Physica D: Nonlinear Phenomena最新文献

{"title":"On the role of 5-wave resonances in the nonlinear dynamics of the Fermi–Pasta–Ulam–Tsingou lattice","authors":"Tiziana Comito,&nbsp;Matteo Lotriglia,&nbsp;Miguel D. Bustamante","doi":"10.1016/j.physd.2025.134813","DOIUrl":"10.1016/j.physd.2025.134813","url":null,"abstract":"<div><div>We study the dynamics of the <span><math><mrow><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow></math></span> Fermi–Pasta–Ulam–Tsingou lattice (FPUT lattice, for short) for an arbitrary number <span><math><mi>N</mi></math></span> of interacting particles, in regimes of small enough nonlinearity so that a Birkhoff-Gustavson type of normal form can be found using tools from wave-turbulence theory. Specifically, we develop the theory that leads to the so-called Zakharov equation for 4-wave resonant interactions and its extension to 5-wave resonant interactions by Krasitskii, but we introduce an important new feature: by insisting that even the generic terms in these normal forms contain <em>resonant interactions only</em>, we obtain <em>unique</em> canonical transformations and normal forms that give rise to analytical approximations to the original FPUT lattice that possess a significant number of exact quadratic conservation laws, beyond the quadratic part of the Hamiltonian. We call the new equations “exact-resonance evolution equations” and examine their properties. First, because they consist of exact-resonant terms only, the evolution is very slow in the Heisenberg representation and we implement numerical methods with large time steps to obtain relevant information about the dynamics, such as Lyapunov exponents. Second, we introduce and execute successfully a number of tests, such as convergence of the normal form transformation and truncation error verification, to validate our exact-resonance evolution equations, by quantifying how well the solution to these equations serves to approximate the original FPUT lattice dynamics. Third, we use our theoretical underpinnings (based on the so-called resonant cluster matrix) in terms of the new quadratic invariants found, to propose and implement a method, based on finite-time Lyapunov exponent calculations applied to long-time dynamics, to quantify the level of nonlinearity at which the original FPUT lattice is well approximated by the exact-resonance evolution equations. Most of the numerical experiments presented are done in the case <span><math><mrow><mi>N</mi><mo>=</mo><mn>9</mn></mrow></math></span>, but the theory and the numerical methods presented are valid for arbitrary values of <span><math><mi>N</mi></math></span>. We conclude that, when <span><math><mi>N</mi></math></span> is divisible by 3, at small enough nonlinearity the FPUT lattice’s dynamics and nontrivial hyperchaos are governed by 5-wave resonant interactions, in qualitative and quantitative agreement with the theory developed in this paper.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134813"},"PeriodicalIF":2.7,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614285","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":"Bulk and surface dominated phenomena and the formation of pentagonal structures in 2-D strongly coupled finite dust clusters","authors":"Mamta Yadav,&nbsp;Aman Singh Katariya,&nbsp;Animesh Sharma,&nbsp;Amita Das","doi":"10.1016/j.physd.2025.134821","DOIUrl":"10.1016/j.physd.2025.134821","url":null,"abstract":"<div><div>This paper explores the prevalence of size-dependent aspects in the context of dust clusters with the help of Molecular Dynamics (MD) simulations in two dimensions. The transition from macroscale (identified by the dominance of the number of dust particles in bulk) to microscale (where the number of particles on the surface dominates) is explored systematically. The dust particles organize in a multi-ringed structure when confined in the 2-D plane. The ring size and the number of rings increase with the increasing number of dust particles. Interestingly, the formation of an additional ring is always preceded by structures with a pentagonal symmetry in the core. A detailed study of this formation has been investigated under various symmetries of the boundary condition and different values of the shielding potential.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134821"},"PeriodicalIF":2.7,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144606154","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":"New pathways to stability and instability in non-premixed Rayleigh-Taylor flames","authors":"Nitesh Attal,&nbsp;Madhav Nagori,&nbsp;Prashant Tarey,&nbsp;Praveen Ramaprabhu","doi":"10.1016/j.physd.2025.134830","DOIUrl":"10.1016/j.physd.2025.134830","url":null,"abstract":"<div><div>We report on detailed numerical simulations of a non-premixed, turbulent Rayleigh-Taylor (RT) flame, where multimode perturbations were imposed on the initial interface. In a previous article, the stability of this configuration to single-mode perturbations was investigated, which we now extend to multimode disturbances. The sharp initial interface separating the fuel and oxidizer evolved under the influence of the RT instability, while the instability-driven mixing in turn enhanced burning at the flame site. Simulations at two different Atwood numbers were performed. At an Atwood number greater than 0.5, the growth of the two layer RT flame was enhanced by bubble expansion and the additional buoyancy due to combustion. At lower Atwood numbers, burning within the flame region resulted in the formation of a third layer with a lower density than either the air or fuel streams. The behavior of the resulting three-layer RT problem depended on the direction of the applied acceleration. When the applied acceleration was such that the initial configuration was globally unstable, burning within the reaction zone resulted in the formation of an active third layer which caused the fuel-flame interface to be stable near the spikes. If the initial configuration was globally stable, burning and formation of the reaction zone resulted in a fuel-flame surface that was RT-unstable. The problem configuration and our findings are relevant to ultra compact combustors. In addition, the novel flow configuration investigated here can potentially provide a fundamentally new framework for understanding the properties of several non-premixed flames.