Physica D: Nonlinear Phenomena最新文献_第3页

Uncertainty quantification analysis of bifurcations of the Allen–Cahn equation with random coefficients 具有随机系数的艾伦-卡恩方程分岔的不确定性量化分析

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-04 DOI: 10.1016/j.physd.2024.134390

Christian Kuehn , Chiara Piazzola , Elisabeth Ullmann

{"title":"Uncertainty quantification analysis of bifurcations of the Allen–Cahn equation with random coefficients","authors":"Christian Kuehn , Chiara Piazzola , Elisabeth Ullmann","doi":"10.1016/j.physd.2024.134390","DOIUrl":"10.1016/j.physd.2024.134390","url":null,"abstract":"<div><div>In this work we consider the Allen–Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we introduce a random coefficient in the linear reaction part of the equation, thereby accounting for random, spatially-heterogeneous effects. Importantly, we assume a spatially constant, deterministic mean value of the random coefficient. We show that this mean value is in fact a bifurcation parameter in the Allen–Cahn equation with random coefficients. Moreover, we show that the bifurcation points and bifurcation curves become random objects. We consider two distinct modeling situations: <span><math><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></math></span> for a spatially-homogeneous coefficient we derive analytical expressions for the distribution of the bifurcation points and show that the bifurcation curves are random shifts of a fixed reference curve; <span><math><mrow><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span> for a spatially-heterogeneous coefficient we employ a generalized polynomial chaos expansion to approximate the statistical properties of the random bifurcation points and bifurcation curves. We present numerical examples in 1D physical space, where we combine the popular software package Continuation Core and Toolboxes (COCO) for numerical continuation and the Sparse Grids Matlab Kit for the polynomial chaos expansion. Our exposition addresses both dynamical systems and uncertainty quantification, highlighting how analytical and numerical tools from both areas can be combined efficiently for the challenging uncertainty quantification analysis of bifurcations in random differential equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The effect of Lévy index coefficient on modulational instability and rogue wave excitation in nonlocal media with cubic–quintic nonlinearities 莱维指数系数对具有三次-五次非线性的非局部介质中的调制不稳定性和流氓波激励的影响

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-03 DOI: 10.1016/j.physd.2024.134395

Camus Gaston Latchio Tiofack , Conrad Bertrand Tabi , Hippolyte Tagwo , Timoléon Crépin Kofané

{"title":"The effect of Lévy index coefficient on modulational instability and rogue wave excitation in nonlocal media with cubic–quintic nonlinearities","authors":"Camus Gaston Latchio Tiofack , Conrad Bertrand Tabi , Hippolyte Tagwo , Timoléon Crépin Kofané","doi":"10.1016/j.physd.2024.134395","DOIUrl":"10.1016/j.physd.2024.134395","url":null,"abstract":"<div><div>This paper explores the modulational instability (MI) of a plane wave and its behavior in the nonlinear Schrödinger equation (NLSE) with a fractional diffraction term quantified by its Lévy index coefficient and nonlocal cubic–quintic nonlinearities. First, we analyze the stability of the plane wave solution and examine how nonlocal nonlinearities and the Lévy index coefficient affect the MI gain. We observe that the stability in the fractional NLSE exhibits new features that differ from those in the standard NLSE. Specifically, when dealing with competing cubic and quintic nonlinearities, the interaction between nonlocality and the Lévy index coefficient <span><math><mi>α</mi></math></span> can eliminate MI for low values of <span><math><mi>α</mi></math></span>, unlike the classical NLSE with <span><math><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></math></span>, where we find the plane wave to be unstable. Besides the linear stability analysis, numerical simulations are performed to understand further the plane wave dynamics from its nonlinear stage in this model. The results reveal the generation of periodic chains of localized peaks. Guided by analytical predictions and using the plane wave solution subject to Gaussian perturbation, we numerically investigate the possibility of exciting rogue waves in the parameter spaces where MI exists. We find that the different combinations of signs of the cubic and quintic nonlinearities (focusing and defocusing) and the fractional diffraction term significantly impact the formation of rogue waves. These results may pave the way for the theoretical and experimental study of nonlinear phenomena in physical models with fractional derivatives and nonlocal nonlinearities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529726","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}

引用次数: 0

Reduced Markovian models of dynamical systems 动态系统的还原马尔可夫模型

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-03 DOI: 10.1016/j.physd.2024.134393

Ludovico Theo Giorgini , Andre N. Souza , Peter J. Schmid

引用次数: 0

Sufficient and necessary conditions for self-similar motions of three point vortices in generalized fluid systems 广义流体系统中三点旋涡自相似运动的充分和必要条件

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-01 DOI: 10.1016/j.physd.2024.134392

Jiahe Chen, Qihuai Liu

引用次数: 0

Algebraic design of physical computing system 物理计算系统的代数设计

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-01 DOI: 10.1016/j.physd.2024.134382

Mizuka Komatsu , Takaharu Yaguchi , Kohei Nakajima

{"title":"Algebraic design of physical computing system","authors":"Mizuka Komatsu , Takaharu Yaguchi , Kohei Nakajima","doi":"10.1016/j.physd.2024.134382","DOIUrl":"10.1016/j.physd.2024.134382","url":null,"abstract":"<div><div>Recently, computational techniques that employ physical systems (physical computing systems) have been developed. To utilize physical computing systems, their design strategy is important. Although there are practical learning-based methods and theoretical approaches, no general method exists that provides specific design guidelines for given systems with rigorous theoretical support. In this paper, we propose a novel algebraic design framework for a physical computing system, which is capable of extracting specific design guidelines. Our approach describes input–output relationships algebraically and relates them to given target tasks. Two theorems are presented in this paper. The first theorem offers a basic strategy for algebraic design. The second theorem explores the “replaceability” of such systems. Their possible implementations are investigated through experiments. In particular, the design of inputs of a system so that it generates multiple target time-series and the replacement of stationary or non-stationary target systems by a given system that is designed algebraically are included. The proposed framework is shown to have the potential of designing given physical computing systems with theoretical support.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability of asymptotic waves in the Fisher–Stefan equation 费舍尔-斯特凡方程中渐近波的稳定性

