Physica D: Nonlinear Phenomena最新文献

{"title":"Kernel Sum of Squares for data adapted kernel learning of dynamical systems from data: A global optimization approach","authors":"Daniel Lengyel ,&nbsp;Boumediene Hamzi ,&nbsp;Houman Owhadi ,&nbsp;Panos Parpas","doi":"10.1016/j.physd.2025.134693","DOIUrl":"10.1016/j.physd.2025.134693","url":null,"abstract":"<div><div>This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness and numerical efficiency, frequently struggle with selecting optimal base kernels and parameter tuning, especially with gradient-based methods prone to local optima. KSOS mitigates these issues by leveraging a global optimization framework with kernel-based surrogate functions, thereby achieving more reliable and precise learning of dynamical systems. Through comprehensive numerical experiments on the Logistic Map, Henon Map, and Lorentz System, KSOS is shown to consistently outperform gradient descent in minimizing the relative-<span><math><mi>ρ</mi></math></span> metric and improving kernel accuracy. These results highlight KSOS’s effectiveness in predicting the behavior of chaotic dynamical systems, demonstrating its capability to adapt kernels to underlying dynamics and enhance the robustness and predictive power of kernel-based approaches, making it a valuable asset for time series analysis in various scientific fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"478 ","pages":"Article 134693"},"PeriodicalIF":2.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098858","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":"Aperiodically intermittent H∞ synchronization of coupled complex-valued neural networks with and without parameter uncertainties","authors":"Yanli Huang,&nbsp;Yuqing Jia","doi":"10.1016/j.physd.2025.134694","DOIUrl":"10.1016/j.physd.2025.134694","url":null,"abstract":"<div><div>In this paper, we investigate aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization and robustly aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization for both coupled complex-valued neural networks (CCVNNs) and coupled complex-valued delayed neural networks (CCVDNNs). Initially, certain synchronization criteria for CCVNNs are established using suitable Lyapunov functionals in conjunction with a variety of inequality techniques. Furthermore, we also examine robust synchronization of CCVNNs, taking into account the impact of parameter uncertainties in neural networks. In addition, the corresponding aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization and robustly aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization results are generalized to the network of CCVDNNs, in which the activation function is time-varying delayed. Finally, two numerical examples prove the reliability and the benefits of the proposed results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134694"},"PeriodicalIF":2.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942296","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":"Analysis of power law behavior of local cortical neurodynamics","authors":"Karolina Armonaite ,&nbsp;Livio Conti ,&nbsp;Marco Balsi ,&nbsp;Luca Paulon ,&nbsp;Franca Tecchio","doi":"10.1016/j.physd.2025.134733","DOIUrl":"10.1016/j.physd.2025.134733","url":null,"abstract":"<div><div>Growing evidence suggests that neuronal electrical activity, the neurodynamics, contains specific signatures for distinct cortical parcels of the brain, potentially enabling cortex classification based on it, even in resting states. However, existing algorithms for extracting specific characteristics may succeed only in specific cases, or well selected groups, but often fail to identify stable features across the general populations. Our study examines intracranial stereotactic-electroencephalographic (sEEG) recordings, assessing power-law behavior in power spectral density during wakefulness and sleep stages across three gyri: precentral, postcentral and superior temporal, in 55 subjects. Results indicate the presence of a power-law behavior, implying scale-free dynamics in investigated areas. Notably, power-law exponent in high frequency range distinguishes cortical parcels both in wakefulness and sleep and suggests a stable scale-free pattern within each region possibly regardless of the state. This insight offers valuable guidance for evaluating physiological aspects of local neurodynamics and supports population-level functional cortex parceling.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134733"},"PeriodicalIF":2.7,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089792","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 bound state attractor in optical turbulence","authors":"Clément Colléaux ,&nbsp;Jonathan Skipp ,&nbsp;Sergey Nazarenko ,&nbsp;Jason Laurie","doi":"10.1016/j.physd.2025.134687","DOIUrl":"10.1016/j.physd.2025.134687","url":null,"abstract":"<div><div>We study numerically the nonintegrable dynamics of coherent, solitonic, nonlinear waves, in a spatially nonlocal nonlinear Schrödinger equation relevant to realistic modelling of optical systems: the Schrödinger–Helmholtz equation. We observe a single oscillating, coherent solitary wave emerging from a variety of initial conditions. Using the direct scattering transform of the (integrable) cubic nonlinear Schrödinger equation, we find that this structure is a bound state, comprising of a primary and secondary soliton whose amplitudes oscillate in phase opposition. We interpret this as the solitons periodically exchanging mass. We also observe bound states comprising of three oscillating solitons, hinting at the existence of a family of multi-soliton bound states. Focusing on the two-soliton bound state, we observe it self-organising from an initial state of incoherent turbulence, and from solitonic structures launched into the system. When a single (primary) solitonic structure is launched, a resonance process between it and waves in the system generates the secondary soliton, resulting in the bound state. Further, when two solitons are initially launched, we show that they can merge if their phases are synchronised when they collide. When the system is launched from a turbulent state comprised of many initial solitons, we propose that the bound state formation is preceded by a sequence of binary collisions, in which the mass is transferred on average from the weak soliton to the strong one, with occasional soliton mergers. Both processes lead to increasingly stronger and fewer dominant solitons. The final state – a solitary bound state surrounded by weakly nonlinear waves – is robust and ubiquitous. We propose that for nonlocal media, a bound state comprising of at least two solitons is a more typical statistical attractor than the single-soliton attractor suggested in previous literature.