In recent years, Couder and collaborators have initiated a series of studies on walking droplets. Experimentally, they found that at frequencies and amplitudes close to the onset of Faraday waves, droplets on the surface of silicone oil can survive and walk at a roughly constant speed due to resonance. Droplets excite local ripples from the Faraday instability when they bounce from the liquid surface. This tightly coupled particle-wave entity, although a complex yet entirely classical system, exhibits many phenomena that are strikingly similar to those of quantum systems, such as slit interference and diffraction, tunneling probability, and Anderson localization. In this Letter, we focus on the tunneling time of droplets. Specifically, we explore (1) how it changes with the width of an acrylic barrier, which gives rise to the potential barrier when the depth of the silicone oil is reduced to prevent the generation of ripples that can feed energy back to the droplet, and (2) the distribution of tunneling times at the same barrier width. Both results turn out to be similar to the numerical outcome of the Bohmian mechanics, which strengthens the analogy to a quantum system. Furthermore, we successfully derive analytic expressions for these properties by revising the multiple scattering theory and constructing a ``skipping stone" model. Provided that the resemblance in tunneling behavior of walking droplets to Bohmian particles is not coincidental, we discuss the lessons for the Copenhagen interpretation of quantum mechanics that so far fails to explain both characteristics adequately.
{"title":"Tunneling Time for Walking Droplets on an Oscillating Liquid Surface","authors":"Chuan-Yu Hung, Ting-Heng Hsieh, Tzay-Ming Hong","doi":"arxiv-2409.11934","DOIUrl":"https://doi.org/arxiv-2409.11934","url":null,"abstract":"In recent years, Couder and collaborators have initiated a series of studies\u0000on walking droplets. Experimentally, they found that at frequencies and\u0000amplitudes close to the onset of Faraday waves, droplets on the surface of\u0000silicone oil can survive and walk at a roughly constant speed due to resonance.\u0000Droplets excite local ripples from the Faraday instability when they bounce\u0000from the liquid surface. This tightly coupled particle-wave entity, although a\u0000complex yet entirely classical system, exhibits many phenomena that are\u0000strikingly similar to those of quantum systems, such as slit interference and\u0000diffraction, tunneling probability, and Anderson localization. In this Letter,\u0000we focus on the tunneling time of droplets. Specifically, we explore (1) how it\u0000changes with the width of an acrylic barrier, which gives rise to the potential\u0000barrier when the depth of the silicone oil is reduced to prevent the generation\u0000of ripples that can feed energy back to the droplet, and (2) the distribution\u0000of tunneling times at the same barrier width. Both results turn out to be\u0000similar to the numerical outcome of the Bohmian mechanics, which strengthens\u0000the analogy to a quantum system. Furthermore, we successfully derive analytic\u0000expressions for these properties by revising the multiple scattering theory and\u0000constructing a ``skipping stone\" model. Provided that the resemblance in\u0000tunneling behavior of walking droplets to Bohmian particles is not\u0000coincidental, we discuss the lessons for the Copenhagen interpretation of\u0000quantum mechanics that so far fails to explain both characteristics adequately.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248099","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}
When an electron in a semiconductor gets excited to the conduction band the missing electron can be viewed as a positively charged particle, the hole. Due to the Coulomb interaction electrons and holes can form a hydrogen-like bound state called exciton. For cuprous oxide a Rydberg series up to high principle quantum numbers has been observed by Kazimierczuk et al. [Nature 514, 343 (2014)] with the extension of excitons up to the $mu$m-range. In this region the correspondence principle should hold and quantum mechanics turn into classical dynamics. Due to the complex valence band structure of Cu$_2$O the classical dynamics deviates from a purely hydrogen-like behavior. The uppermost valence band in cuprous oxide splits into various bands resulting in a yellow and green exciton series. Since the system exhibits no spherical symmetry, the angular momentum is not conserved. Thus, the classical dynamics becomes non-integrable, resulting in the possibility of chaotic motion. Here we investigate the classical dynamics of the yellow and green exciton series in cuprous oxide for two-dimensional orbits in the symmetry planes as well as fully three-dimensional orbits. The analysis reveals substantial differences between the dynamics of the yellow and green exciton series. While it is mostly regular for the yellow series large regions in phase space with classical chaos do exist for the green exciton series.
