arXiv - PHYS - Chaotic Dynamics最新文献_第5页

Three-Dimensional Acoustic Turbulence: Weak Versus Strong 三维声湍流：弱湍流与强湍流

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-11 DOI: arxiv-2407.08352

E. A. Kochurin, E. A. Kuznetsov

引用次数: 0

Nonlinear vibration and stability of a dielectric elastomer balloon based on a strain-stiffening model 基于应变刚度模型的介电弹性体球囊的非线性振动和稳定性

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-11 DOI: arxiv-2407.08370

Amin Alibakhshi, Weiqiu Chen, Michel Destrade

{"title":"Nonlinear vibration and stability of a dielectric elastomer balloon based on a strain-stiffening model","authors":"Amin Alibakhshi, Weiqiu Chen, Michel Destrade","doi":"arxiv-2407.08370","DOIUrl":"https://doi.org/arxiv-2407.08370","url":null,"abstract":"Limiting chain extensibility is a characteristic that plays a vital role in\u0000the stretching of highly elastic materials. The Gent model has been widely used\u0000to capture this behaviour, as it performs very well in fitting stress-stretch\u0000data in simple tension, and involves two material parameters only. Recently,\u0000Anssari-Benam and Bucchi [Int. J. Non. Linear. Mech. 2021, 128, 103626]\u0000introduced a different form of generalised neo-Hookean model, focusing on the\u0000molecular structure of elastomers, and showed that their model encompasses all\u0000ranges of deformations, performing better than the Gent model in many respects,\u0000also with only two parameters. Here we investigate the nonlinear vibration and\u0000stability of a dielectric elastomer balloon modelled by that strain energy\u0000function. We derive the deformation field in spherical coordinates and the\u0000governing equations by the Euler-Lagrange method, assuming that the balloon\u0000retains its spherical symmetry as it inflates. We consider in turn that the\u0000balloon is under two types of voltages, a pure DC voltage and a DC voltage\u0000superimposed on an AC voltage. We analyse the dynamic response of the balloon\u0000and identify the influential parameters in the model. We find that the\u0000molecular structure of the material, as tracked by the number of segments in a\u0000single chain, can control the instability and the pull-in/snap-through critical\u0000voltage, as well as chaos and quasi-periodicity. The main result is that\u0000balloons made of materials exhibiting early strain-stiffening effects are more\u0000stable and less prone to generate chaotic nonlinear vibrations than softer\u0000materials, such as those modelled by the neo-Hookean strain-energy density\u0000function.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609607","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

Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More 图排列熵：扩展到连续情况，向正序深度学习迈出一步，以及更多内容

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-10 DOI: arxiv-2407.07524

Om Roy, Avalon Campbell-Cousins, John Stewart Fabila Carrasco, Mario A Parra, Javier Escudero

{"title":"Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More","authors":"Om Roy, Avalon Campbell-Cousins, John Stewart Fabila Carrasco, Mario A Parra, Javier Escudero","doi":"arxiv-2407.07524","DOIUrl":"https://doi.org/arxiv-2407.07524","url":null,"abstract":"Nonlinear dynamics play an important role in the analysis of signals. A\u0000popular, readily interpretable nonlinear measure is Permutation Entropy. It has\u0000recently been extended for the analysis of graph signals, thus providing a\u0000framework for non-linear analysis of data sampled on irregular domains. Here,\u0000we introduce a continuous version of Permutation Entropy, extend it to the\u0000graph domain, and develop a ordinal activation function akin to the one of\u0000neural networks. This is a step towards Ordinal Deep Learning, a potentially\u0000effective and very recently posited concept. We also formally extend ordinal\u0000contrasts to the graph domain. Continuous versions of ordinal contrasts of\u0000length 3 are also introduced and their advantage is shown in experiments. We\u0000also integrate specific contrasts for the analysis of images and show that it\u0000generalizes well to the graph domain allowing a representation of images,\u0000represented as graph signals, in a plane similar to the entropy-complexity one.\u0000Applications to synthetic data, including fractal patterns and popular\u0000non-linear maps, and real-life MRI data show the validity of these novel\u0000extensions and potential benefits over the state of the art. By extending very\u0000recent concepts related to permutation entropy to the graph domain, we expect\u0000to accelerate the development of more graph-based entropy methods to enable\u0000nonlinear analysis of a broader kind of data and establishing relationships\u0000with emerging ideas in data science.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587155","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