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134687"},"PeriodicalIF":2.7,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934567","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":"Model reduction of nonlinear time-delay systems via ODE approximation and spectral submanifolds","authors":"Yuan Tang,&nbsp;Mingwu Li","doi":"10.1016/j.physd.2025.134701","DOIUrl":"10.1016/j.physd.2025.134701","url":null,"abstract":"<div><div>Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate approximations or numerical methods. These requirements present considerable challenges for the real-time simulation and analysis of their nonlinear dynamics. To address these challenges, we present a model reduction framework for nonlinear time-delay systems using spectral submanifolds (SSMs). We first approximate the time-delay systems as ordinary differential equations (ODEs) without delay and then compute the SSMs and their associated reduced-order models (ROMs) of the ODE approximations. These SSM-based ROMs successfully predict the nonlinear dynamical behaviors of the time-delay systems, including free and forced vibrations, and accurately identify critical features such as isolated branches in the forced response curves and bifurcations of periodic and quasi-periodic orbits. The efficiency and accuracy of the ROMs are demonstrated through examples of increasing complexity.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134701"},"PeriodicalIF":2.7,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934658","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":"Detecting causality in the frequency domain with Cross-Mapping Coherence","authors":"Zsigmond Benkő ,&nbsp;Bálint Varga ,&nbsp;Marcell Stippinger ,&nbsp;Zoltán Somogyvári","doi":"10.1016/j.physd.2025.134708","DOIUrl":"10.1016/j.physd.2025.134708","url":null,"abstract":"<div><div>Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time series data, hold the potential to significantly advance scientific and engineering fields.</div><div>This study introduces the Cross-Mapping Coherence (CMC) method, designed to reveal causal connections in the frequency domain between time series. CMC builds upon nonlinear state-space reconstruction and extends the Convergent Cross-Mapping algorithm to the frequency domain by utilizing coherence metrics for evaluation. We tested the CMC method using simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson–Cowan model of the visual cortex. CMC accurately identified the direction of causal connections in these simulated scenarios. When applied to the Wilson–Cowan model, CMC was able to disentangle feedforward alpha and feedback gamma coupling between the V1 and V4 areas, supporting the results of previous analysis.</div><div>Furthermore, CMC could detect weak connections (<span><math><mrow><mi>C</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn></mrow></math></span>), demonstrated sample efficiency (<span><math><mrow><mi>L</mi><mo>=</mo><mn>700</mn></mrow></math></span>), and maintained robustness in the presence of noise up to <span><math><mrow><mi>SNR</mi><mo>=</mo><mn>10</mn></mrow></math></span> on unidirectionally coupled logistic map systems.</div><div>In conclusion, the capability to determine directed causal influences across different frequency bands allows CMC to provide valuable insights into the dynamics of complex, nonlinear systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134708"},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071343","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":"The motion and mass growth of droplets with phase transitions in a homogeneous medium","authors":"Peiyu Zhang ,&nbsp;Aifang Qu ,&nbsp;Hairong Yuan","doi":"10.1016/j.physd.2025.134683","DOIUrl":"10.1016/j.physd.2025.134683","url":null,"abstract":"<div><div>In this paper, we focus on the motion and mass growth of droplets with phase transitions in a homogeneous medium. We characterize the problem by the unsteady non-isentropic compressible Euler system together with its Radon measure-valued solutions. That is, the gas is described by the regular part of Radon measure, while the droplets are illustrated by the atomic part. The difficulty lies in finding a suitable formulation of the constitutive equation in the sense of measure, such that it is physically meaningful and mathematically reasonable. We overcome it by proposing one, which can express the process of heat release by liquefaction and heat absorption by vaporization. Then we prove the local-in-time and global-in-time existence of a single droplet with different initial data. Also, we analyze the collision of two droplets and deduce the state of the new droplet formed by collisions. This provides a downscaling new approach to investigating the two-phase flows with phase transitions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134683"},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934660","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":"The three-body problem on the sphere and its reversing symmetries","authors":"Abimael Bengochea,&nbsp;Ernesto Pérez-Chavela,&nbsp;Carlos Barrera-Anzaldo","doi":"10.1016/j.physd.2025.134707","DOIUrl":"10.1016/j.physd.2025.134707","url":null,"abstract":"<div><div>In this work, we establish the concept of reversing symmetry in the three-body problem on the sphere, a novel approach that has not been previously explored. We introduce three reversing symmetries: one valid for arbitrary masses, and two that require two equal masses. We also provide a thorough characterization of their fixed points, which are crucial for understanding the dynamics of the system due to their connection with the symmetric periodic orbits of the system. Using two reversing symmetries, we numerically compute a choreography in the three-body problem on the sphere, a particular type of symmetric periodic orbit. This orbit is closely related to the classical figure-eight choreography, a well-known symmetric periodic orbit in the Newtonian planar three-body problem.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134707"},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942297","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":"Perturbation and determinacy of nonsmooth systems","authors":"Sal Catsis,&nbsp;Cameron L. Hall,&nbsp;Mike R. Jeffrey","doi":"10.1016/j.physd.2025.134679","DOIUrl":"10.1016/j.physd.2025.134679","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Take a system where several variables &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;) cause decision states &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; to be set independently to values &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, at any instant, and the outcome then affects how each &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; 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 &lt;em&gt;how&lt;/em&gt; the decisions are enacted, and even how the system’s evolution is calculated. If the probability that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; decides ‘&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;’ is &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; decides ‘&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;’ is &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, for instance, the probability that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; decides ‘&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;’ and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; decides ‘&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;’ at any moment is not generally &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, despite the independence of their decisions (nor is it any other determinable quantity such as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;). Only certain weighted sums of probabilities of being in different decision states are determined by the logic of the system.&lt;/div&gt;&lt;div&gt;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}