arXiv - PHYS - Chaotic Dynamics最新文献

Tunneling Time for Walking Droplets on an Oscillating Liquid Surface 振荡液面上行走液滴的隧道时间

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-18 DOI: arxiv-2409.11934

Chuan-Yu Hung, Ting-Heng Hsieh, Tzay-Ming Hong

{"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}

引用次数: 0

Rydberg excitons in cuprous oxide: A two-particle system with classical chaos 氧化亚铜中的里贝格激子：具有经典混沌的双粒子系统

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-12 DOI: arxiv-2409.08225

Jan Ertl, Sebastian Rentschler, Jörg Main

{"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}

引用次数: 0

Disruption of exo-asteroids around white dwarfs and the release of dust particles in debris rings in co-orbital motion 白矮星周围外行星的扰动和共轨运动碎片环中尘埃粒子的释放

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-04 DOI: arxiv-2409.03002

Kyriaki I. Antoniadou, Dimitri Veras

{"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}

引用次数: 0

Machine-aided guessing and gluing of unstable periodic orbits 机器辅助猜测和粘合不稳定周期轨道

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-04 DOI: arxiv-2409.03033

Pierre Beck, Jeremy P. Parker, Tobias M. Schneider

{"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}

引用次数: 0

Nonequilibrium dynamics of coupled oscillators under the shear-velocity boundary condition 剪切速度边界条件下耦合振荡器的非平衡动力学

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-04 DOI: arxiv-2409.02515

Hidetsugu Sakaguchi

引用次数: 0

The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation 仓本-西瓦申斯基方程中混沌吸引子的拓扑结构

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-03 DOI: arxiv-2409.01719

Marie Abadie, Pierre Beck, Jeremy P. Parker, Tobias M. Schneider

{"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}

引用次数: 0

Quantifying predictability and basin structure in infinite-dimensional delayed systems: a stochastic basin entropy approach 量化无穷维延迟系统中的可预测性和盆地结构：随机盆地熵方法

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-03 DOI: arxiv-2409.01878

Juan P. Tarigo, Cecilia Stari, Arturo C. Marti

引用次数: 0

Stabilization of a transition state by excited vibration and impact on the reaction rate in the three-body Lennard-Jones system 三体伦纳德-琼斯系统中激发振动稳定过渡态及其对反应速率的影响

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-02 DOI: arxiv-2409.00932

Yoshiyuki Y. Yamaguchi

引用次数: 0

Cycle-Star Motifs: Network Response to Link Modifications 循环-星形图案：网络对链接修改的响应

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-09-02 DOI: arxiv-2409.01244

Sajjad Bakrani, Narcicegi Kiran, Deniz Eroglu, Tiago Pereira

{"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}

引用次数: 0

Inertial Particle Dynamics in Traveling Wave Flow 行进波流中的惯性粒子动力学

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-31 DOI: arxiv-2409.00484

P. Swaathi, Sanjit Das, N. Nirmal Thyagu

{"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}

引用次数: 0