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

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• 作者：Eduard Kirr (1)
  Mark Wilkinson (2)
  Arghir Zarnescu (3)
  
• 关键词：Asymptotics of dynamics ; Heat equation ; Landau–de Gennes theory ; Self ; similarity ; Statistical solutions of evolution equations
• 刊名：Journal of Statistical Physics
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：155
• 期：4
• 页码：625-657
• 全文大小：378 KB
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• 作者单位：Eduard Kirr (1)
  Mark Wilkinson (2)
  Arghir Zarnescu (3)
  
  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Champaign, IL, USA
  2. Département de Mathématiques et Applications, école Normale Supérieure, Paris, France
  3. Department of Mathematics, University of Sussex, Brighton, UK
  
• ISSN：1572-9613

文摘

In this article, we investigate the long time behaviour of a correlation function $c_{\mu _{0}}$ 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 $$\begin{aligned} \left\| c_{\mu _{0}}(r, t)-e^{-\frac{|r|^{2}}{8t}}\right\| _{L^{\infty }(\mathbb {R}^{3}, \,dr)}=\mathcal {O}(t^{-\frac{1}{2}}) \quad \mathrm as \quad t\longrightarrow \infty . \end{aligned}$$ In the final sections, we also pass comment on other scaling regimes of the correlation function.