Temporal Convolution Derived Multi-Layered Reservoir Computing 时间卷积衍生多层储层计算

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-09 DOI: arxiv-2407.06771

Johannes Viehweg, Dominik Walther, Prof. Dr. -Ing. Patrick Mäder

{"title":"Temporal Convolution Derived Multi-Layered Reservoir Computing","authors":"Johannes Viehweg, Dominik Walther, Prof. Dr. -Ing. Patrick Mäder","doi":"arxiv-2407.06771","DOIUrl":"https://doi.org/arxiv-2407.06771","url":null,"abstract":"The prediction of time series is a challenging task relevant in such diverse\u0000applications as analyzing financial data, forecasting flow dynamics or\u0000understanding biological processes. Especially chaotic time series that depend\u0000on a long history pose an exceptionally difficult problem. While machine\u0000learning has shown to be a promising approach for predicting such time series,\u0000it either demands long training time and much training data when using deep\u0000recurrent neural networks. Alternative, when using a reservoir computing\u0000approach it comes with high uncertainty and typically a high number of random\u0000initializations and extensive hyper-parameter tuning when using a reservoir\u0000computing approach. In this paper, we focus on the reservoir computing approach\u0000and propose a new mapping of input data into the reservoir's state space.\u0000Furthermore, we incorporate this method in two novel network architectures\u0000increasing parallelizability, depth and predictive capabilities of the neural\u0000network while reducing the dependence on randomness. For the evaluation, we\u0000approximate a set of time series from the Mackey-Glass equation, inhabiting\u0000non-chaotic as well as chaotic behavior and compare our approaches in regard to\u0000their predictive capabilities to echo state networks and gated recurrent units.\u0000For the chaotic time series, we observe an error reduction of up to $85.45%$\u0000and up to $87.90%$ in contrast to echo state networks and gated recurrent\u0000units respectively. Furthermore, we also observe tremendous improvements for\u0000non-chaotic time series of up to $99.99%$ in contrast to existing approaches.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574035","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

Fuzzy Spheres in Stringy Matrix Models: Quantifying Chaos in a Mixed Phase Space 弦矩阵模型中的模糊球：量化混合相空间中的混沌

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-09 DOI: arxiv-2407.07259

Paolo Amore, Leopoldo A. Pando Zayas, Juan F. Pedraza, Norma Quiroz, César A. Terrero-Escalante

{"title":"Fuzzy Spheres in Stringy Matrix Models: Quantifying Chaos in a Mixed Phase Space","authors":"Paolo Amore, Leopoldo A. Pando Zayas, Juan F. Pedraza, Norma Quiroz, César A. Terrero-Escalante","doi":"arxiv-2407.07259","DOIUrl":"https://doi.org/arxiv-2407.07259","url":null,"abstract":"We consider a truncation of the BMN matrix model to a configuration of two\u0000fuzzy spheres, described by two coupled non-linear oscillators dependent on the\u0000mass parameter $mu$. The classical phase diagram of the system generically\u0000($mu neq 0$) contains three equilibrium points: two centers and a\u0000center-saddle; as $mu to 0$ the system exhibits a pitchfork bifurcation. We\u0000demonstrate that the system is exactly integrable in quadratures for $mu=0$,\u0000while for very large values of $mu$, it approaches another integrable point\u0000characterized by two harmonic oscillators. The classical phase space is mixed,\u0000containing both integrable islands and chaotic regions, as evidenced by the\u0000classical Lyapunov spectrum. At the quantum level, we explore indicators of\u0000early and late time chaos. The eigenvalue spacing is best described by a Brody\u0000distribution, which interpolates between Poisson and Wigner distributions; it\u0000dovetails, at the quantum level, the classical results and reemphasizes the\u0000notion that the quantum system is mixed. We also study the spectral form factor\u0000and the quantum Lyapunov exponent, as defined by out-of-time-ordered\u0000correlators. These two indicators of quantum chaos exhibit weak correlations\u0000with the Brody distribution. We speculate that the behavior of the system as\u0000$mu to 0$ dominates the spectral form factor and the quantum Lyapunov\u0000exponent, making these indicators of quantum chaos less effective in the\u0000context of a mixed phase space.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587253","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

Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method 通过多粒子法计算广义对齐指数（GALI）高效探测混沌

