Physica D: Nonlinear Phenomena最新文献

{"title":"Perturbation and determinacy of nonsmooth systems","authors":"Sal Catsis, Cameron L. Hall, Mike R. Jeffrey","doi":"10.1016/j.physd.2025.134679","DOIUrl":"10.1016/j.physd.2025.134679","url":null,"abstract":"<div><div>Take a system where several variables <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> (for <span><math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo></mrow></math></span>) cause decision states <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> to be set independently to values <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, at any instant, and the outcome then affects how each <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> evolves according to a differential equation. We show here that the probability that the system lies in a given decision state at any instant cannot be determined solely from these differential equations, but is determined by the emergence of a dynamical attractor. Moreover this attractor is sensitive to small perturbations in <em>how</em> the decisions are enacted, and even how the system’s evolution is calculated. If the probability that <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> decides ‘<span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>’ is <span><math><mrow><mi>P</mi><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span> and <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> decides ‘<span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>’ is <span><math><mrow><mi>P</mi><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>, for instance, the probability that <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> decides ‘<span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>’ and <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> decides ‘<span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>’ at any moment is not generally <span><math><mrow><mi>P</mi><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mi>P</mi><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>, despite the independence of their decisions (nor is it any other determinable quantity such as <span><math><mrow><mi>P</mi><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mi>P</mi><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>). Only certain weighted sums of probabilities of being in different decision states are determined by the logic of the system.</div><div>This result comes from formulating this simple decisio","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134679"},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of interface coupling in three-layer viscous fluid systems","authors":"A. Simon,&nbsp;J.C. Brändle de Motta,&nbsp;C. Dumouchel,&nbsp;M.-C. Renoult","doi":"10.1016/j.physd.2025.134670","DOIUrl":"10.1016/j.physd.2025.134670","url":null,"abstract":"<div><div>Linear stability analysis is performed to study the effect of viscosity and surface tension on a system composed of three superimposed immiscible incompressible Newtonian fluids under the gravity field. The eigenvalue problem is formulated in a general way to highlight an analytical solution and other solutions to be determined numerically for a given set of physical parameters. The behaviour of these solutions is analysed using a coupling parameter equal to the product between the thickness of the middle layer and the wave number of the disturbance. When this parameter is large enough, the study of this three-layer fluid system is reduced to the study of two-layer fluid subsystems. The solutions were determined for a three-layer fluid system of interest with a gravitationally unstable interface at the bottom and a gravitationally stable interface at the top to highlight respectively the Rayleigh–Taylor instability and a gravity wave as well as the coupling between these two phenomena. The temporal evolution of the physical quantities is obtained by solving the initial value problem. For this purpose, single-mode disturbances at the two interfaces are imposed as initial conditions. Direct numerical simulations performed with an in-house code initialized by the interface positions and the fluid velocities allow us to compare their temporal evolutions. Results show an excellent agreement with the theory until the amplitude of one interface becomes too large in the same way as the nonlinear effects of the flow. Three main regimes are observed depending on which solutions initially influence the flow the most.