Dynamic Statistical Scaling in the Landau-de Gennes Theory of Nematic Liquid Crystals

被引：10

作者：

Kirr, Eduard ^{[1
]}

Wilkinson, Mark ^{[2
]}

Zarnescu, Arghir ^{[3
]}

机构：

[1] Univ Illinois, Dept Math, Champaign, IL 61820 USA

[2] Ecole Normale Super, Dept Math & Applicat, F-75231 Paris, France

[3] Univ Sussex, Dept Math, Brighton, E Sussex, England

来源：

JOURNAL OF STATISTICAL PHYSICS | 2014年 / 155卷 / 04期

关键词：

Asymptotics of dynamics; Heat equation; Landau-de Gennes theory; Self-similarity; Statistical solutions of evolution equations; DIFFUSION; EQUATIONS;

D O I：

10.1007/s10955-014-0970-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this article, we investigate the long time behaviour of a correlation function which is associated with a nematic liquid crystal system that is undergoing an isotropic-nematic phase transition. Within the setting of Landau-de Gennes theory, we confirm a hypothesis in the condensed matter physics literature on the average self-similar behaviour of this correlation function in the asymptotic regime at time infinity, namely parallel to c(mu 0)(r, t) - e(-[r]2/8t)parallel to(L infinity(R3,dr)) = O(t(-1/2)) as t -> infinity. In the final sections, we also pass comment on other scaling regimes of the correlation function.

引用

页码：625 / 657

页数：33