Dissipative solitons in reaction diffusion systems
Dissipative solitons in reaction diffusion systems
复制标题
反应扩散系统中的耗散孤子
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Liehr
中科院分区：
文献类型：
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作者：
A. Liehr
自然科学的一个主要目标是了解各种物理、化学、生物和其他系统中空间延伸模式的形成。在许多情况下，根据某些空间定位良好的基本模式（我们可以称为“粒子”）的叠加来解释所考虑的整体模式是有利的。在最简单的情况下，所有这些粒子都是同一类型，并且扩展图案的复杂行为可以用粒子的简单个体属性及其相互作用来描述。这种方法的一个明显的说明性例子是原子的概念。在这种情况下，基本图案或粒子是原子，而复杂的空间延伸图案是例如晶体。从理论角度来看，图案形成系统由具有无限多个自由度的场方程来描述。然而，描述其时间演化的一种强大技术是使用“粒子方法”。在这种方法中，场方程的良好局部解被视为粒子。这些粒子的动态行为和相互作用由常微分方程描述，使用质心坐标和可能的一些其他变量。这种方法的决定性优势在于，具有无限多个自由度的基础场方程可以简化为具有有限且可能少量自由度的阶次参数方程，而不会丢失重要信息。原子的概念是一个极其强大且影响深远的应用。我们记得，宏观物理系统可以根据其长期行为分为两类。一类接近热力学平衡，导致与周围环境的能量交换消失。第二类的特点是外部驱动“力”，导致有限的能量转移到系统，相应地，从长远来看，导致有限的耗散。对于第一类系统，已经开发出了寻找物理解决方案的通用技术。热力学平衡的系统可以用热力学势来描述，必须找到其中的绝对值
A major goal of natural science is to understand the formation of spatiallyextended patterns in all kinds of physical, chemical, biological and other systems. In many cases, it is advantageous to interpret the overall pattern under consideration in terms of a superposition of certain spatially well-localized elementary patterns that we may refer to as “particles”. In the simplest case, all these particles are of the same kind and the complex behavior of the extended pattern can be described in terms of simple individual properties of the particles and their interaction. A clear illustrative example for this approach is the concept of atoms. In this case, the elementary pattern or particle is the atom and the complex spatially-extended pattern is, e.g., the crystal. From a theoretical point of view, pattern forming systems are described by field equations with infinitely many degrees of freedom. However, a powerful technique for describing their temporal evolution is to use a “particle approach”. In this approach, well-localized solutions of the field equation are viewed as particles. The dynamic behavior and the interaction of these particles are described by ordinary differential equations, using center-of-mass co-ordinates and possibly some other variables. The decisive advantage of such an approach is that the underlying field equations, with infinitely many degrees of freedom, can be reduced to order-parameter equations with a finite and possibly small number of degrees of freedom, without losing the important information. An extremely powerful and far-reaching application is the notion of atoms. We recall that macroscopic physical systems can be separated into two classes, according to their long-time behavior. One class approaches thermodynamic equilibrium, resulting in a vanishing exchange of energy with the surroundings. The second class is characterized by external driving “forces” which lead to a finite energy transfer to the system, and, correspondingly, to a finite dissipation in the long run. For the first class of systems, general techniques to find physical solutions have been developed. Systems in thermodynamic equilibrium can be described by a thermodynamic potential, of which one has to find the absolute