Direct numerical simulation of three-dimensional acoustic turbulence has been performed for both weak and strong regimes. Within the weak turbulence, we demonstrate the existence of the Zakharov-Sagdeev spectrum $propto k^{-3/2}$ not only for weak dispersion but in the non-dispersion (ND) case as well. Such spectra in the $k$-space are accompanied by jets in the form of narrow cones. These distributions are realized due to small nonlinearity compared with both dispersion/diffraction. Increasing pumping in the ND case due to dominant nonlinear effects leads to the formation of shocks. As a result, the acoustic turbulence turns into an ensemble of random shocks with the Kadomtsev-Petviashvili spectrum.
{"title":"Three-Dimensional Acoustic Turbulence: Weak Versus Strong","authors":"E. A. Kochurin, E. A. Kuznetsov","doi":"arxiv-2407.08352","DOIUrl":"https://doi.org/arxiv-2407.08352","url":null,"abstract":"Direct numerical simulation of three-dimensional acoustic turbulence has been\u0000performed for both weak and strong regimes. Within the weak turbulence, we\u0000demonstrate the existence of the Zakharov-Sagdeev spectrum $propto k^{-3/2}$\u0000not only for weak dispersion but in the non-dispersion (ND) case as well. Such\u0000spectra in the $k$-space are accompanied by jets in the form of narrow cones.\u0000These distributions are realized due to small nonlinearity compared with both\u0000dispersion/diffraction. Increasing pumping in the ND case due to dominant\u0000nonlinear effects leads to the formation of shocks. As a result, the acoustic\u0000turbulence turns into an ensemble of random shocks with the\u0000Kadomtsev-Petviashvili spectrum.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141615058","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}
Limiting chain extensibility is a characteristic that plays a vital role in the stretching of highly elastic materials. The Gent model has been widely used to capture this behaviour, as it performs very well in fitting stress-stretch data in simple tension, and involves two material parameters only. Recently, Anssari-Benam and Bucchi [Int. J. Non. Linear. Mech. 2021, 128, 103626] introduced a different form of generalised neo-Hookean model, focusing on the molecular structure of elastomers, and showed that their model encompasses all ranges of deformations, performing better than the Gent model in many respects, also with only two parameters. Here we investigate the nonlinear vibration and stability of a dielectric elastomer balloon modelled by that strain energy function. We derive the deformation field in spherical coordinates and the governing equations by the Euler-Lagrange method, assuming that the balloon retains its spherical symmetry as it inflates. We consider in turn that the balloon is under two types of voltages, a pure DC voltage and a DC voltage superimposed on an AC voltage. We analyse the dynamic response of the balloon and identify the influential parameters in the model. We find that the molecular structure of the material, as tracked by the number of segments in a single chain, can control the instability and the pull-in/snap-through critical voltage, as well as chaos and quasi-periodicity. The main result is that balloons made of materials exhibiting early strain-stiffening effects are more stable and less prone to generate chaotic nonlinear vibrations than softer materials, such as those modelled by the neo-Hookean strain-energy density function.
{"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}
Om Roy, Avalon Campbell-Cousins, John Stewart Fabila Carrasco, Mario A Parra, Javier Escudero
Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for non-linear analysis of data sampled on irregular domains. Here, we introduce a continuous version of Permutation Entropy, extend it to the graph domain, and develop a ordinal activation function akin to the one of neural networks. This is a step towards Ordinal Deep Learning, a potentially effective and very recently posited concept. We also formally extend ordinal contrasts to the graph domain. Continuous versions of ordinal contrasts of length 3 are also introduced and their advantage is shown in experiments. We also integrate specific contrasts for the analysis of images and show that it generalizes well to the graph domain allowing a representation of images, represented as graph signals, in a plane similar to the entropy-complexity one. Applications to synthetic data, including fractal patterns and popular non-linear maps, and real-life MRI data show the validity of these novel extensions and potential benefits over the state of the art. By extending very recent concepts related to permutation entropy to the graph domain, we expect to accelerate the development of more graph-based entropy methods to enable nonlinear analysis of a broader kind of data and establishing relationships with emerging ideas in data science.
