Journal of Nonlinear Science最新文献_第8页

Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions 微磁能量的随机同质化与磁天幕的出现

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-23 DOI: 10.1007/s00332-023-10005-3

{"title":"Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions","authors":"","doi":"10.1007/s00332-023-10005-3","DOIUrl":"https://doi.org/10.1007/s00332-023-10005-3","url":null,"abstract":"<h3>Abstract</h3> <p>We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"97-98 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

The Statistical Theory of the Angiogenesis Equations 血管生成方程的统计理论

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-22 DOI: 10.1007/s00332-023-10006-2

Björn Birnir, Luis Bonilla, Manuel Carretero, Filippo Terragni

引用次数: 0

Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process 具有免疫反应和 Ornstein-Uhlenbeck 过程的登革热感染随机宿主内模型分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-01-02 DOI: 10.1007/s00332-023-10004-4

Qun Liu, Daqing Jiang

引用次数: 0

Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations 非自治偏函微分方程的具有显式分形维数的回拉指数吸引子

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-30 DOI: 10.1007/s00332-023-10003-5

Wenjie Hu, Tomás Caraballo

{"title":"Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations","authors":"Wenjie Hu, Tomás Caraballo","doi":"10.1007/s00332-023-10003-5","DOIUrl":"https://doi.org/10.1007/s00332-023-10003-5","url":null,"abstract":"<p>The aim of this paper is to propose a new method to construct pullback exponential attractors with explicit fractal dimensions for non-autonomous infinite-dimensional dynamical systems in Banach spaces. The approach is established by combining the squeezing properties and the covering of finite subspace of Banach spaces, which generalize the method established for autonomous systems in Hilbert spaces (Eden A, Foias C, Nicolaenko B, and Temam R Exponential attractors for dissipative evolution equations, Wiley, New York, 1994). The method is especially effective for non-autonomous partial functional differential equations for which phase space decomposition based on the exponential dichotomy of the linear part or variation techniques are available for proving squeezing property. The theoretical results are illustrated by applications to several specific non-autonomous partial functional differential equations, including a retarded reaction–diffusion equation, a retarded 2D Navier–Stokes equation and a retarded semilinear wave equation. The constructed exponential attractors possess explicit fractal dimensions which do not depend on the entropy number but only on some inner characteristics of the studied equations including the spectra of the linear part and the Lipschitz constants of the nonlinear terms and hence do not require the smooth embedding between two spaces in the previous work.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"16 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Geometry-Preserving Numerical Methods for Physical Systems with Finite-Dimensional Lie Algebras 有限维李代数物理系统的几何保全数值方法

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-23 DOI: 10.1007/s00332-023-10000-8

L. Blanco, F. Jiménez, J. de Lucas, C. Sardón

{"title":"Geometry-Preserving Numerical Methods for Physical Systems with Finite-Dimensional Lie Algebras","authors":"L. Blanco, F. Jiménez, J. de Lucas, C. Sardón","doi":"10.1007/s00332-023-10000-8","DOIUrl":"https://doi.org/10.1007/s00332-023-10000-8","url":null,"abstract":"<h3>Abstract</h3> <p>We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie group action and then generates the discrete solution of the Lie system on the manifold via a solution of the Lie system on the Lie group. One major result from the integration of a Lie system on a Lie group is that one is able to solve all associated Lie systems on manifolds at the same time, and that Lie systems on Lie groups can be described through first-order systems of linear homogeneous ordinary differential equations (ODEs) in normal form. This brings a lot of advantages, since solving a linear system of ODEs involves less numerical cost. Specifically, we use two families of numerical schemes on the Lie group, which are designed to preserve its geometrical structure: the first one is based on the Magnus expansion, whereas the second is based on Runge–Kutta–Munthe–Kaas (RKMK) methods. Moreover, since the aforementioned action relates the Lie group and the manifold where the Lie system evolves, the resulting integrator preserves any geometric structure of the latter. We compare both methods for Lie systems with geometric invariants, particularly a class on Lie systems on curved spaces. We also illustrate the superiority of our method for describing long-term behavior and for differential equations admitting solutions whose geometric features depends heavily on initial conditions. As already mentioned, our milestone is to show that the method we propose preserves all the geometric invariants very faithfully, in comparison with non-geometric numerical methods.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"80 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Geometric Methods for Adjoint Systems 用于邻接系统的几何方法

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-19 DOI: 10.1007/s00332-023-09999-7

