格上Nagumo方程行进锋的传播失效

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2024-12-20 DOI:10.1016/j.wavemoti.2024.103483

José Fernando Bustamante-Castañeda , Gustavo Cruz-Pacheco

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引用次数: 0

摘要

本文研究了一维和二维晶格上双稳态反应扩散方程中锋面的传播失效现象。利用渐近方法和调制理论，在由耦合系数和双稳性参数定义的参数空间中逼近了锚定区域。在一维情况下，调制理论产生了一个周期的、随时间变化的波前速度，由佩尔斯-纳巴罗势控制。我们对Mallet-Paret、Hoffman和Mallet-Paret（2010）在之前的工作中所做的数值观测提供了一个简单的解释，即当其方向受到干扰时，静止的垂直波前开始前进。我们还提供了数值证据来证明我们的近似的准确性。

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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Propagation failure for traveling fronts of the Nagumo equation on a lattice

In this work, we study the phenomenon of propagation failure for fronts in a bistable reaction–diffusion equation on a lattice in one and two dimensions. Using asymptotic methods and modulation theory, we approximate the anchoring region in the parameter space defined by the coupling coefficient and the bistability parameter. For the one-dimensional case, modulation theory yields a periodic, time-dependent velocity of the wavefront, governed by a Peierls–Nabarro potential. We provide a simple explanation for a numerical observation made in previous work by Mallet-Paret, Hoffman and Mallet-Paret (2010), regarding the fact that a stationary vertical wavefront begins to advance when its direction is perturbed. We also present numerical evidence demonstrating the accuracy of our approximations.

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.