{"title":"Rydberg excitons in cuprous oxide: A two-particle system with classical chaos","authors":"Jan Ertl, Sebastian Rentschler, Jörg Main","doi":"arxiv-2409.08225","DOIUrl":"https://doi.org/arxiv-2409.08225","url":null,"abstract":"When an electron in a semiconductor gets excited to the conduction band the\u0000missing electron can be viewed as a positively charged particle, the hole. Due\u0000to the Coulomb interaction electrons and holes can form a hydrogen-like bound\u0000state called exciton. For cuprous oxide a Rydberg series up to high principle\u0000quantum numbers has been observed by Kazimierczuk et al. [Nature 514, 343\u0000(2014)] with the extension of excitons up to the $mu$m-range. In this region\u0000the correspondence principle should hold and quantum mechanics turn into\u0000classical dynamics. Due to the complex valence band structure of Cu$_2$O the\u0000classical dynamics deviates from a purely hydrogen-like behavior. The uppermost\u0000valence band in cuprous oxide splits into various bands resulting in a yellow\u0000and green exciton series. Since the system exhibits no spherical symmetry, the\u0000angular momentum is not conserved. Thus, the classical dynamics becomes\u0000non-integrable, resulting in the possibility of chaotic motion. Here we\u0000investigate the classical dynamics of the yellow and green exciton series in\u0000cuprous oxide for two-dimensional orbits in the symmetry planes as well as\u0000fully three-dimensional orbits. The analysis reveals substantial differences\u0000between the dynamics of the yellow and green exciton series. While it is mostly\u0000regular for the yellow series large regions in phase space with classical chaos\u0000do exist for the green exciton series.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"99 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222674","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}
Close to the Roche radius of a white dwarf (WD), an asteroid on a circular orbit sheds material that then adopts a very similar orbit. Observations of the resulting debris show a periodic behavior and changes in flux on short timescales, implying ongoing dynamical activity. Additional encounters from other minor planets may then yield co-orbital rings of debris at different inclinations. The structure, dynamics, and lifetime of these debris discs remains highly uncertain, but is important for understanding WD planetary systems. We aim to identify and quantify the locations of co-orbitals in WD-asteroid-dust particle 3-body systems by exploring the influence of 1:1 resonant periodic orbits. We begin this exploration with co-planar and inclined orbits in the circular restricted 3-body problem (CRTBP) and model the dynamical evolution of these exosystems over observable timescales. The mass ratio parameter for this class of systems ($~2times 10^{-11}$) is one of the lowest ever explored in this dynamical configuration. We computed the periodic orbits, deduced their linear stability, and suitably seeded the dynamical stability maps. We carried out a limited suite of N-body simulations to provide direct comparisons with the maps. We derive novel results for this extreme mass ratio in the CRTBP, including new unstable 3D families. We illustrate through the maps and N-body simulations where dust can exist in a stable configuration over observable timescales across a wide expanse of parameter space in the absence of strong external forces. Over a timescale of 10 yr, the maximum orbital period deviations of stable debris due to the co-orbital perturbations of the asteroid is about a few seconds. Unstable debris in a close encounter with the asteroid typically deviates from the co-orbital configuration by more than about 20 km and is on a near-circular orbit with an eccentricity lower than ~0.01.