非线性动力学在信号分析中发挥着重要作用。常用的、易于解释的非线性测量方法是置换熵（Permutation Entropy）。最近，它被扩展用于图信号分析，从而为不规则域采样数据的非线性分析提供了一个框架。在这里，我们引入了连续版本的置换熵，将其扩展到图域，并开发了一种类似于神经网络的序激活函数。这是向序数深度学习（Ordinal Deep Learning）迈出的一步，序数深度学习是最近提出的一个潜在有效的概念。我们还正式将顺序对比扩展到图领域。我们还引入了长度为 3 的连续版本序对比，并在实验中展示了它们的优势。我们还整合了用于图像分析的特定对比度，并证明它可以很好地推广到图领域，从而可以在类似于熵复杂性的平面上表示以图信号表示的图像。对合成数据（包括分形模式和流行的非线性地图）和现实生活中的 MRI 数据的应用表明了这些新扩展的有效性，以及与现有技术相比的潜在优势。通过将与置换熵相关的最新概念扩展到图领域，我们希望能加速开发更多基于图的熵方法，以便对更广泛的数据进行非线性分析，并与数据科学领域的新兴思想建立联系。
{"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}
Johannes Viehweg, Dominik Walther, Prof. Dr. -Ing. Patrick Mäder
The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long history pose an exceptionally difficult problem. While machine learning has shown to be a promising approach for predicting such time series, it either demands long training time and much training data when using deep recurrent neural networks. Alternative, when using a reservoir computing approach it comes with high uncertainty and typically a high number of random initializations and extensive hyper-parameter tuning when using a reservoir computing approach. In this paper, we focus on the reservoir computing approach and propose a new mapping of input data into the reservoir's state space. Furthermore, we incorporate this method in two novel network architectures increasing parallelizability, depth and predictive capabilities of the neural network while reducing the dependence on randomness. For the evaluation, we approximate a set of time series from the Mackey-Glass equation, inhabiting non-chaotic as well as chaotic behavior and compare our approaches in regard to their predictive capabilities to echo state networks and gated recurrent units. For the chaotic time series, we observe an error reduction of up to $85.45%$ and up to $87.90%$ in contrast to echo state networks and gated recurrent units respectively. Furthermore, we also observe tremendous improvements for non-chaotic time series of up to $99.99%$ in contrast to existing approaches.
{"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}
Paolo Amore, Leopoldo A. Pando Zayas, Juan F. Pedraza, Norma Quiroz, César A. Terrero-Escalante
We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter $mu$. The classical phase diagram of the system generically ($mu neq 0$) contains three equilibrium points: two centers and a center-saddle; as $mu to 0$ the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for $mu=0$, while for very large values of $mu$, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as $mu to 0$ dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.
我们考虑将BMN矩阵模型截断为两个模糊球的配置，由两个依赖于质量参数$mu$的耦合非线性振荡器来描述。该系统的经典相图一般（$mu neq 0$）包含三个平衡点：两个中心和一个中心-马鞍；当$mu to 0$时，该系统表现出一个叉形分叉。我们证明，当 $mu=0$ 时，系统在四元数上是完全可积分的，而当 $mu$ 的值非常大时，系统会接近另一个由两个谐振子构成的可积分点。经典相空间是混合的，既包含可积分岛，也包含混沌区，经典李亚普诺夫谱就是证明。在量子层面，我们探索了早期和晚期混沌的指标。布罗迪分布是对特征值间距的最佳描述，它介于泊松分布和维格纳分布之间；在量子层面，它与经典结果相吻合，并再次强调了量子系统是混合系统的说法。我们还研究了谱形式因子和量子李亚普诺夫指数，它们由超时序相关器定义。这两个量子混沌指标与布罗迪分布呈现出微弱的相关性。我们推测，系统在$mu to 0$时的行为主导了谱形式因子和量子李亚普诺夫指数，使得这些量子混沌指标在混合相空间的背景下不那么有效。
{"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}
Bertin Many Manda, Malcolm Hillebrand, Charalampos Skokos
We present a thorough analysis of computing the Generalized Alignment Index (GALI), a rapid and effective chaos indicator, through a simple multi-particle approach, which avoids the use of variational equations. We develop a theoretical leading-order estimation of the error in the computed GALI for both the variational method (VM) and the multi-particle method (MPM), and confirm its predictions through extensive numerical simulations of two well-known Hamiltonian models: the H'enon-Heiles and the $beta$-Fermi-Pasta-Ulam-Tsingou systems. For these models the GALIs of several orders are computed and the MPM results are compared to the VM outcomes. The dependence of the accuracy of the MPM on the renormalization time, integration time step, as well as the deviation vector size, is studied in detail. We find that the implementation if the MPM in double machine precision ($varepsilon approx 10^{-16}$) is reliable for deviation vector magnitudes centred around $d_0approx varepsilon^{1/2}$, renormalization times $tau lesssim 1$, and relative energy errors $E_r lesssim varepsilon^{1/2}$. These results are valid for systems with many degrees of freedom and for several orders of the GALIs, with the MPM particularly capturing very accurately the $textrm{GALI}_2$ behavior. Our results show that the computation of the GALIs by the MPM is a robust and efficient method for investigating the global chaotic dynamics of autonomous Hamiltonian systems, something which is of distinct importance in cases where it is difficult to explicitly write the system's variational equation or when these equations are too cumbersome.
{"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}
We consider the trick of balancing a vertical stick on a horizontal plate. It is shown that the horizontal stochastic driving of the point of contact can prevent the stick from falling provided that the stochasticity is that of a coloured noise with a correlation strength stronger than a critical value.
