Journal of Nonlinear Science最新文献_第5页

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

Parametric Nonlinear Model Reduction Using Machine Learning on Grassmann Manifold with an Application on a Flow Simulation 利用机器学习在格拉斯曼漫域上减少参数非线性模型，并将其应用于流动模拟

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-07 DOI: 10.1007/s00332-024-10039-1

Norapon Sukuntee, Saifon Chaturantabut

{"title":"Parametric Nonlinear Model Reduction Using Machine Learning on Grassmann Manifold with an Application on a Flow Simulation","authors":"Norapon Sukuntee, Saifon Chaturantabut","doi":"10.1007/s00332-024-10039-1","DOIUrl":"https://doi.org/10.1007/s00332-024-10039-1","url":null,"abstract":"This work introduces a parametric model order reduction (PMOR) approach that enhances an existing widely used technique based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) for parametrized nonlinear dynamical systems by employing machine learning procedures performed on a Grassmann manifold. In particular, distances between parameters are first computed based on a metric defined on the Grassmann manifold of solution spaces. Then, the distance information is utilized in the K-medoids clustering algorithm to partition parameters into classes with corresponding local solution spaces, which are further used to form a dictionary of local bases. The artificial neural network (ANN) is next used to build a classifier that can automatically identify the most suitable local basis from the dictionary for a given input parameter to construct a parametrized reduced-order model by the POD–DEIM approach. This work numerically demonstrates the significance of using distance on the Grassmann manifold of the solution spaces, instead of directly using the Euclidean distance on the parameter space. To validate the proposed method, numerical studies are performed on a parametrized 1D Burger’s equation and a viscous fingering in a horizontal flow through a 2D porous media domain. The proposed method is shown to have advantage in terms of accuracy when compared to the traditional global basis approach, as well as the local reduced-order basis approach based on the Euclidean metric.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"82 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885335","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

Cycle-Star Motifs: Network Response to Link Modifications 循环-星形图案：网络对链接修改的响应

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-06 DOI: 10.1007/s00332-024-10034-6

Sajjad Bakrani, Narcicegi Kiran, Deniz Eroglu, Tiago Pereira

{"title":"Cycle-Star Motifs: Network Response to Link Modifications","authors":"Sajjad Bakrani, Narcicegi Kiran, Deniz Eroglu, Tiago Pereira","doi":"10.1007/s00332-024-10034-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10034-6","url":null,"abstract":"Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master–slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as Rössler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"22 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885547","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

Chaos of Multi-dimensional Weakly Hyperbolic Equations with General Nonlinear Boundary Conditions 具有一般非线性边界条件的多维弱双曲方程的混沌问题

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-02 DOI: 10.1007/s00332-024-10038-2

Qiaomin Xiang, Qigui Yang

引用次数: 0

Modulation Analysis of the Stochastic Camassa–Holm Equation with Pure Jump Noise 带有纯跳跃噪声的随机卡马萨-霍姆方程的调制分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-04-28 DOI: 10.1007/s00332-024-10037-3

Yong Chen, Jinqiao Duan, Hongjun Gao, Xingyu Guo

引用次数: 0

Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms 欧几里得曲线空间上的弹性度量：理论与算法

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-04-25 DOI: 10.1007/s00332-024-10035-5

Martin Bauer, Nicolas Charon, Eric Klassen, Sebastian Kurtek, Tom Needham, Thomas Pierron

{"title":"Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms","authors":"Martin Bauer, Nicolas Charon, Eric Klassen, Sebastian Kurtek, Tom Needham, Thomas Pierron","doi":"10.1007/s00332-024-10035-5","DOIUrl":"https://doi.org/10.1007/s00332-024-10035-5","url":null,"abstract":"A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis framework is to define such a metric by starting with a reparametrization-invariant Riemannian metric on the space of parametrized shapes and inducing a metric on the quotient by the group of diffeomorphisms. This quotient metric is computed, in practice, by finding a registration of two shapes over the diffeomorphism group. For spaces of Euclidean curves, the initial Riemannian metric is frequently chosen from a two-parameter family of Sobolev metrics, called elastic metrics. Elastic metrics are especially convenient because, for several parameter choices, they are known to be locally isometric to Riemannian metrics for which one is able to solve the geodesic boundary problem explicitly—well-known examples of these local isometries include the complex square root transform of Younes, Michor, Mumford and Shah and square root velocity (SRV) transform of Srivastava, Klassen, Joshi and Jermyn. In this paper, we show that the SRV transform extends to elastic metrics for all choices of parameters, for curves in any dimension, thereby fully generalizing the work of many authors over the past two decades. We give a unified treatment of the elastic metrics: we extend results of Trouvé and Younes, Bruveris as well as Lahiri, Robinson and Klassen on the existence of solutions to the registration problem, we develop algorithms for computing distances and geodesics, and we apply these algorithms to metric learning problems, where we learn optimal elastic metric parameters for statistical shape analysis tasks.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"15 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806816","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

