Continuum approach to discreteness.
Continuum approach to discreteness.
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DOI：
10.1103/physreve.65.046613
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发表时间：
2002-04
期刊：
影响因子：
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通讯作者：
P. Kevrekidis;I. Kevrekidis;A. Bishop;E. Titi
中科院分区：
文献类型：
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作者：
P. Kevrekidis;I. Kevrekidis;A. Bishop;E. Titi
我们研究的解析和数值连续模型的基础上Padé近似及其有效性建模空间离散系统。我们不仅分析可以通过这些连续体方法捕获的时间动态的特征（例如，形状振荡，辐射效应和捕获），但也指出了那些不能被捕获（如Peierls-Nabarro障碍和布洛赫振荡）。我们分析了这种方法在提供一个有效的“均匀化”的空间离散，以及异质连续方程的作用。最后，我们开发了数值方法来解决这些方程，并使用它们来建立这些连续近似的有效性范围，以及与其他连续近似比较。
We study analytically and numerically continuum models derived on the basis of Padé approximations and their effectiveness in modeling spatially discrete systems. We not only analyze features of the temporal dynamics that can be captured through these continuum approaches (e.g., shape oscillations, radiation effects, and trapping) but also point out ones that cannot be captured (such as Peierls-Nabarro barriers and Bloch oscillations). We analyze the role of such methods in providing an effective "homogenization" of spatially discrete, as well as of heterogeneous continuum equations. Finally, we develop numerical methods for solving such equations and use them to establish the range of validity of these continuum approximations, as well as to compare them with other semicontinuum approximations.