Brian Kha Tran, Melvin Leok

{"title":"Geometric Methods for Adjoint Systems","authors":"Brian Kha Tran, Melvin Leok","doi":"10.1007/s00332-023-09999-7","DOIUrl":"https://doi.org/10.1007/s00332-023-09999-7","url":null,"abstract":"<p>Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or differential-algebraic equations. In this paper, we explore the geometric properties and develop methods for such adjoint systems. In particular, we utilize symplectic and presymplectic geometry to investigate the properties of adjoint systems associated with ordinary differential equations and differential-algebraic equations, respectively. We show that the adjoint variational quadratic conservation laws, which are key to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems. We discuss various additional geometric properties of adjoint systems, such as symmetries and variational characterizations. For adjoint systems associated with a differential-algebraic equation, we relate the index of the differential-algebraic equation to the presymplectic constraint algorithm of Gotay et al. (J Math Phys 19(11):2388–2399, 1978). As an application of this geometric framework, we discuss how the adjoint variational quadratic conservation laws can be used to compute sensitivities of terminal or running cost functions. Furthermore, we develop structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators (Leok and Zhang in IMA J. Numer. Anal. 31(4):1497–1532, 2011) which admit discrete analogues of these quadratic conservation laws. We additionally show that such methods are natural, in the sense that reduction, forming the adjoint system, and discretization all commute, for suitable choices of these processes. We utilize this naturality to derive a variational error analysis result for the presymplectic variational integrator that we use to discretize the adjoint DAE system. Finally, we discuss the application of adjoint systems in the context of optimal control problems, where we prove a similar naturality result.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"20 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138744862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Numerical Computation of Dark Solitons of a Nonlocal Nonlinear Schrödinger Equation 非局部非线性薛定谔方程暗孤子的数值计算

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-18 DOI: 10.1007/s00332-023-10001-7

André de Laire, Guillaume Dujardin, Salvador López-Martínez

引用次数: 0

Spike Solutions to the Supercritical Fractional Gierer–Meinhardt System 超临界分式吉勒-梅因哈特系统的尖峰解决方案

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-18 DOI: 10.1007/s00332-023-10002-6

Daniel Gomez, Markus De Medeiros, Jun-cheng Wei, Wen Yang

{"title":"Spike Solutions to the Supercritical Fractional Gierer–Meinhardt System","authors":"Daniel Gomez, Markus De Medeiros, Jun-cheng Wei, Wen Yang","doi":"10.1007/s00332-023-10002-6","DOIUrl":"https://doi.org/10.1007/s00332-023-10002-6","url":null,"abstract":"<p>Localized solutions are known to arise in a variety of singularly perturbed reaction–diffusion systems. The Gierer–Meinhardt (GM) system is one such example and has been the focus of numerous rigorous and formal studies. A more recent focus has been the study of localized solutions in systems exhibiting anomalous diffusion, particularly with Lévy flights. In this paper, we investigate localized solutions to a one-dimensional fractional GM system for which the inhibitor’s fractional order is supercritical. Specifically, we assume the fractional orders of the activator and inhibitor are, respectively, in the ranges <span>(s_1in (1/4,1))</span> and <span>(s_2in (0,1/2))</span>. Using the method of matched asymptotic expansions, we reduce the construction of multi-spike solutions to solving a nonlinear algebraic system. The linear stability of the resulting multi-spike solutions is then addressed by studying a globally coupled eigenvalue problem. In addition to these formal results, we also rigorously establish the existence and stability of ground state solutions when the inhibitor’s fractional order is nearly critical. The fractional Green’s function, for which we present a rapidly converging series expansion, is prominently featured throughout both the formal and rigorous analysis in this paper. Moreover, we emphasize that the striking similarities between the one-dimensional supercritical GM system and the classical three-dimensional GM system can be attributed to the leading-order singular behaviour of the fractional Green’s function.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"236 1 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138745963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds 未知不变曲面附近慢-快随机系统的非线性模型还原

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-08 DOI: 10.1007/s00332-023-09998-8

Felix X.-F. Ye, Sichen Yang, Mauro Maggioni

{"title":"Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds","authors":"Felix X.-F. Ye, Sichen Yang, Mauro Maggioni","doi":"10.1007/s00332-023-09998-8","DOIUrl":"https://doi.org/10.1007/s00332-023-09998-8","url":null,"abstract":"<p>We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics and high-dimensional, large fast modes. Given only access to a black-box simulator from which short bursts of simulation can be obtained, we design an algorithm that outputs an estimate of the invariant manifold, a process of the effective stochastic dynamics on it, which has averaged out the fast modes, and a simulator thereof. This simulator is efficient in that it exploits of the low dimension of the invariant manifold, and takes time-steps of size dependent on the regularity of the effective process, and therefore typically much larger than that of the original simulator, which had to resolve the fast modes. The algorithm and the estimation can be performed on the fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"229 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138562677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Error Estimates of hp Spectral Element Methods in Nonlinear Optimal Control Problem 非线性最优控制问题中hp谱元方法的误差估计

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-01 DOI: 10.1007/s00332-023-09991-1

Xiuxiu Lin, Yanping Chen, Yunqing Huang

引用次数: 0