A Generalized Sine-Gordon Equation: Reductions and Integrable Discretizations 广义正弦-戈登方程：还原与积分离散化

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-04-17 DOI: 10.1007/s00332-024-10030-w

Han-Han Sheng, Bao-Feng Feng, Guo-Fu Yu

{"title":"A Generalized Sine-Gordon Equation: Reductions and Integrable Discretizations","authors":"Han-Han Sheng, Bao-Feng Feng, Guo-Fu Yu","doi":"10.1007/s00332-024-10030-w","DOIUrl":"https://doi.org/10.1007/s00332-024-10030-w","url":null,"abstract":"In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation (u_{t x}=left( 1+nu partial _x^2right) sin u). The key points of the construction are based on the bilinear discrete KP hierarchy and appropriate definition of discrete reciprocal transformations. We derive semi-discrete analogues of the gsG equation from the fully discrete gsG equation by taking the temporal parameter limit (brightarrow 0). In particular, one fully discrete gsG equation is reduced to a semi-discrete gsG equation in the case of (nu =-1) (Feng et al. in Numer Algorithms 94:351–370, 2023). Furthermore, N-soliton solutions to the semi- and fully discrete analogues of the gsG equation in the determinant form are presented. Dynamics of one- and two-soliton solutions for the discrete gsG equations are analyzed. By introducing a parameter c, we demonstrate that the gsG equation can reduce to the sine-Gordon equation and the short pulse at the levels of continuous, semi-discrete and fully discrete cases. The limiting forms of the N-soliton solutions to the gsG equation in each level also correspond to those of the sine-Gordon equation and the short pulse equation.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"301 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609412","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

2D Smagorinsky-Type Large Eddy Models as Limits of Stochastic PDEs 作为随机 PDEs 极限的二维 Smagorinsky 型大涡流模型

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-04-12 DOI: 10.1007/s00332-024-10028-4

Franco Flandoli, Dejun Luo, Eliseo Luongo

引用次数: 0

Strong Symmetry Breaking in Coupled, Identical Lengyel–Epstein Oscillators via Folded Singularities 通过折叠奇异性打破耦合同源伦盖尔-爱泼斯坦振荡器中的强对称性

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-04-11 DOI: 10.1007/s00332-024-10033-7

Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, Theodore Vo

{"title":"Strong Symmetry Breaking in Coupled, Identical Lengyel–Epstein Oscillators via Folded Singularities","authors":"Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, Theodore Vo","doi":"10.1007/s00332-024-10033-7","DOIUrl":"https://doi.org/10.1007/s00332-024-10033-7","url":null,"abstract":"We study pairs of symmetrically coupled, identical Lengyel-Epstein oscillators, where the coupling can be through both the fast and slow variables. We find a plethora of strong symmetry breaking rhythms, in which the two oscillators exhibit qualitatively different oscillations, and their amplitudes differ by as much as an order of magnitude. Analysis of the folded singularities in the coupled system shows that a key folded node, located off the symmetry axis, is the primary mechanism responsible for the strong symmetry breaking. Passage through the neighborhood of this folded node can result in splitting between the amplitudes of the oscillators, in which one is constrained to remain of small amplitude, while the other makes a large-amplitude oscillation or a mixed-mode oscillation. The analysis also reveals an organizing center in parameter space, where the system undergoes an asymmetric canard explosion, in which one oscillator exhibits a sequence of limit cycle canards, over an interval of parameter values centered at the explosion point, while the other oscillator executes small amplitude oscillations. Other folded singularities can also impact properties of the strong symmetry breaking rhythms. We contrast these strong symmetry breaking rhythms with asymmetric rhythms that are close to symmetric states, such as in-phase or anti-phase oscillations. In addition to the symmetry breaking rhythms, we also find an explosion of anti-phase limit cycle canards, which mediates the transition from small-amplitude, anti-phase oscillations to large-amplitude, anti-phase oscillations.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"9 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576021","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