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134830"},"PeriodicalIF":2.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144606155","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":"Hyperelliptic sigma functions and the Kadomtsev–Petviashvili equation","authors":"Takanori Ayano ,&nbsp;Victor M. Buchstaber","doi":"10.1016/j.physd.2025.134819","DOIUrl":"10.1016/j.physd.2025.134819","url":null,"abstract":"<div><div>In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev–Petviashvili equations KP-I and KP-II are obtained. The long-standing problem of describing the dependence of these solutions on the variation of the coefficients of the defining equation of a hyperelliptic curve, which are integrals of the equations, is solved.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134819"},"PeriodicalIF":2.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614286","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":"Learning dynamical systems from data: Gradient-based dictionary optimization","authors":"Mohammad Tabish ,&nbsp;Neil K. Chada ,&nbsp;Stefan Klus","doi":"10.1016/j.physd.2025.134822","DOIUrl":"10.1016/j.physd.2025.134822","url":null,"abstract":"<div><div>The Koopman operator plays a crucial role in analyzing the global behavior of dynamical systems. Existing data-driven methods for approximating the Koopman operator or discovering the governing equations of the underlying system typically require a fixed set of basis functions, also called <em>dictionary</em>. The optimal choice of basis functions is highly problem-dependent and often requires domain knowledge. We present a novel gradient descent-based optimization framework for learning suitable and interpretable basis functions from data and show how it can be used in combination with EDMD, SINDy, and PDE-FIND. We illustrate the efficacy of the proposed approach with the aid of various benchmark problems such as the Ornstein–Uhlenbeck process, Chua’s circuit, a nonlinear heat equation, as well as protein-folding data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134822"},"PeriodicalIF":2.7,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144581180","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":"Continuum limit of the Kuramoto model with random natural frequencies on uniform graphs","authors":"Kazuyuki Yagasaki","doi":"10.1016/j.physd.2025.134818","DOIUrl":"10.1016/j.physd.2025.134818","url":null,"abstract":"<div><div>We study the Kuramoto model (KM) having random natural frequencies and defined on uniform graphs that may be complete, random dense or random sparse. The natural frequencies are assumed to be independent and identically distributed on a bounded interval. In the previous work, the corresponding continuum limit (CL) was proven to approximate stable motions in the KM well when the natural frequencies are deterministic, even if the graph is not uniform, although it may not do so for unstable motions and bifurcations. We show that the method of CLs is still valid even when the natural frequencies are random, especially uniformly distributed. In particular, an asymptotically stable family of solutions to the CL is proven to behave in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> sense as if it is an asymptotically stable one in the KM, under an appropriate uniform random permutation. We demonstrate the theoretical results by numerical simulations for the KM with uniformly distributed random natural frequencies.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134818"},"PeriodicalIF":2.7,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655951","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":"Modulational instability and decomposition of nonlinear localized waves for the principal chiral field equation","authors":"Xue-Ke Liu ,&nbsp;Zhen Wang ,&nbsp;Xiao-Yong Wen","doi":"10.1016/j.physd.2025.134810","DOIUrl":"10.1016/j.physd.2025.134810","url":null,"abstract":"<div><div>In this paper, we focus on the principal chiral field equation possessing the features of asymptotic freedom and dimensional transmutation, which may characterize the chiral properties of particles. Firstly, we analyze the modulational instability based on plane wave solutions. Secondly, we develop the iterative generalized <span><math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>N</mi><mo>−</mo><mi>n</mi><mo>)</mo></mrow></math></span>-fold Darboux transformation for this model to obtain rogue waves, periodic waves and their interaction states. Moreover, the higher-order rogue waves can be separated into multiple simple rogue waves, and the central locations of these simple rogue waves form triangles, pentagons and other shapes. Then, the movements and decomposition mechanisms of rogue waves on the constant backgrounds are studied with the large-parameter asymptotic analysis technique. We find that rogue waves can be separated along specific trajectories. Finally, the motion trajectories and distributions of magnetic vector and self-consistent potential are also taken into account. In contrast to other regions, the area where rogue waves are excited can cause remarkable changes in direction of magnetic vector and self-consistent potential. Our findings may contribute to understand the nonlinear localized waves in associated fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134810"},"PeriodicalIF":2.