图上的非局部交叉相互作用系统:能源景观和动力学

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2022-04-20 DOI:10.3934/krm.2023008

G. Heinze, Jan-Frederik Pietschmann, M. Schmidtchen

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引用次数: 5

摘要

我们探讨了有限图上非局部相互作用的两种模型的动力学行为和能量性质。作者最近在具有非线性移动的广义图上的非二次芬斯勒梯度流的背景下引入了该模型。在连续和局部环境中，这类系统表现出各种各样的模式，包括两种物质的混合、部分吞没或相分离。这项工作展示了这种丰富的行为如何延续到图结构中。我们提出了分析和数值证据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nonlocal cross-interaction systems on graphs: Energy landscape and dynamics

We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. The authors recently introduced the model in the context of nonquadratic Finslerian gradient flows on generalized graphs featuring nonlinear mobilities. In a continuous and local setting, this class of systems exhibits a wide variety of patterns, including mixing of the two species, partial engulfment, or phase separation. This work showcases how this rich behavior carries over to the graph structure. We present analytical and numerical evidence thereof.

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.