The angular momentum of radiation from an arbitrarily moving relativistic charge is studied. The angular momentum is presented as the sum of the angular momentum relative to the point where the charge is located at a retarded moment of time and the angular momentum relative to an arbitrary stationary center. In particular, the instantaneous center of curvature of the trajectory is considered as such a center. Explicit expressions for the angular distribution of these components of angular momentum fluxes are obtained and studied. It is shown that the angular momentum of the field relative to the position of the charge is determined only by the properties of the electromagnetic radiation field, and the angular momentum relative to an arbitrarily distant point is the vector product of the displacement of this point and the force corresponding to radiation pressure. It is shown that in the ultrarelativistic limit, the canonical angular momentum of the radiation coincides with the angular momentum following from the symmetrized energy-momentum tensor of the electromagnetic field.
{"title":"Angular momentum of radiation from ultrarelativistic charge","authors":"Vladimir Epp, Ulyana Guselnikova, Julia Janz","doi":"arxiv-2408.13272","DOIUrl":"https://doi.org/arxiv-2408.13272","url":null,"abstract":"The angular momentum of radiation from an arbitrarily moving relativistic\u0000charge is studied. The angular momentum is presented as the sum of the angular\u0000momentum relative to the point where the charge is located at a retarded moment\u0000of time and the angular momentum relative to an arbitrary stationary center. In\u0000particular, the instantaneous center of curvature of the trajectory is\u0000considered as such a center. Explicit expressions for the angular distribution\u0000of these components of angular momentum fluxes are obtained and studied. It is\u0000shown that the angular momentum of the field relative to the position of the\u0000charge is determined only by the properties of the electromagnetic radiation\u0000field, and the angular momentum relative to an arbitrarily distant point is the\u0000vector product of the displacement of this point and the force corresponding to\u0000radiation pressure. It is shown that in the ultrarelativistic limit, the\u0000canonical angular momentum of the radiation coincides with the angular momentum\u0000following from the symmetrized energy-momentum tensor of the electromagnetic\u0000field.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the motion of two massive particles along a straight line. A lighter particle bounces back and forth between a heavier particle and a stationary wall, with all collisions being ideally elastic. It is known that if the lighter particle moves much faster than the heavier one, and the kinetic energies of the particles are of the same order, then the product of the speed of the lighter particle and the distance between the heavier particle and the wall is an adiabatic invariant: its value remains approximately constant over a long period. We show that the value of this adiabatic invariant, calculated at the collisions of the lighter particle with the wall, is a constant of motion (i.e., {an exact adiabatic invariant}). On the other hand, the value of this adiabatic invariant at the collisions between the particles slowly and monotonically decays with each collision. The model we consider is a highly simplified version of the classical adiabatic piston problem, where the lighter particle represents a gas particle, and the heavier particle represents the piston.
{"title":"Unusual Properties of Adiabatic Invariance in a Billiard Model Related to the Adiabatic Piston Problem","authors":"Joshua Skinner, Anatoly Neishtadt","doi":"arxiv-2409.07458","DOIUrl":"https://doi.org/arxiv-2409.07458","url":null,"abstract":"We consider the motion of two massive particles along a straight line. A\u0000lighter particle bounces back and forth between a heavier particle and a\u0000stationary wall, with all collisions being ideally elastic. It is known that if\u0000the lighter particle moves much faster than the heavier one, and the kinetic\u0000energies of the particles are of the same order, then the product of the speed\u0000of the lighter particle and the distance between the heavier particle and the\u0000wall is an adiabatic invariant: its value remains approximately constant over a\u0000long period. We show that the value of this adiabatic invariant, calculated at\u0000the collisions of the lighter particle with the wall, is a constant of motion\u0000(i.e., {an exact adiabatic invariant}). On the other hand, the value of this\u0000adiabatic invariant at the collisions between the particles slowly and\u0000monotonically decays with each collision. The model we consider is a highly simplified version of the classical\u0000adiabatic piston problem, where the lighter particle represents a gas particle,\u0000and the heavier particle represents the piston.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is certain that electrical properties-whether slow (sec) or fast (nsec), even optical (fsec)-are described by Maxwell's equations, and there are terms that depend on the rate of change of the electric and magnetic fields. In particular, Maxwell's equation for the curl of the magnetic field contains both the steady current and a term depending upon the temporal derivative of the electric displacement field. The latter is referred to as displacement current, and is generally believed to have been included originally by Maxwell himself, although there is evidence it was earlier considered by Kirchhoff. Maxwell's equations and Kirchoff's circuit laws both are important over the wide range of frequencies with which electronics traditionally deals. And, displacement current is an important contribution to these in both classical and quantum mechanics. Here, the development of displacement current, its importance in both classical and quantum mechanics, and some applications are provided to illustrate the fundamental role that it plays in the dynamics of a wide range of systems.