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572432","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 comprehensive review on controlled supersonic jets in improving their mixing characteristics","authors":"Paramesh T ,&nbsp;Tamal Jana ,&nbsp;Mrinal Kaushik","doi":"10.1016/j.physd.2025.134825","DOIUrl":"10.1016/j.physd.2025.134825","url":null,"abstract":"<div><div>This article thoroughly reviews the studies on enhancing the mixing and controlling of supersonic jets through passive and active control techniques. At first, the behavior of jets and their interactions with the environment, such as entrainment of surrounding fluid and vortex formation, are explored. Subsequently, the control mechanisms for supersonic jets are described. The impacts of the jet-jet interactions are explicitly demonstrated. The jet behaviors for different nozzle geometries and nozzle lip modification are reviewed, emphasizing the introduction of asymmetry by generating the vortices promoting jet mixing. The asymmetric jets perform better mixing performance than the axisymmetric jets due to the axis-switching behavior and azimuthal asymmetry. The tab-like vortex generators at the nozzle exit and their impact on jet spreading and mixing characteristics are particularly emphasized; different tab shapes, locations, and aspect ratios are reviewed, highlighting their effects on jet mixing and core length reduction. The paper focuses on understanding the behavior of vortices generated by tabs of varying designs and their effect on mixing enhancement. The findings underscore the effectiveness of both passive and active control techniques in promoting jet mixing and reducing core length. Subsequently, the active controls such as fluidic actuators, air tabs, and plasma jets are explored. The main objective of the controlled jet is to introduce additional controlled vortices and to alter the jet instabilities to enhance the interaction between the jet and its surroundings. These strategies lead to enhanced mixing, reduced core length, and are beneficial for jet noise mitigation, combustion augmentation, and the improvement of stealth capabilities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134825"},"PeriodicalIF":2.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655900","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":"Existence and destruction of tori in a discontinuous oscillator under quasi-periodic excitations","authors":"Pengcheng Miao ,&nbsp;Jicheng Duan ,&nbsp;Denghui Li ,&nbsp;Jianhua Xie ,&nbsp;Celso Grebogi","doi":"10.1016/j.physd.2025.134804","DOIUrl":"10.1016/j.physd.2025.134804","url":null,"abstract":"<div><div>We investigate the existence and destruction of invariant tori in a discontinuous oscillator under quasi-periodic excitation. For the conservative case, by constructing a quasi-periodic twist map, we prove the existence of infinitely many invariant tori and show that all solutions of the system are bounded when the frequencies satisfy the non-resonance condition. For the dissipative case, by taking a quasi-periodic forcing with two frequencies, we employ numerical methods to explore the breakdown mechanisms of torus attractors and multistability phenomena. The multistability includes the coexistence of multiple torus attractors and the coexistence of torus and chaotic attractors. In addition, we show that grazing bifurcations induce the destruction of torus attractors with the emergence of either chaotic attractors or strange nonchaotic attractors.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134804"},"PeriodicalIF":2.7,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522336","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":"Two-dimensional quantum droplets in quadrupolar Bose–Einstein condensates","authors":"Xiao-ting Zheng ,&nbsp;Xiao-wei Chen ,&nbsp;Manna Chen ,&nbsp;Hongcheng Wang ,&nbsp;Gui-hua Chen","doi":"10.1016/j.physd.2025.134807","DOIUrl":"10.1016/j.physd.2025.134807","url":null,"abstract":"<div><div>The discovery of stable quantum droplets in dipolar Bose–Einstein condensates has spurred interest in exploring their existence in other polar Bose–Einstein condensates systems. Among these, quadrupolar Bose–Einstein condensates—known for their unique anisotropic interactions—hold strong potential for the emergence of quantum droplets. In this study, we investigate the existence and stability of two-dimensional quantum droplets in systems with electric quadrupole–quadrupole interactions, supplemented by Lee–Huang–Yang quantum corrections. These systems exhibit anisotropic behavior, with droplets that elongate along the polarization axis due to the interplay of quadrupolar interactions and quantum fluctuations, as described by a two-dimensional extended Gross–Pitaevskii equation. Using theoretical analysis and numerical simulations, we demonstrate the stable existence of both fundamental and vortex quantum droplets (with topological charge <span><math><mrow><mi>S</mi><mo>=</mo><mn>1</mn></mrow></math></span>). Key parameters such as peak density, chemical potential, and effective area are examined to elucidate the characteristics of these quantum droplets. Furthermore, we examine collision dynamics under both transverse and longitudinal configurations, shedding light on the anisotropic nature of droplet interactions. These findings pave the way for experimental realization and enrich the theoretical understanding of quantum droplets in quadrupolar Bose–Einstein condensates.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134807"},"PeriodicalIF":2.7,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522478","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}