{"title":"Balancing a vertical stick on a stochastically driven horizontal plate : a variation on the Kapitza effect","authors":"Nachiketh M, J K Bhattacharjee","doi":"arxiv-2407.04112","DOIUrl":"https://doi.org/arxiv-2407.04112","url":null,"abstract":"We consider the trick of balancing a vertical stick on a horizontal plate. It\u0000is shown that the horizontal stochastic driving of the point of contact can\u0000prevent the stick from falling provided that the stochasticity is that of a\u0000coloured noise with a correlation strength stronger than a critical value.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573832","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}
N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin
The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a field theoretic renormalization group. The environment motion is modelled by the stochastic Navier--Stokes equation, which includes both a fluid in thermal equilibrium and a turbulent fluid. The surface is described by the generalized Pavlik's stochastic equation. As a result of fulfilling the renormalizability requirement, the model necessarily involves an infinite number of coupling constants. The one-loop counterterm is derived in an explicit closed form. The corresponding renormalization group equations demonstrate the existence of three two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain IR attractive regions, the problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field $Delta_{h}$, the response field $Delta_{h'}$ and the frequency $Delta_{omega}$ are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) the dimensions are universal and they are found exactly.
{"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}
We investigate the $1: 2$ resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance or forming independently, coexisting with the primary resonance. We compute the steady-state asymptotic solution - the amplitude-frequency implicit function. Working in the differential properties of implicit functions framework, we describe complicated metamorphoses of the $1:2$ resonance and its interaction with the primary resonance.
{"title":"Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance","authors":"Jan Kyziol, Andrzej Okniński","doi":"arxiv-2407.03423","DOIUrl":"https://doi.org/arxiv-2407.03423","url":null,"abstract":"We investigate the $1: 2$ resonance in the periodically forced asymmetric\u0000Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance\u0000or forming independently, coexisting with the primary resonance. We compute the\u0000steady-state asymptotic solution - the amplitude-frequency implicit function.\u0000Working in the differential properties of implicit functions framework, we\u0000describe complicated metamorphoses of the $1:2$ resonance and its interaction\u0000with the primary resonance.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574037","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}
Predicting chaotic systems is crucial for understanding complex behaviors, yet challenging due to their sensitivity to initial conditions and inherent unpredictability. Probabilistic Reservoir Computing (RC) is well-suited for long-term chaotic predictions by handling complex dynamic systems. Spin-Orbit Torque (SOT) devices in spintronics, with their nonlinear and probabilistic operations, can enhance performance in these tasks. This study proposes an RC system utilizing SOT devices for predicting chaotic dynamics. By simulating the reservoir in an RC network with SOT devices that achieve nonlinear resistance changes with random distribution, we enhance the robustness for the predictive capability of the model. The RC network predicted the behaviors of the Mackey-Glass and Lorenz chaotic systems, demonstrating that stochastic SOT devices significantly improve long-term prediction accuracy.
预测混沌系统对于理解复杂行为至关重要，但由于其对初始条件的敏感性和固有的不可预测性，预测具有挑战性。概率存储计算（RC）非常适合通过处理复杂的动态系统来进行长期混沌预测。自旋电子学中的自旋轨道力矩（SOT）器件具有非线性和概率操作特性，可以提高这些任务的性能。本研究提出了一种利用 SOT 设备预测混沌动力学的 RC 系统。通过模拟 RC 网络中的蓄水池，利用 SOT 器件实现随机分布的非线性电阻变化，我们增强了模型预测能力的稳健性。RC 网络预测了麦基-格拉斯和洛伦兹混沌系统的行为，证明随机 SOT 装置显著提高了长期预测的准确性。
{"title":"Improved Long-Term Prediction of Chaos Using Reservoir Computing Based on Stochastic Spin-Orbit Torque Devices","authors":"Cen Wang, Xinyao Lei, Kaiming Cai, Xiaofei Yang, Yue Zhang","doi":"arxiv-2407.02384","DOIUrl":"https://doi.org/arxiv-2407.02384","url":null,"abstract":"Predicting chaotic systems is crucial for understanding complex behaviors,\u0000yet challenging due to their sensitivity to initial conditions and inherent\u0000unpredictability. Probabilistic Reservoir Computing (RC) is well-suited for\u0000long-term chaotic predictions by handling complex dynamic systems. Spin-Orbit\u0000Torque (SOT) devices in spintronics, with their nonlinear and probabilistic\u0000operations, can enhance performance in these tasks. This study proposes an RC\u0000system utilizing SOT devices for predicting chaotic dynamics. By simulating the\u0000reservoir in an RC network with SOT devices that achieve nonlinear resistance\u0000changes with random distribution, we enhance the robustness for the predictive\u0000capability of the model. The RC network predicted the behaviors of the\u0000Mackey-Glass and Lorenz chaotic systems, demonstrating that stochastic SOT\u0000devices significantly improve long-term prediction accuracy.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515127","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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