Maxwell limit is the de Sitter-Anti-de Sitter-Kerr-Newman black hole solution.On superstatistics and black hole quasinormal modeshttps://zbmath.org/1496.830302022-11-17T18:59:28.764376Z"Martínez-Merino, A."https://zbmath.org/authors/?q=ai:martinez-merino.aldo-a"Sabido, M."https://zbmath.org/authors/?q=ai:sabido.miguelSummary: It is known that using Boltzmann-Gibbs statistics, Bekenstein-Hawking entropy \(S_{HB}\), and the quasinormal modes of black holes, one finds that the lowest value of spin is \(j_{min} = 1\). In this paper, we determine \(j_{min}\), using non-extensive entropies that depend only on the probability (known as Obregon's entropies and have been derived from superstatistics). We also calculate \(j_{min}\) for a set of non-extensive entropies that have free parameters and are written in terms of \(S_{BH}\). We find that \(j_{min}\) depends on the area and the non-extensive parameter.
For the non-extensive entropies that only depend on the probability, we find that the modification is only present for micro black holes. For classical black holes the results are the same as for the Boltzmann-Gibbs statistics.The accidental flatness constraint does not mean a wrong classical limithttps://zbmath.org/1496.830322022-11-17T18:59:28.764376Z"Engle, Jonathan"https://zbmath.org/authors/?q=ai:engle.jonathan-s"Rovelli, Carlo"https://zbmath.org/authors/?q=ai:rovelli.carloLaplacian on fuzzy de Sitter spacehttps://zbmath.org/1496.830332022-11-17T18:59:28.764376Z"Brkić, Bojana"https://zbmath.org/authors/?q=ai:brkic.bojana"Burić, Maja"https://zbmath.org/authors/?q=ai:buric.maja"Latas, Duško"https://zbmath.org/authors/?q=ai:latas.duskoAsymmetrically twisted stringshttps://zbmath.org/1496.830432022-11-17T18:59:28.764376Z"Lipinski Jusinskas, Renann"https://zbmath.org/authors/?q=ai:lipinski-jusinskas.renannSummary: In this letter a new class of twisted strings is presented, with an asymmetry between the holomorphic and antiholomorphic sectors parametrized by an integer \(N\). Their physical content is given by the massless resonances of the closed string plus the mass-level \(N\) spectrum of the open string. The appeal of this model is the singling out of the (higher spin) massive levels of string theory together with their self/gauge/gravity interactions. Motivated by the original tree level Kawai-Lewellen-Tye relation for closed strings, its asymmetrically twisted version at four points is conjectured and shown to naturally interpolate with conventional and twisted strings. The resulting four-point amplitudes have a generalized Virasoro-Shapiro dressing factor.Observational constraints on inflection point quintessence with a cubic potentialhttps://zbmath.org/1496.830482022-11-17T18:59:28.764376Z"Storm, S. David"https://zbmath.org/authors/?q=ai:storm.s-david"Scherrer, Robert J."https://zbmath.org/authors/?q=ai:scherrer.robert-jSummary: We examine the simplest inflection point quintessence model, with a potential given by \(V(\phi) = V_0 + V_3\phi^3\). This model can produce either asymptotic de Sitter expansion or transient acceleration, and we show that it does not correspond to either pure freezing or thawing behavior. We derive observational constraints on the initial value of the scalar field, \(\phi_i\), and \(V_3/V_0\) and find that small values of either \(\phi_i\) or \(V_3/V_0\) are favored. While most of the observationally-allowed parameter space yields asymptotic de Sitter evolution, there is a small region, corresponding to large \(V_3/V_0\) and small \(\phi_i\), for which the current accelerated expansion is transient. The latter behavior is potentially consistent with a cyclic universe.Quark condensate and chiral symmetry restoration in neutron starshttps://zbmath.org/1496.850012022-11-17T18:59:28.764376Z"Jin, Hao-Miao"https://zbmath.org/authors/?q=ai:jin.hao-miao"Xia, Cheng-Jun"https://zbmath.org/authors/?q=ai:xia.cheng-jun"Sun, Ting-Ting"https://zbmath.org/authors/?q=ai:sun.tingting"Peng, Guang-Xiong"https://zbmath.org/authors/?q=ai:peng.guang-xiongSummary: Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of \(\rho^3\), we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of reach for neutron stars.Regions without invariant tori of given class for the planar circular restricted three-body problemhttps://zbmath.org/1496.850022022-11-17T18:59:28.764376Z"Kallinikos, N."https://zbmath.org/authors/?q=ai:kallinikos.n"MacKay, R. S."https://zbmath.org/authors/?q=ai:mackay.robert-s"Syndercombe, T."https://zbmath.org/authors/?q=ai:syndercombe.tSummary: A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for planets around a binary star are deduced. It is expected that lessons learnt from this problem will be useful for applications of the method to other contexts such as flux surfaces for magnetic fields, guiding centre motion in magnetic fields, and classical models of chemical reaction dynamics.Port-Hamiltonian systems theory: an introductory overviewhttps://zbmath.org/1496.930552022-11-17T18:59:28.764376Z"van der Schaft, Arjan"https://zbmath.org/authors/?q=ai:van-der-schaft.arjan-j"Bernoulli, Johann"https://zbmath.org/authors/?q=ai:bernoulli.johannSummary: An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief introduction to control of port-Hamiltonian systems.