{"title":"Disruption of exo-asteroids around white dwarfs and the release of dust particles in debris rings in co-orbital motion","authors":"Kyriaki I. Antoniadou, Dimitri Veras","doi":"arxiv-2409.03002","DOIUrl":"https://doi.org/arxiv-2409.03002","url":null,"abstract":"Close to the Roche radius of a white dwarf (WD), an asteroid on a circular\u0000orbit sheds material that then adopts a very similar orbit. Observations of the\u0000resulting debris show a periodic behavior and changes in flux on short\u0000timescales, implying ongoing dynamical activity. Additional encounters from\u0000other minor planets may then yield co-orbital rings of debris at different\u0000inclinations. The structure, dynamics, and lifetime of these debris discs\u0000remains highly uncertain, but is important for understanding WD planetary\u0000systems. We aim to identify and quantify the locations of co-orbitals in\u0000WD-asteroid-dust particle 3-body systems by exploring the influence of 1:1\u0000resonant periodic orbits. We begin this exploration with co-planar and inclined\u0000orbits in the circular restricted 3-body problem (CRTBP) and model the\u0000dynamical evolution of these exosystems over observable timescales. The mass\u0000ratio parameter for this class of systems ($~2times 10^{-11}$) is one of the\u0000lowest ever explored in this dynamical configuration. We computed the periodic\u0000orbits, deduced their linear stability, and suitably seeded the dynamical\u0000stability maps. We carried out a limited suite of N-body simulations to provide\u0000direct comparisons with the maps. We derive novel results for this extreme mass\u0000ratio in the CRTBP, including new unstable 3D families. We illustrate through\u0000the maps and N-body simulations where dust can exist in a stable configuration\u0000over observable timescales across a wide expanse of parameter space in the\u0000absence of strong external forces. Over a timescale of 10 yr, the maximum\u0000orbital period deviations of stable debris due to the co-orbital perturbations\u0000of the asteroid is about a few seconds. Unstable debris in a close encounter\u0000with the asteroid typically deviates from the co-orbital configuration by more\u0000than about 20 km and is on a near-circular orbit with an eccentricity lower\u0000than ~0.01.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222563","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}
Pierre Beck, Jeremy P. Parker, Tobias M. Schneider
Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult. Matrix-free loop convergence algorithms deform entire space-time fields (loops) until they satisfy the evolution equations. Initial guesses for these robust variational convergence algorithms are thus periodic space-time fields in a high-dimensional state space, rendering their generation highly challenging. Usually guesses are generated with recurrency methods, which are most suited to shorter and more stable periodic orbits. Here we propose an alternative, data-driven method for generating initial guesses: while the dimension of the space used to discretize fluid flows is prohibitively large to construct suitable initial guesses, the dissipative dynamics will collapse onto a chaotic attractor of far lower dimension. We use an autoencoder to obtain a low-dimensional representation of the discretized physical space for the one-dimensional Kuramoto-Sivashinksy equation, in chaotic and hyperchaotic regimes. In this low-dimensional latent space, we construct loops based on the latent POD modes with random periodic coefficients, which are then decoded to physical space and used as initial guesses. These loops are found to be realistic initial guesses and, together with variational convergence algorithms, these guesses help us to quickly converge to UPOs. We further attempt to 'glue' known UPOs in the latent space to create guesses for longer ones. This gluing procedure is successful and points towards a hierarchy of UPOs where longer UPOs shadow sequences of shorter ones.
不稳定周期轨道（UPO）被认为是时空混沌和湍流的基本动力学结构。然而，要找到这些不稳定周期轨道却非常困难。这些稳健变分收敛算法的初始猜测是高维状态空间中的周期性时空场，因此它们的生成极具挑战性。通常情况下，猜测是通过递归方法生成的，这种方法最适用于较短和较稳定的周期轨道。在这里，我们提出了另一种数据驱动的初始猜测生成方法：虽然用于离散流体流的空间维度过大，无法构建合适的初始猜测，但离散动力学会坍缩到维度更低的混沌吸引子上。我们使用自动编码器获得了一维 Kuramoto-Sivashinksy 方程在混沌和超混沌状态下离散物理空间的低维表示。在这个低维潜在空间中，我们根据具有随机周期性系数的潜在 POD 模式构建环路，然后将其解码到物理空间并用作初始猜测。我们发现这些环路是现实的初始猜测，再加上变分收敛算法，这些猜测有助于我们快速收敛到 UPO。我们进一步尝试在潜空间中 "粘合 "已知的 UPO，以创建更长的猜测。这一粘合过程取得了成功，并指向了 UPO 的层次结构，其中较长的 UPO 是较短的 UPO 序列的影子。