{"title":"Displacement Current in Classical and Quantum Systems","authors":"David K. Ferry, Xavier Oriols, Robert Eisenberg","doi":"arxiv-2408.13268","DOIUrl":"https://doi.org/arxiv-2408.13268","url":null,"abstract":"It is certain that electrical properties-whether slow (sec) or fast (nsec),\u0000even optical (fsec)-are described by Maxwell's equations, and there are terms\u0000that depend on the rate of change of the electric and magnetic fields. In\u0000particular, Maxwell's equation for the curl of the magnetic field contains both\u0000the steady current and a term depending upon the temporal derivative of the\u0000electric displacement field. The latter is referred to as displacement current,\u0000and is generally believed to have been included originally by Maxwell himself,\u0000although there is evidence it was earlier considered by Kirchhoff. Maxwell's\u0000equations and Kirchoff's circuit laws both are important over the wide range of\u0000frequencies with which electronics traditionally deals. And, displacement\u0000current is an important contribution to these in both classical and quantum\u0000mechanics. Here, the development of displacement current, its importance in\u0000both classical and quantum mechanics, and some applications are provided to\u0000illustrate the fundamental role that it plays in the dynamics of a wide range\u0000of systems.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shortcuts to adiabaticity are strategies for conserving adiabatic invariants under non-adiabatic (i.e. fast-driving) conditions. Here, we show how to extend classical, Hamiltonian shortcuts to adiabaticity to allow the crossing of a phase-space separatrix -- a situation in which a corresponding adiabatic protocol does not exist. Specifically, we show how to construct a time-dependent Hamiltonian that evolves one energy shell to another energy shell across a separatrix. Leveraging this method, we design an erasure procedure whose energy cost and fidelity do not depend on the protocol's duration.
{"title":"Shortcuts to adiabaticity across a separatrix","authors":"Roi Holtzman, Oren Raz, Christopher Jarzynski","doi":"arxiv-2408.06916","DOIUrl":"https://doi.org/arxiv-2408.06916","url":null,"abstract":"Shortcuts to adiabaticity are strategies for conserving adiabatic invariants\u0000under non-adiabatic (i.e. fast-driving) conditions. Here, we show how to extend\u0000classical, Hamiltonian shortcuts to adiabaticity to allow the crossing of a\u0000phase-space separatrix -- a situation in which a corresponding adiabatic\u0000protocol does not exist. Specifically, we show how to construct a\u0000time-dependent Hamiltonian that evolves one energy shell to another energy\u0000shell across a separatrix. Leveraging this method, we design an erasure\u0000procedure whose energy cost and fidelity do not depend on the protocol's\u0000duration.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yimeng Sun, Jiacheng Xing, Li-Hua Shao, Jianxiang Wang
Continuum lattice structures which consist of joined elastic beams subject to flexural deformations are ubiquitous in nature and engineering. Here, first, we reveal the topological dynamics of continuous beam structures by rigorously proving the existence of infinitely many topological edge states within the bandgaps. Then, we obtain the analytical expressions for the topological phases of bulk bands, and propose a topological index related to the Zak phase that determines the existence of the edge states. The theoretical approach is directly applicable to general continuum lattice structures. We demonstrate the topological edge states of bridge-like frames, plates, and continuous beams on elastic foundations and springs, and the topological corner states of kagome frames. The continuum lattice structures serve as excellent platforms for exploring various kinds of topological phases and demonstrating the topologically protected states at multifrequencies, and their topological dynamics has significant implications in safety assessment, structural health monitoring, and energy harvesting.
{"title":"Topological dynamics of continuum lattice structures","authors":"Yimeng Sun, Jiacheng Xing, Li-Hua Shao, Jianxiang Wang","doi":"arxiv-2408.06898","DOIUrl":"https://doi.org/arxiv-2408.06898","url":null,"abstract":"Continuum lattice structures which consist of joined elastic beams subject to\u0000flexural deformations are ubiquitous in nature and engineering. Here, first, we\u0000reveal the topological dynamics of continuous beam structures by rigorously\u0000proving the existence of infinitely many topological edge states within the\u0000bandgaps. Then, we obtain the analytical expressions for the topological phases\u0000of bulk bands, and propose a topological index related to the Zak phase that\u0000determines the existence of the edge states. The theoretical approach is\u0000directly applicable to general continuum lattice structures. We demonstrate the\u0000topological edge states of bridge-like frames, plates, and continuous beams on\u0000elastic foundations and springs, and the topological corner states of kagome\u0000frames. The continuum lattice structures serve as excellent platforms for\u0000exploring various kinds of topological phases and demonstrating the\u0000topologically protected states at multifrequencies, and their topological\u0000dynamics has significant implications in safety assessment, structural health\u0000monitoring, and energy harvesting.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"392 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic behavior in its classical limit: the kicked top model, whose classical dynamics are governed by Hamilton's equations on phase space, whereas its quantum dynamics are described by the Schr"odinger equation in Hilbert space. We explore the critical degree of non-linearity signifying the onset of chaos in the kicked top by modifying the original Hamiltonian so that the non-linearity is parametrized by a quantity $p$. We find two distinct behaviors of the modified kicked top depending on the value of $p$. Chaos intensifies as $p$ varies within the range of $1leq p leq 2$, whereas it diminishes for $p > 2$, eventually transitioning to a purely regular oscillating system as $p$ tends to infinity. We also comment on the complicated phase space structure for non-chaotic dynamics. Our investigation sheds light on the relationship between non-linearity and chaos in classical systems, offering insights into their dynamic behavior.
