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Strict/Uniform Physicality of a Gradient Flow Generated by the Anisotropic Landau-de Gennes Energy with a Singular Potential

When: 

Oct 15, 2019 - 10:00am to 11:00am

Where: 

Rettaliata Engineering Center, Room 122

Speaker: 

Xiang Xu
Department of Mathematics & Statistics, Old Dominion University

Description: 

We study a gradient flow generated by the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the Q-tensor space. This free energy density functional is composed of three quadratic terms as the elastic energy density part, and a singular potential in the bulk part that is considered as a natural enforcement of a physical constraint on the eigenvalues of Q. Specifically, we give a rigorous proof that if initially the Q-tensor is physical (with the free energy possibly being infinite), then it immediately becomes strictly physical as time evolves, and it becomes uniformly physical at all large times.

Event Type: 

Department of Applied Mathematics - Stochastic & Multiscale Modeling and Computation Seminar