{"title":"Machine-aided guessing and gluing of unstable periodic orbits","authors":"Pierre Beck, Jeremy P. Parker, Tobias M. Schneider","doi":"arxiv-2409.03033","DOIUrl":"https://doi.org/arxiv-2409.03033","url":null,"abstract":"Unstable periodic orbits (UPOs) are believed to be the underlying dynamical\u0000structures of spatio-temporal chaos and turbulence. Finding these UPOs is\u0000however notoriously difficult. Matrix-free loop convergence algorithms deform\u0000entire space-time fields (loops) until they satisfy the evolution equations.\u0000Initial guesses for these robust variational convergence algorithms are thus\u0000periodic space-time fields in a high-dimensional state space, rendering their\u0000generation highly challenging. Usually guesses are generated with recurrency\u0000methods, which are most suited to shorter and more stable periodic orbits. Here\u0000we propose an alternative, data-driven method for generating initial guesses:\u0000while the dimension of the space used to discretize fluid flows is\u0000prohibitively large to construct suitable initial guesses, the dissipative\u0000dynamics will collapse onto a chaotic attractor of far lower dimension. We use\u0000an autoencoder to obtain a low-dimensional representation of the discretized\u0000physical space for the one-dimensional Kuramoto-Sivashinksy equation, in\u0000chaotic and hyperchaotic regimes. In this low-dimensional latent space, we\u0000construct loops based on the latent POD modes with random periodic\u0000coefficients, which are then decoded to physical space and used as initial\u0000guesses. These loops are found to be realistic initial guesses and, together\u0000with variational convergence algorithms, these guesses help us to quickly\u0000converge to UPOs. We further attempt to 'glue' known UPOs in the latent space\u0000to create guesses for longer ones. This gluing procedure is successful and\u0000points towards a hierarchy of UPOs where longer UPOs shadow sequences of\u0000shorter ones.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222564","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}
Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various relationships with wide research areas such as the coupled limit-cycle oscillators, the dislocation theory, a block-spring model of earthquakes, and the nonequilibrium molecular dynamics. We show numerically several unique nonequilibrium properties of the coupled oscillators. We find that the spatial profiles of the average value and variance of the velocity become non-uniform when the dissipation rate is large. The probability distribution of the velocity sometimes deviates from the Gaussian distribution. The time evolution of kinetic energy becomes intermittent when the shear rate is small and the temperature is small but not zero. The intermittent jumps of the kinetic energy cause a long tail in the velocity distribution.
{"title":"Nonequilibrium dynamics of coupled oscillators under the shear-velocity boundary condition","authors":"Hidetsugu Sakaguchi","doi":"arxiv-2409.02515","DOIUrl":"https://doi.org/arxiv-2409.02515","url":null,"abstract":"Deterministic and stochastic coupled oscillators with inertia are studied on\u0000the rectangular lattice under the shear-velocity boundary condition. Our\u0000coupled oscillator model exhibits various nontrivial phenomena and there are\u0000various relationships with wide research areas such as the coupled limit-cycle\u0000oscillators, the dislocation theory, a block-spring model of earthquakes, and\u0000the nonequilibrium molecular dynamics. We show numerically several unique\u0000nonequilibrium properties of the coupled oscillators. We find that the spatial\u0000profiles of the average value and variance of the velocity become non-uniform\u0000when the dissipation rate is large. The probability distribution of the\u0000velocity sometimes deviates from the Gaussian distribution. The time evolution\u0000of kinetic energy becomes intermittent when the shear rate is small and the\u0000temperature is small but not zero. The intermittent jumps of the kinetic energy\u0000cause a long tail in the velocity distribution.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222565","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}
Marie Abadie, Pierre Beck, Jeremy P. Parker, Tobias M. Schneider
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a chaotic attractor in a partial differential equation (PDE) is less than three, even though that attractor is embedded within an infinite-dimensional space. Here we study the Kuramoto-Sivashinsky PDE at the onset of chaos. We use two different dimensionality-reduction techniques - proper orthogonal decomposition and an autoencoder neural network - to find two different approximate embeddings of the chaotic attractor into three dimensions. By finding the projection of the attractor's UPOs in these reduced spaces and examining their linking numbers, we construct templates for the branched manifold which encodes the topological properties of the attractor. The templates obtained using two different dimensionality reduction methods mirror each other. Hence, the organization of the periodic orbits is identical (up to a global change of sign) and consistent symbolic names for low-period UPOs are derived. This is strong evidence that the dimensional reduction is robust, in this case, and that an accurate topological characterization of the chaotic attractor of the chaotic PDE has been achieved.
