Journal of Nonlinear Science最新文献_第4页

Optimal Reconstruction of Vector Fields from Data for Prediction and Uncertainty Quantification 从数据中优化重建矢量场以进行预测和不确定性量化

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-13 DOI: 10.1007/s00332-024-10047-1

Sean P. McGowan, William S. P. Robertson, Chantelle Blachut, Sanjeeva Balasuriya

{"title":"Optimal Reconstruction of Vector Fields from Data for Prediction and Uncertainty Quantification","authors":"Sean P. McGowan, William S. P. Robertson, Chantelle Blachut, Sanjeeva Balasuriya","doi":"10.1007/s00332-024-10047-1","DOIUrl":"https://doi.org/10.1007/s00332-024-10047-1","url":null,"abstract":"Predicting the evolution of dynamics from a given trajectory history of an unknown system is an important and challenging problem. This paper presents a model-free method of forecasting unknown chaotic systems through reconstructing vector fields from noisy measured data via an adaptation of optimal control methods. This technique is also applicable to partially observed systems using a Takens delay embedding approach. The algorithms are validated on the Lorenz system and the four-dimensional hyperchaotic Rössler system, and demonstrate successful predictions well beyond the Lyapunov timescale. It is found that for small datasets or datasets with large levels of noise, the prediction accuracy of partially observed systems approaches that of fully observed systems. The presented approach also allows the model-free assessment of local predictability on the attractor by evolving initial condition density through the reconstructed vector fields via estimation of the transfer operator. The method is compared to predictions made by an imperfect model which highlights the utility of model-free approaches when the only available models have significant model error. The capability of this method for reconstruction of continuous and global vector fields may be applied to model validation, forecasting of initial conditions not in the training set, and model-free filtering. ","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"25 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503471","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 Discrete Nonlinear Schrödinger Equation with Linear Gain and Nonlinear Loss: The Infinite Lattice with Nonzero Boundary Conditions and Its Finite-Dimensional Approximations 具有线性增益和非线性损耗的离散非线性薛定谔方程：具有非零边界条件的无限晶格及其有限维近似值

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-11 DOI: 10.1007/s00332-024-10050-6

G. Fotopoulos, N. I. Karachalios, V. Koukouloyannis, P. Kyriazopoulos, K. Vetas

{"title":"The Discrete Nonlinear Schrödinger Equation with Linear Gain and Nonlinear Loss: The Infinite Lattice with Nonzero Boundary Conditions and Its Finite-Dimensional Approximations","authors":"G. Fotopoulos, N. I. Karachalios, V. Koukouloyannis, P. Kyriazopoulos, K. Vetas","doi":"10.1007/s00332-024-10050-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10050-6","url":null,"abstract":"The study of nonlinear Schrödinger-type equations with nonzero boundary conditions introduces challenging problems both for the continuous (partial differential equation) and the discrete (lattice) counterparts. They are associated with fascinating dynamics emerging by the ubiquitous phenomenon of modulation instability. In this work, we consider the discrete nonlinear Schrödinger equation with linear gain and nonlinear loss. For the infinite lattice supplemented with nonzero boundary conditions, which describe solutions decaying on the top of a finite background, we provide a rigorous proof that for the corresponding initial boundary value problem, solutions exist for any initial condition, if and only if, the amplitude of the background has a precise value (A_*) defined by the gain-loss parameters. We argue that this essential property of this infinite lattice cannot be captured by finite lattice approximations of the problem. Commonly, such approximations are provided by lattices with periodic boundary conditions or as it is shown herein, by a modified problem closed with Dirichlet boundary conditions. For the finite-dimensional dynamical system defined by the periodic lattice, the dynamics for all initial conditions are captured by a global attractor. Analytical arguments corroborated by numerical simulations show that the global attractor is trivial, defined by a plane wave of amplitude (A_*). Thus, any instability effects or localized phenomena simulated by the finite system can be only transient prior the convergence to this trivial attractor. Aiming to simulate the dynamics of the infinite lattice as accurately as possible, we study the dynamics of localized initial conditions on the constant background and investigate the potential impact of the global asymptotic stability of the background with amplitude (A_*) in the long-time evolution of the system.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"9 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503472","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

Finite Time Blow-Up and Chemotactic Collapse in Keller–Segel Model with Signal Consumption 带有信号消耗的凯勒-西格尔模型中的有限时间膨胀和趋化崩溃

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-10 DOI: 10.1007/s00332-024-10045-3

Chunhua Jin

引用次数: 0

Sliding Mode on Tangential Sets of Filippov Systems 菲利波夫系统切向集上的滑动模式

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-09 DOI: 10.1007/s00332-024-10052-4