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134670"},"PeriodicalIF":2.7,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase-space quantum distorted stability pattern for Aubry–André–Harper dynamics","authors":"A.E. Bernardini ,&nbsp;O. Bertolami","doi":"10.1016/j.physd.2025.134700","DOIUrl":"10.1016/j.physd.2025.134700","url":null,"abstract":"<div><div>Instability features associated to topological quantum domains which emerge from the Weyl–Wigner (WW) quantum phase-space description of Gaussian ensembles driven by Aubry–André–Harper (AAH) Hamiltonians are investigated. Hyperbolic equilibrium and stability patterns are then identified and classified according to the associated (nonlinear) AAH Hamiltonian parameters. Besides providing the tools for quantifying the information content of AAH systems, the Wigner flow patterns here discussed suggest a systematic procedure for identifying the role of quantum fluctuations over equilibrium and stability, in a framework which can be straightforwardly extended to describe the evolution of similar/modified AAH systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134700"},"PeriodicalIF":2.7,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extraction and reconstruction of variable-coefficient governing equations using Res-KAN integrating sparse regression","authors":"Ming-Hui Guo ,&nbsp;Xing Lü ,&nbsp;Yu-Xi Jin","doi":"10.1016/j.physd.2025.134689","DOIUrl":"10.1016/j.physd.2025.134689","url":null,"abstract":"<div><div>Extracting the governing equations for complex systems plays a crucial role in scientific discovery and engineering applications. Previous research often focus on static properties of governing equations, while real-world dynamics involve complex, evolving factors that influence the system behavior. This work proposes a novel approach that integrates the single-layer Kolmogorov-Arnold networks (KANs) in the downstream operations of physics-informed neural networks (PINNs), combined with an alternating training strategy using sparse regression algorithms. Different from the traditional methods, this approach relies solely on sparse data, without any prior knowledge, to reconstruct precise form of governing equations and simultaneously identify the variable-coefficient functions depending on single variables. By symbolizing the spline functions in the KAN layer, it can also derive the exact expressions of these coefficient functions and reveal the key parameters of real physical significance. Furthermore, when extending the framework to high-dimensional problems, KAN’s regularization enables weight sparsity enforcement, which removes redundant neurons and optimizes the network. Experiments on various benchmark problems demonstrate the robustness of our method to varying levels of data sparsity and noise, offering a new solution to the reconstruction and analysis of the governing equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134689"},"PeriodicalIF":2.7,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence network reconstruction from discrete time-series of count data modelled by multidimensional Hawkes processes","authors":"Naratip Santitissadeekorn ,&nbsp;Martin Short ,&nbsp;David J.B. Lloyd","doi":"10.1016/j.physd.2025.134705","DOIUrl":"10.1016/j.physd.2025.134705","url":null,"abstract":"<div><div>Identifying key influencers from time series data without a known prior network structure is a challenging problem in various applications, from crime analysis to social media. While much work has focused on event-based time series (timestamp) data, fewer methods address count data, where event counts are recorded in fixed intervals. We develop network inference methods for both batched and sequential count data. Here the strong network connection represents the key influences among the nodes. We introduce an ensemble-based algorithm, rooted in the expectation–maximization (EM) framework, and demonstrate its utility to identify node dynamics and connections through a discrete-time Cox or Hawkes process. For the linear multidimensional Hawkes model, we employ a minimization–majorization (MM) approach, allowing for parallelized inference of networks. For sequential inference, we use a second-order approximation of the Bayesian inference problem. Under certain assumptions, a rank-1 update for the covariance matrix reduces computational costs. We validate our methods on synthetic data and real-world datasets, including email communications within European academic communities. Our approach effectively reconstructs underlying networks, accounting for both excitation and diffusion influences. This work advances network reconstruction from count data in real-world scenarios.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134705"},"PeriodicalIF":2.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the multi-component Fokas–Lenells system: KP reductions and various soliton solutions","authors":"Han-Han Sheng ,&nbsp;Bao-Feng Feng ,&nbsp;Guo-Fu Yu","doi":"10.1016/j.physd.2025.134706","DOIUrl":"10.1016/j.physd.2025.134706","url":null,"abstract":"<div><div>In this paper, the multi-component Fokas–Lenells (mFL) system is studied by Hirota’s bilinear method and Kadomtsev–Petviashvili (KP)-Toda reduction approach. We demonstrate that the bilinear equations of the mFL system and their Gram-type determinant solutions can be reduced from a set of bilinear equations in the KP-Toda hierarchy. Moreover, we derive the set of bilinear equations from the discrete KP hierarchy by Miwa transformation. Dark solitons, breathers, and resonant breathers are presented. In particular, the breathers are classified into three different types, such as Akhmediev breather and Kuznetsov–Ma breather. The resonance phenomena of the breathers are also investigated. We give three- and four-resonant breather solutions for the three-component Fokas–Lenells system. Dynamics of the derived solutions are illustrated and analyzed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134706"},"PeriodicalIF":2.