经典混沌产生于动力学系统固有的非线性。然而，量子映射是线性的；因此，混沌的定义并不直接。为了解决这个问题，我们研究了一个在经典极限中表现出混沌行为的量子系统：踢顶模型，其经典动力学受相空间上的汉密尔顿方程支配，而其量子动力学则由希尔伯特空间上的施dinger方程描述。我们发现修改后的踢顶有两种截然不同的行为，这取决于 $p$ 的值。当$p$在$1leq p leq2$范围内变化时，混沌会加剧；而当$p>2$时，混沌会减弱。我们还评论了非混沌动力学的复杂相空间结构。我们的研究揭示了经典系统中非线性与混沌之间的关系，为其动力学行为提供了启示。
{"title":"Non-linearity and chaos in the kicked top","authors":"Amit Anand, Robert B. Mann, Shohini Ghose","doi":"arxiv-2408.05869","DOIUrl":"https://doi.org/arxiv-2408.05869","url":null,"abstract":"Classical chaos arises from the inherent non-linearity of dynamical systems.\u0000However, quantum maps are linear; therefore, the definition of chaos is not\u0000straightforward. To address this, we study a quantum system that exhibits\u0000chaotic behavior in its classical limit: the kicked top model, whose classical\u0000dynamics are governed by Hamilton's equations on phase space, whereas its\u0000quantum dynamics are described by the Schr\"odinger equation in Hilbert space.\u0000We explore the critical degree of non-linearity signifying the onset of chaos\u0000in the kicked top by modifying the original Hamiltonian so that the\u0000non-linearity is parametrized by a quantity $p$. We find two distinct behaviors\u0000of the modified kicked top depending on the value of $p$. Chaos intensifies as\u0000$p$ varies within the range of $1leq p leq 2$, whereas it diminishes for $p >\u00002$, eventually transitioning to a purely regular oscillating system as $p$\u0000tends to infinity. We also comment on the complicated phase space structure for\u0000non-chaotic dynamics. Our investigation sheds light on the relationship between\u0000non-linearity and chaos in classical systems, offering insights into their\u0000dynamic behavior.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wanyue Xiao, Wenjian Kuang, Sibo Huang, Shanjun Liang, Din Ping Tsai, Shubo Wang
Common wisdom believes that the Pancharatnam-Berry (PB) geometric phase is absent in acoustics due to the spin-0 nature of sound waves. We theoretically and experimentally demonstrate that the PB phase can emerge in surface sound waves (SSWs) carrying transverse spin. The phase differs for the SSWs propagating in opposite directions due to spin-momentum locking. We further realize acoustic PB metasurfaces for nearly arbitrary wavefront manipulation. Our work provides the missing piece of acoustic geometric phases, offering new insights into the fundamental properties of sound waves and opening a new avenue for sound manipulation based on the PB phase.
{"title":"Acoustic Pancharatnam-Berry Geometric Phase Induced by Transverse Spin","authors":"Wanyue Xiao, Wenjian Kuang, Sibo Huang, Shanjun Liang, Din Ping Tsai, Shubo Wang","doi":"arxiv-2408.03513","DOIUrl":"https://doi.org/arxiv-2408.03513","url":null,"abstract":"Common wisdom believes that the Pancharatnam-Berry (PB) geometric phase is\u0000absent in acoustics due to the spin-0 nature of sound waves. We theoretically\u0000and experimentally demonstrate that the PB phase can emerge in surface sound\u0000waves (SSWs) carrying transverse spin. The phase differs for the SSWs\u0000propagating in opposite directions due to spin-momentum locking. We further\u0000realize acoustic PB metasurfaces for nearly arbitrary wavefront manipulation.\u0000Our work provides the missing piece of acoustic geometric phases, offering new\u0000insights into the fundamental properties of sound waves and opening a new\u0000avenue for sound manipulation based on the PB phase.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"371 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The geometry of 2D Minkowski spacetime $mathbb{R}^{1,1}$ (or Minkowski plane) is similar but fundamentally different from the more familiar Euclidean plane geometry. This note gives an elementary discussion on some basic properties of a triangle on the Minkowski plane. In particular, we show that the theorem of Feuerbach also holds and a use of the incenter/excenters is pointed out.