{"title":"The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation","authors":"Marie Abadie, Pierre Beck, Jeremy P. Parker, Tobias M. Schneider","doi":"arxiv-2409.01719","DOIUrl":"https://doi.org/arxiv-2409.01719","url":null,"abstract":"The Birman-Williams theorem gives a connection between the collection of\u0000unstable periodic orbits (UPOs) contained within a chaotic attractor and the\u0000topology of that attractor, for three-dimensional systems. In certain cases,\u0000the fractal dimension of a chaotic attractor in a partial differential equation\u0000(PDE) is less than three, even though that attractor is embedded within an\u0000infinite-dimensional space. Here we study the Kuramoto-Sivashinsky PDE at the\u0000onset of chaos. We use two different dimensionality-reduction techniques -\u0000proper orthogonal decomposition and an autoencoder neural network - to find two\u0000different approximate embeddings of the chaotic attractor into three\u0000dimensions. By finding the projection of the attractor's UPOs in these reduced\u0000spaces and examining their linking numbers, we construct templates for the\u0000branched manifold which encodes the topological properties of the attractor.\u0000The templates obtained using two different dimensionality reduction methods\u0000mirror each other. Hence, the organization of the periodic orbits is identical\u0000(up to a global change of sign) and consistent symbolic names for low-period\u0000UPOs are derived. This is strong evidence that the dimensional reduction is\u0000robust, in this case, and that an accurate topological characterization of the\u0000chaotic attractor of the chaotic PDE has been achieved.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222567","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 Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of the long-term dynamics is especially challenging in these systems, where the dimensionality is infinite and initial conditions must be specified as a function in a finite time interval. In this paper we extend the recently proposed basin entropy to randomly sample arbitrarily high-dimensional spaces. By complementing this stochastic approach with the basin fraction of the attractors in the initial conditions space we can understand the structure of the basins of attraction and how they are intermixed. The results reported here allow us to quantify the predictability and provide indicators of the presence of bifurcations. The tools employed can result very useful in the study of complex systems of infinite dimension.
{"title":"Quantifying predictability and basin structure in infinite-dimensional delayed systems: a stochastic basin entropy approach","authors":"Juan P. Tarigo, Cecilia Stari, Arturo C. Marti","doi":"arxiv-2409.01878","DOIUrl":"https://doi.org/arxiv-2409.01878","url":null,"abstract":"The Mackey-Glass system is a paradigmatic example of a delayed model whose\u0000dynamics is particularly complex due to, among other factors, its\u0000multistability involving the coexistence of many periodic and chaotic\u0000attractors. The prediction of the long-term dynamics is especially challenging\u0000in these systems, where the dimensionality is infinite and initial conditions\u0000must be specified as a function in a finite time interval. In this paper we\u0000extend the recently proposed basin entropy to randomly sample arbitrarily\u0000high-dimensional spaces. By complementing this stochastic approach with the\u0000basin fraction of the attractors in the initial conditions space we can\u0000understand the structure of the basins of attraction and how they are\u0000intermixed. The results reported here allow us to quantify the predictability\u0000and provide indicators of the presence of bifurcations. The tools employed can\u0000result very useful in the study of complex systems of infinite dimension.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"112 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222578","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 three-body Lennard-Jones system on the plane has a transition state, which is the straight conformation located at a saddle point of the potential energy landscape. We show that the transition state can be dynamically stabilized by excited vibration of particle distances. The stabilization mechanism is explained theoretically, and is verified by performing molecular dynamics simulations. We also examine whether the dynamical stabilization gives an impact on the reaction rate between the two isomers of equilateral triangle conformations by comparing with the transition state theory.
{"title":"Stabilization of a transition state by excited vibration and impact on the reaction rate in the three-body Lennard-Jones system","authors":"Yoshiyuki Y. Yamaguchi","doi":"arxiv-2409.00932","DOIUrl":"https://doi.org/arxiv-2409.00932","url":null,"abstract":"The three-body Lennard-Jones system on the plane has a transition state,\u0000which is the straight conformation located at a saddle point of the potential\u0000energy landscape. We show that the transition state can be dynamically\u0000stabilized by excited vibration of particle distances. The stabilization\u0000mechanism is explained theoretically, and is verified by performing molecular\u0000dynamics simulations. We also examine whether the dynamical stabilization gives\u0000an impact on the reaction rate between the two isomers of equilateral triangle\u0000conformations by comparing with the transition state theory.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222568","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}
Sajjad Bakrani, Narcicegi Kiran, Deniz Eroglu, Tiago Pereira
Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master-slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as R"ossler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.