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-05 DOI: arxiv-2407.04397

Bertin Many Manda, Malcolm Hillebrand, Charalampos Skokos

{"title":"Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method","authors":"Bertin Many Manda, Malcolm Hillebrand, Charalampos Skokos","doi":"arxiv-2407.04397","DOIUrl":"https://doi.org/arxiv-2407.04397","url":null,"abstract":"We present a thorough analysis of computing the Generalized Alignment Index\u0000(GALI), a rapid and effective chaos indicator, through a simple multi-particle\u0000approach, which avoids the use of variational equations. We develop a\u0000theoretical leading-order estimation of the error in the computed GALI for both\u0000the variational method (VM) and the multi-particle method (MPM), and confirm\u0000its predictions through extensive numerical simulations of two well-known\u0000Hamiltonian models: the H'enon-Heiles and the $beta$-Fermi-Pasta-Ulam-Tsingou\u0000systems. For these models the GALIs of several orders are computed and the MPM\u0000results are compared to the VM outcomes. The dependence of the accuracy of the\u0000MPM on the renormalization time, integration time step, as well as the\u0000deviation vector size, is studied in detail. We find that the implementation if\u0000the MPM in double machine precision ($varepsilon approx 10^{-16}$) is\u0000reliable for deviation vector magnitudes centred around $d_0approx\u0000varepsilon^{1/2}$, renormalization times $tau lesssim 1$, and relative\u0000energy errors $E_r lesssim varepsilon^{1/2}$. These results are valid for\u0000systems with many degrees of freedom and for several orders of the GALIs, with\u0000the MPM particularly capturing very accurately the $textrm{GALI}_2$ behavior.\u0000Our results show that the computation of the GALIs by the MPM is a robust and\u0000efficient method for investigating the global chaotic dynamics of autonomous\u0000Hamiltonian systems, something which is of distinct importance in cases where\u0000it is difficult to explicitly write the system's variational equation or when\u0000these equations are too cumbersome.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574036","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

Balancing a vertical stick on a stochastically driven horizontal plate : a variation on the Kapitza effect 在随机驱动的水平板上平衡垂直棍：卡皮查效应的变体

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-04 DOI: arxiv-2407.04112

Nachiketh M, J K Bhattacharjee

引用次数: 0

Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment 随机环境中随机表面生长的无限维模型中的场论重正化群

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-03 DOI: arxiv-2407.13783

N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin

{"title":"Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment","authors":"N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin","doi":"arxiv-2407.13783","DOIUrl":"https://doi.org/arxiv-2407.13783","url":null,"abstract":"The influence of a random environment on the dynamics of a fluctuating rough\u0000surface is investigated using a field theoretic renormalization group. The\u0000environment motion is modelled by the stochastic Navier--Stokes equation, which\u0000includes both a fluid in thermal equilibrium and a turbulent fluid. The surface\u0000is described by the generalized Pavlik's stochastic equation. As a result of\u0000fulfilling the renormalizability requirement, the model necessarily involves an\u0000infinite number of coupling constants. The one-loop counterterm is derived in\u0000an explicit closed form. The corresponding renormalization group equations\u0000demonstrate the existence of three two-dimensional surfaces of fixed points in\u0000the infinite-dimensional parameter space. If the surfaces contain IR attractive\u0000regions, the problem allows for the large-scale, long-time scaling behaviour.\u0000For the first surface (advection is irrelevant) the critical dimensions of the\u0000height field $Delta_{h}$, the response field $Delta_{h'}$ and the frequency\u0000$Delta_{omega}$ are non-universal through the dependence on the effective\u0000couplings. For the other two surfaces (advection is relevant) the dimensions\u0000are universal and they are found exactly.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738605","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

Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance 不对称达芬振荡器：1:2$共振的变形及其与主共振的相互作用

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-03 DOI: arxiv-2407.03423

Jan Kyziol, Andrzej Okniński

引用次数: 0

Improved Long-Term Prediction of Chaos Using Reservoir Computing Based on Stochastic Spin-Orbit Torque Devices 利用基于随机自旋-轨道扭矩装置的水库计算改进混沌的长期预测

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-02 DOI: arxiv-2407.02384

Cen Wang, Xinyao Lei, Kaiming Cai, Xiaofei Yang, Yue Zhang

引用次数: 0