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-01 DOI: 10.1016/j.physd.2024.134383

T.T.H. Bui , P. van Heijster , R. Marangell

引用次数: 0

Solitons moving on background waves of the focusing nonlinear Schrödinger equation with step-like initial condition 在具有阶梯状初始条件的聚焦非线性薛定谔方程背景波上运动的孤子

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-01 DOI: 10.1016/j.physd.2024.134389

Deng-Shan Wang , Guo-Fu Yu , Dinghao Zhu

引用次数: 0

Dispersion management and optical soliton engineering in nonuniform inhomogeneous PT-symmetric nonlinear media 非均匀非均质 PT 对称非线性介质中的色散管理和光学孤子工程

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-01 DOI: 10.1016/j.physd.2024.134388

K. Manikandan , K. Sakkaravarthi , S. Sabari

{"title":"Dispersion management and optical soliton engineering in nonuniform inhomogeneous PT-symmetric nonlinear media","authors":"K. Manikandan , K. Sakkaravarthi , S. Sabari","doi":"10.1016/j.physd.2024.134388","DOIUrl":"10.1016/j.physd.2024.134388","url":null,"abstract":"<div><div>Studies on optical solitons in inhomogeneous media continue to attract immense interest. This work is devoted to exploring the evolution dynamics of solitons in inhomogeneous nonuniform optical media with parity-time reversal <span><math><mrow><mo>(</mo><mi>PT</mi><mo>)</mo></mrow></math></span>-symmetric rational potential and variable dispersion through explicit solutions. For this purpose, we consider a variable-coefficient nonlinear Schrödinger (vcNLS) equation containing <span><math><mi>PT</mi></math></span>-symmetric rational potential consisting of constant nonlinearity and longitudinally-varying dispersion and tapering effects. By implementing a similarity transformation, one of the efficient methods to analyze variable-coefficient (non-autonomous) nonlinear models, we construct explicit soliton (similariton) solutions and investigate deformations occurring in the characteristics of the optical solitons resulting from various dispersion modulations. Notably, we unravel the dynamical changes in the amplitude, width, shape, speed/velocity, and localization of solitons for periodic, localized well/barrier-type, and step-like dispersion modulations leading to periodic, localized, and single-step suppression or amplification, broadening and narrowing of width, and advancing or delaying the transitions during soliton propagation in inhomogeneous media. Besides, we execute a direct numerical experiment to validate the identified analytical findings. The observed results shall enhance the understanding of solitons in inhomogeneous <span><math><mi>PT</mi></math></span>-symmetric media. As future perspectives, the present analysis can be extended to study the deformation dynamics of several other nonlinear waves in inhomogeneous media and their experimental realizations in the context of optics and other fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420457","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}

引用次数: 0

Warning signs for boundary noise and their application to an ocean Boussinesq model 边界噪声的预警信号及其在海洋布森斯克模型中的应用

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-10-01 DOI: 10.1016/j.physd.2024.134391

P. Bernuzzi , H.A. Dijkstra , C. Kuehn

引用次数: 0

Chaotic responses across the potential barrier of bistable vortex-induced vibration energy harvesters 双稳态涡旋诱导振动能量收集器跨越势垒的混沌响应

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-09-30 DOI: 10.1016/j.physd.2024.134374

Zhiyuan Li , Jiaqin Zhang , Haitao Xu , Shengxi Zhou , Li Cheng

{"title":"Chaotic responses across the potential barrier of bistable vortex-induced vibration energy harvesters","authors":"Zhiyuan Li , Jiaqin Zhang , Haitao Xu , Shengxi Zhou , Li Cheng","doi":"10.1016/j.physd.2024.134374","DOIUrl":"10.1016/j.physd.2024.134374","url":null,"abstract":"<div><div>Large-amplitude interwell limit cycle oscillations (LCOs) are regarded as an ideal high-output state of multistable vibration energy harvesters. However, chaotic responses, which result in lower output voltages than interwell LCOs, can be observed in bistable vortex-induced vibration energy harvesters (VIVEHs). In this paper, the chaos in bistable VIVEHs is investigated through numerical simulation, theoretical analyses, and experimental validation. The distribution of the periodic solutions obtained by the incremental harmonic balance (IHB) method and chaos judgment using Lyapunov exponents are elucidated. It is found that the bistable VIVEH shows intrawell periodic solutions at high reduced wind speeds (RWSs) and period-doubling bifurcation appears with the periodic solutions turning into chaos with decreasing RWS. Analyses of the influence of nonlinear parameters on the chaotic responses identify the nonlinear stiffness as the dominant factor contributing to the chaos. Meanwhile, the chaotic responses and interwell LCOs would exist at the same RWS with different initial states. Finally, wind tunnel experiments confirm the occurrence of homologous chaotic responses of the bistable VIVEH which feature aperiodic jumping back and forth motion between two potential wells, in agreement with numerical simulations. Overall, this paper provides a framework for analyzing the chaotic responses of bistable VIVEHs, offering valuable insights for complex response mechanism understanding.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358189","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}

引用次数: 0