Short-wavelength instability in systems with slow long-wavelength dynamics.
Short-wavelength instability in systems with slow long-wavelength dynamics.
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长波长动力学缓慢的系统中的短波长不稳定性。
DOI：
10.1103/physreve.54.4973
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Velarde
中科院分区：
文献类型：
--
作者：
Tribelsky;Velarde
本文研究了一维空间均匀态的短波不稳定性。假设均匀态k的微扰谱有一个长波长的慢弛豫分支，它与波数为零的中性稳定Goldstone模分离，它的存在是问题对称性的结果。这个问题的另一个重要特征是二次非线性，它提供了缓慢变化的短波长和长波长模式之间的耦合。结果表明，这种情况下的特点是混合不同的尺度在微扰计算。后者使得模式稳定性问题本质上是非局部的，并且对谱k和非线性模式耦合的非常微妙的特性敏感。作为这种系统的最简单的特例，详细研究了粘弹性介质中的纵向地震波方程。所获得的结果可能扩展到其他物理问题，包括电对流在一个垂直排列的胆甾类药物或smectics在毛细管中的渗透，进行了讨论。S1063-651X9611910-3
One-dimensional systems undergoing short-wavelength instability of spatially uniform states are studied. It is assumed that the spectrum of perturbations of the uniform states k has a long-wavelength slowly-relaxing branch, detaching from a neutrally stable Goldstone mode with zero wave number, whose existence is a consequence of the problem’s symmetry. The other important feature of the problem is quadratic nonlinearity that provides coupling between slowly-varying short-wavelength and long-wavelength modes. It is shown that the case is characterized by mixing of different scales in perturbative calculations. The latter makes the pattern stability problem essentially nonlocal and sensitive to very subtle characteristics of the spectrum k and nonlinear mode-coupling. The equation governing longitudinal seismic waves in viscoelastic media is studied in detail as the simplest particular example of such systems. Possible extension of the obtained results to other physical problems, including electroconvection in a homeotropically aligned nematic layer and permeation of cholesterics or smectics in capillaries, is discussed. S1063-651X9611910-3