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the dynamics of the Craik–Okamoto and the Euler top","authors":"Jaume Llibre ,&nbsp;Claudia Valls","doi":"10.1016/j.physd.2025.134684","DOIUrl":"10.1016/j.physd.2025.134684","url":null,"abstract":"<div><div>We study the dynamics of the Craik–Okamoto system and its relation with the dynamics of the Euler top. We show that both systems exhibit the same dynamics in a neighborhood of infinity and we describe completely the phase portraits of the Euler top. Additionally we provide explicitly the Euler top solutions in function of the time. We show that the orbits given by the invariant straight lines of the Craik–Okamoto system are in fact center manifolds of equilibrium points at infinity. Moreover, we show that while in the Euler top all the orbits lie on invariant algebraic surfaces, in the Craik–Okamoto system any orbit is on an invariant algebraic surface.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134684"},"PeriodicalIF":2.7,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143905893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A front-tracking/ghost-fluid method for the numerical simulations of Richtmyer–Meshkov Instability","authors":"Ryan Holley ,&nbsp;Tulin Kaman","doi":"10.1016/j.physd.2025.134696","DOIUrl":"10.1016/j.physd.2025.134696","url":null,"abstract":"<div><div>We present an increasingly accurate and robust front-tracking (FT) method coupled with the ghost-fluid method (GFM) for the numerical simulations of shock-induced turbulent mixing. The FT-GFM method with the higher-order weighted essentially non-oscillatory (WENO) schemes is used to study the evolution of the complex and moving fluid interfaces in compressible flows. We demonstrate the improvements in the late-time dynamics of the fluid interfaces and the effect of the high-order WENO schemes with monotonicity preserving bounds on several test problems. One-dimensional scalar advection, Sod’s shock tube, shock-entropy wave interaction problems, and two-dimensional shock tube Richtmyer–Meshkov instability (RMI) between air and SF<span><math><msub><mrow></mrow><mrow><mn>6</mn></mrow></msub></math></span> simulations are performed in order to show the improvements achieved using the new method. The fifth- and ninth-order WENO schemes with and without monotonicity preserving bounds are explored in the numerical solution of the shock-driven interface problem.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134696"},"PeriodicalIF":2.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-fluxon bubble dynamics in a rapid oscillatory microwave field","authors":"Alicia G. Castro-Montes ,&nbsp;Elram S. Figueroa ,&nbsp;Juan F. Marín ,&nbsp;Mónica A. García-Ñustes","doi":"10.1016/j.physd.2025.134704","DOIUrl":"10.1016/j.physd.2025.134704","url":null,"abstract":"<div><div>In this article, we numerically study the dynamics of a two-dimensional quasi-fluxon bubble in an oscillatory regime stabilized by a localized annular force under a rapidly oscillating microwave field. The bubble exhibits two distinctly dynamical regimes. At first, the oscillation of the bubble wall scales up linearly with the microwave field frequency until it reaches a cutoff, after which it detaches from the external field, returning to its natural oscillation frequency. The amplitude of the quasi-fluxon oscillations is inversely proportional to the square of the microwave field frequency. Following a simplified model based on the Kapitza approach, we proved that this dynamical behavior is characteristic of systems with a harmonic potential subjected to a rapidly oscillating field. Possible applications of microwave detection are discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134704"},"PeriodicalIF":2.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A classification of solitons for the surface diffusion flow of entire graphs","authors":"Piotr Rybka ,&nbsp;Glen Wheeler","doi":"10.1016/j.physd.2025.134702","DOIUrl":"10.1016/j.physd.2025.134702","url":null,"abstract":"<div><div>In this article we classify solitons (equilibria, self-similar solutions and travelling waves) for the surface diffusion flow of entire graphs of function over <span><math><mi>R</mi></math></span>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134702"},"PeriodicalIF":2.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}