论文标题
在定期进行的渐进调制中波浪：python教程
Waves over a periodic progressive modulation: A python tutorial
论文作者
论文摘要
本章介绍了适合于时间依赖性介质研究波传播的理论和数值工具的选择。重点是一维弹簧质链，其属性在时空和时间上以周期性的方式调节。本章是为初学者以及理论上倾斜的数字经验家编写的。因此，只要有可能，部署的理论就会进行数值动机和利用，例如模拟的代码是用Python编写的。本章首先是使用Monodromy Matrix介绍Mathieu方程及其稳定性分析。然后追求对具有多个自由度的系统的概括。调制的渐进特征导致单构矩阵的分解，并提供了“变量的离散变化”，否则仅适用于连续系统。此外，分解允许降低分散图和长期行为的计算复杂性。选定的模拟说明了非股展的显着特征，例如在传播波的速度和力量中强烈的左右偏见。
This chapter presents a selection of theoretical and numerical tools suitable for the study of wave propagation in time-dependent media. The focus is on one-dimensional spring-mass chains whose properties are modulated in space and time in a periodic progressive fashion. The chapter is written for the uninitiated newcomer as well as for the theoretically inclined numerical empiricist. Thus, whenever possible, deployed theory is motivated and exploited numerically, and code for example simulations is written in python. The chapter begins with an introduction to Mathieu's equation and its stability analysis using the monodromy matrix; generalizations to systems with multiple degrees of freedom are then pursued. The progressive character of the modulation leads to a factorization of the monodromy matrix and provides a "discrete change of variables" otherwise only available for continuous systems. Moreover, the factorization allows to reduce the computational complexity of dispersion diagrams and of long term behaviors. Chosen simulations illustrate salient features of non-reciprocity such as strong left-right biases in the speed and power of propagated waves.