Tiago Carvalho, Douglas D. Novaes, Durval J. Tonon

引用次数: 0

Propagation Dynamics for a Degenerate Delayed System with Nonlocal Dispersal in Periodic Habitats 周期性生境中具有非局部散布的退化延迟系统的传播动力学

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-06 DOI: 10.1007/s00332-024-10048-0

Rong Zhou, Shi-Liang Wu, Xiong-Xiong Bao

引用次数: 0

Nonuniqueness of Generalised Weak Solutions to the Primitive and Prandtl Equations 原始方程和普朗特方程广义弱解的非唯一性

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-27 DOI: 10.1007/s00332-024-10032-8

Daniel W. Boutros, Simon Markfelder, Edriss S. Titi

引用次数: 0

Predicting the Emergence of Localised Dihedral Patterns in Models for Dryland Vegetation 预测旱地植被模型中局部二面体模式的出现

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-25 DOI: 10.1007/s00332-024-10046-2

Dan J. Hill

引用次数: 0

On a Nonlocal Two-Phase Flow with Convective Heat Transfer 关于带有对流传热的非局部两相流

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-22 DOI: 10.1007/s00332-024-10042-6

Šárka Nečasová, John Sebastian H. Simon

{"title":"On a Nonlocal Two-Phase Flow with Convective Heat Transfer","authors":"Šárka Nečasová, John Sebastian H. Simon","doi":"10.1007/s00332-024-10042-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10042-6","url":null,"abstract":"We study a system describing the dynamics of a two-phase flow of incompressible viscous fluids influenced by the convective heat transfer of Caginalp-type. The separation of the fluids is expressed by the order parameter which is of diffuse interface and is known as the Cahn–Hilliard model. We shall consider a nonlocal version of the Cahn–Hilliard model which replaces the gradient term in the free energy functional into a spatial convolution operator acting on the order parameter and incorporate with it a potential that is assumed to satisfy an arbitrary polynomial growth. The order parameter is influenced by the fluid velocity by means of convection; the temperature affects the interface via a modification of the Landau–Ginzburg free energy. The fluid is governed by the Navier–Stokes equations which is affected by the order parameter and the temperature by virtue of the capillarity between the two fluids. The temperature on the other hand satisfies a parabolic equation that considers latent heat due to phase transition and is influenced by the fluid via convection. The goal of this paper is to prove the global existence of weak solutions and show that, for an appropriate choice of sequence of convolutional kernels, the solutions of the nonlocal system converge to its local version.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"3 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148536","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

On the Energy and Helicity Conservation of the Incompressible Euler Equations 论不可压缩欧拉方程的能量和螺旋守恒

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-16 DOI: 10.1007/s00332-024-10040-8

Yanqing Wang, Wei Wei, Gang Wu, Yulin Ye

{"title":"On the Energy and Helicity Conservation of the Incompressible Euler Equations","authors":"Yanqing Wang, Wei Wei, Gang Wu, Yulin Ye","doi":"10.1007/s00332-024-10040-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10040-8","url":null,"abstract":"In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli (J Differ Equ 368:350–375, 2023) and Berselli and Georgiadis (Nonlinear Differ Equ Appl 31(33):1–14, 2024), it is shown that the energy of weak solutions is invariant if the velocity (vin L^{p}(0,T;B^{frac{1}{p}}_{frac{2p}{p-1},c(mathbb {N})} )) with (1<ple 3) and the helicity is conserved if (vin L^{p}(0,T;B^{frac{2}{p}}_{frac{2p}{p-1},c(mathbb {N})} )) with (2<ple 3 ) for both the periodic domain and the whole space, which generalizes the classical work of Cheskidov et al. (Nonlinearity 21:1233–1252, 2008). As an application, we deduce the upper bound of energy dissipation rate of the form (o(mu ^{frac{palpha -1}{palpha -2alpha +1}})) of Leray–Hopf weak solutions in (L^{p}( 0,T;underline{B}^{alpha }_{frac{2p}{p-1},VMO}(mathbb {T}^{d}))) in the Navier–Stokes equations, which extends recent corresponding result obtained by Drivas and Eyink (Nonlinearity 32:4465–4482, 2019).","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"54 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060861","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

Asymptotic Analysis for the Generalized Langevin Equation with Singular Potentials 具有奇异势的广义朗文方程的渐近分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-14 DOI: 10.1007/s00332-024-10027-5

Manh Hong Duong, Hung Dang Nguyen

引用次数: 0