{"title":"Notes on the planar triangles in Minkowski spacetime","authors":"Yan Cao","doi":"arxiv-2408.03898","DOIUrl":"https://doi.org/arxiv-2408.03898","url":null,"abstract":"The geometry of 2D Minkowski spacetime $mathbb{R}^{1,1}$ (or Minkowski\u0000plane) is similar but fundamentally different from the more familiar Euclidean\u0000plane geometry. This note gives an elementary discussion on some basic\u0000properties of a triangle on the Minkowski plane. In particular, we show that\u0000the theorem of Feuerbach also holds and a use of the incenter/excenters is\u0000pointed out.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francis Flanagan, Alison O'Connor, Mozhdeh Erfanian, Omer Music, Edward James Brambley, Doireann O'Kiely
In this paper, we carefully develop a finite element (FE) model that gives accurate through-thickness predictions of stress and strain distributions during the steady-state cold rolling process. These through-thickness predictions unveil an oscillatory pattern that is shown to have important consequences for residual stress in the rolled sheet. We believe this is the first time that through-thickness FE results have been accurately validated by comparison to non-FE results, in this case by comparison to a recent analytical model of through-thickness variation in cold rolling. While we use here the ABAQUS commercially available FE software, our observations are relevant to all FE simulations of cold rolling. Care is taken by considering both convergence in number of elements through thickness, convergence to a steady state, and the avoidance of other numerical artefacts such as shear locking and hourglassing. We find that previous FE models of cold rolling are usually woefully under-resolved through-thickness; e.g. using 10 elements through-thickness, while we require 60 here for convergence. Convergence of roll force and roll torque, used in previous studies to validate models, are shown to be poor indicators of through-thickness convergence. We also show that the through-thickness oscillatory pattern may have important consequences for predicting curvature during asymmetric rolling.
{"title":"Careful finite element simulations of cold rolling with accurate through-thickness resolution and prediction of residual stress","authors":"Francis Flanagan, Alison O'Connor, Mozhdeh Erfanian, Omer Music, Edward James Brambley, Doireann O'Kiely","doi":"arxiv-2408.03242","DOIUrl":"https://doi.org/arxiv-2408.03242","url":null,"abstract":"In this paper, we carefully develop a finite element (FE) model that gives\u0000accurate through-thickness predictions of stress and strain distributions\u0000during the steady-state cold rolling process. These through-thickness\u0000predictions unveil an oscillatory pattern that is shown to have important\u0000consequences for residual stress in the rolled sheet. We believe this is the\u0000first time that through-thickness FE results have been accurately validated by\u0000comparison to non-FE results, in this case by comparison to a recent analytical\u0000model of through-thickness variation in cold rolling. While we use here the\u0000ABAQUS commercially available FE software, our observations are relevant to all\u0000FE simulations of cold rolling. Care is taken by considering both convergence\u0000in number of elements through thickness, convergence to a steady state, and the\u0000avoidance of other numerical artefacts such as shear locking and hourglassing.\u0000We find that previous FE models of cold rolling are usually woefully\u0000under-resolved through-thickness; e.g. using 10 elements through-thickness,\u0000while we require 60 here for convergence. Convergence of roll force and roll\u0000torque, used in previous studies to validate models, are shown to be poor\u0000indicators of through-thickness convergence. We also show that the\u0000through-thickness oscillatory pattern may have important consequences for\u0000predicting curvature during asymmetric rolling.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory data points unlike traditional methods that require an averaging procedure, the exploration of phase transition graphs from regular periodic to chaotic dynamics to identify "almost integrable" trajectories where conserved quantities deviate from whole numbers, and the identification of "integrable regions" within chaotic trajectories. These methods are applied and tested on two dynamical systems: "Two objects moving on a rod" and the "Henon-Heiles" systems.
{"title":"Deciphering Complexity: Machine Learning Insights into Chaotic Dynamical Systems","authors":"Lazare Osmanov","doi":"arxiv-2408.02005","DOIUrl":"https://doi.org/arxiv-2408.02005","url":null,"abstract":"We introduce new machine-learning techniques for analyzing chaotic dynamical\u0000systems. The primary objectives of the study include the development of a new\u0000and simple method for calculating the Lyapunov exponent using only two\u0000trajectory data points unlike traditional methods that require an averaging\u0000procedure, the exploration of phase transition graphs from regular periodic to\u0000chaotic dynamics to identify \"almost integrable\" trajectories where conserved\u0000quantities deviate from whole numbers, and the identification of \"integrable\u0000regions\" within chaotic trajectories. These methods are applied and tested on\u0000two dynamical systems: \"Two objects moving on a rod\" and the \"Henon-Heiles\"\u0000systems.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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