{"title":"Cycle-Star Motifs: Network Response to Link Modifications","authors":"Sajjad Bakrani, Narcicegi Kiran, Deniz Eroglu, Tiago Pereira","doi":"arxiv-2409.01244","DOIUrl":"https://doi.org/arxiv-2409.01244","url":null,"abstract":"Understanding efficient modifications to improve network functionality is a\u0000fundamental problem of scientific and industrial interest. We study the\u0000response of network dynamics against link modifications on a weakly connected\u0000directed graph consisting of two strongly connected components: an undirected\u0000star and an undirected cycle. We assume that there are directed edges starting\u0000from the cycle and ending at the star (master-slave formalism). We modify the\u0000graph by adding directed edges of arbitrarily large weights starting from the\u0000star and ending at the cycle (opposite direction of the cutset). We provide\u0000criteria (based on the sizes of the star and cycle, the coupling structure, and\u0000the weights of cutset and modification edges) that determine how the\u0000modification affects the spectral gap of the Laplacian matrix. We apply our\u0000approach to understand the modifications that either enhance or hinder\u0000synchronization in networks of chaotic Lorenz systems as well as R\"ossler. Our\u0000results show that the hindrance of collective dynamics due to link additions is\u0000not atypical as previously anticipated by modification analysis and thus allows\u0000for better control of collective properties.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"73 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222569","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 dynamics of inertial particles in fluid flows have been the focus of extensive research due to their relevance in a wide range of industrial and environmental processes. Earlier studies have examined the dynamics of aerosols and bubbles using the Maxey-Riley equation in some standard systems but their dynamics within the traveling wave flow remain unexplored. In this paper, we study the Lagrangian dynamics of inertial particles in the traveling wave flow which shows mixing, and segregation in phase space as well as the formation of Lagrangian Coherent Structures (LCS). We first obtain the finite-time Lyapunov exponent (FTLEs) for the base fluid flow defined by the traveling wave flow using the Cauchy-Green deformation tensor. Further, we extend our calculations to the inertial particles to get the inertial finite-time Lyapunov exponent (iFTLEs). Our findings reveal that heavier inertial particles tend to be attracted to the ridges of the FTLE fields, while lighter particles are repelled. By understanding how material elements in a flow separate and stretch, one can predict pollutant dispersion, optimize the mixing process, and improve navigation and tracking in fluid environments. This provides insights into the complex and non-intuitive behavior of inertial particles in chaotic fluid flows, and may have implications for pollutant transport in wide-ranging fields such as atmospheric and oceanic sciences.
{"title":"Inertial Particle Dynamics in Traveling Wave Flow","authors":"P. Swaathi, Sanjit Das, N. Nirmal Thyagu","doi":"arxiv-2409.00484","DOIUrl":"https://doi.org/arxiv-2409.00484","url":null,"abstract":"The dynamics of inertial particles in fluid flows have been the focus of\u0000extensive research due to their relevance in a wide range of industrial and\u0000environmental processes. Earlier studies have examined the dynamics of aerosols\u0000and bubbles using the Maxey-Riley equation in some standard systems but their\u0000dynamics within the traveling wave flow remain unexplored. In this paper, we\u0000study the Lagrangian dynamics of inertial particles in the traveling wave flow\u0000which shows mixing, and segregation in phase space as well as the formation of\u0000Lagrangian Coherent Structures (LCS). We first obtain the finite-time Lyapunov\u0000exponent (FTLEs) for the base fluid flow defined by the traveling wave flow\u0000using the Cauchy-Green deformation tensor. Further, we extend our calculations\u0000to the inertial particles to get the inertial finite-time Lyapunov exponent\u0000(iFTLEs). Our findings reveal that heavier inertial particles tend to be\u0000attracted to the ridges of the FTLE fields, while lighter particles are\u0000repelled. By understanding how material elements in a flow separate and\u0000stretch, one can predict pollutant dispersion, optimize the mixing process, and\u0000improve navigation and tracking in fluid environments. This provides insights\u0000into the complex and non-intuitive behavior of inertial particles in chaotic\u0000fluid flows, and may have implications for pollutant transport in wide-ranging\u0000fields such as atmospheric and oceanic sciences.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222566","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：