Nematodynamics and random homogenization

Abstract

We study the homogenization problem for the system of equations of dynamics of a mixture of liquid crystals with random structure. We consider a simplified form of the Ericksen–Leslie equations for an incompressible medium with inhomogeneous density with random structure. Under the assumption that randomness is statistically homogeneous and ergodic, we construct the limit problem and prove almost sure convergence of solutions of the original problem to the solution of the limit (homogenized) problem.

Keywords:

• liquid crystals
• Ericksen–Leslie equations
• nematodynamics
• random homogenization
• director field
• speed of propagation

AMS Subject Classifications:

• 76A15
• 35K61
• 35A01
• 35A02

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

GAC, TPC was partially supported by RFBR [grant number 15-01-07920] and MSR was partially supported by RFBR [grant number 15-01-00838]. TSR was partially supported by NCCR SwissMAP and grant 200020-126630, both from the Swiss National Science Foundation. The final version of the paper was completed in Lausanne during March 2015. GAC thanks the Bernoulli Center of École Polytechnique Fédérale de Lausanne for the support.