Coherent Structures in Granular Crystals: From Experiment and Modelling to Computation and Mathematical Analysis
Coherent Structures in Granular Crystals: From Experiment and Modelling to Computation and Mathematical Analysis
复制标题
粒状晶体中的相干结构：从实验和建模到计算和数学分析
DOI：
10.1007/978-3-319-77884-6
复制
发表时间：
2018
影响因子：
8.6
通讯作者：
P. Kevrekidis
中科院分区：
文献类型：
--
作者：
C. Chong;P. Kevrekidis
这本书总结了一些基本的发展，在界面上的粒状晶体和数学和计算分析的一些关键本地化的非线性波的解决方案。该主题提出了一个混合的吸引力粒状晶体作为一个原型工程测试各种不同的应用，在其相干结构的非线性物理的新奇，以及一系列的数学和计算技术来分析它们的易处理性。虽然重点是在主要的一维解决方案，如冲击波，行波，离散呼吸，讨论的模式，例如，在两个维度，链与缺陷，异质设置，和其他最近的事态发展进行了讨论的许多扩展。对这一主题的重视是由凝聚态物理学、铁电学、高能物理学和统计力学中的模型激发的，导致了数学分析、数值计算和对模型物理方面的见解的发展。这本书呼吁在该领域的研究人员，以及研究生和高级本科生。数学家、物理学家和工程师都会对它感兴趣。
This book summarizes a number of fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a blend of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, eg, in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The emphasis on the subject was motivated by models in condensed matter physics, ferroelectrics, high energy physics, and statistical mechanics, leading to developments in mathematical analysis, numerical computation and insights on the physical aspects of the model. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.