Showing papers by "Chun Liu published in 2002"
TL;DR: In this article, the numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen-Leslie equations is considered and convergence results for this system rely crucially upon energy estimates which involve H2 (Ω) norms of the director field.
Abstract: The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve H2 (Ω) norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
58 citations
TL;DR: In this paper, the authors consider the phenomenology of the transition between chiral nematic and smectic A liquid crystal phases and discuss the behavior of the material constants within the present mathematical framework, the physically observed growth behavior of twist and bend Frank constants, K2 and K3 respectively, plays a major role in determining the transition regime.
Abstract: In this paper we study the Landau-de Gennes free energy used to describe the transition between chiral nematic and smectic A liquid crystal phases. We consider the phenomenology of the transition and discuss the behavior of the material constants. Within the present mathematical framework, the physically observed growth behavior of the twist and bend Frank constants, K2 and K3 respectively, plays a major role in determining the transition regime. We show existence of minimizers in a large class of admissible fields. Then, under the hypothesis that K2 and K3 are large, we establish estimates for the transition regime separating the two phases. The work emphasizes the interplay between two competing effects: the layer formation of the smectic A phase and the twist tendency of the chiral nematic phase. Our discussion also illustrates the analogies as well as the discrepancies in modeling and behavior between smectic A* liquid crystals and superconducting materials described by the Ginzburg-Landau theory.
35 citations
TL;DR: An evolution system, describing the time-dependent behavior of nematic liquid crystals with variable degree of orientation within the continuum model of Ericksen, is considered and a dissipation relation is established that proves both the global existence of weak solutions and the local existence of classical solutions.
Abstract: We consider an evolution system, describing the time-dependent behavior of nematic liquid crystals with variable degree of orientation within the continuum model of Ericksen. We establish a dissipation relation and prove both the global existence of weak solutions and the local existence of classical solutions. Furthermore, we investigate the stability and long-time behavior of solutions and obtain an exact solution of the corresponding stationary system in a one-dimensional case.
32 citations
TL;DR: The Doi kinetic theory is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential and is proven to be well posed in that it warrants a positive entropy production and thereby the second law of thermodynamics.
Abstract: The Doi kinetic theory for flows of homogeneous, rodlike liquid crystalline polymers (LCPs) is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential. The theory features (i) a nonlocal, anisotropic, effective intermolecular potential in an integral form that is consistent with the chemical potential, (ii) short-range elasticity as well as long-range isotropic and anisotropic elasticity, (iii) a closed-form stress expression accounting for the nonlocal molecular interaction, and (iv) an extra elastic body force exclusively associated with the integral form of the intermolecular potential. With the effective intermolecular potential, the theory is proven to be well posed in that it warrants a positive entropy production and thereby the second law of thermodynamics. Approximate theories are obtained by gradient expansions of the number density function in the free energy density.
30 citations
10 citations