Dissipation, surface energy and defects

1997 ◽  
Vol 8 (3) ◽  
pp. 301-310 ◽  
Author(s):  
M. CARME CALDERER
Keyword(s):  
Liquid Crystals ◽  
Surface Energy ◽  
Layered Structure ◽  
Poiseuille Flow ◽  
Nematic Liquid Crystals ◽  
Gradient Flows ◽  
Flow Problems ◽  
Constant Gradient

A model for Poiseuille flow of nematic liquid crystals is examined where a layered structure of defects parallel to the flow is present. Constant gradient flows are discussed, together with symmetric and chevron configurations for such flow problems.

Ondes de surface dans les cristaux liquides smectiques et cholestériques

1975 ◽  
Vol 53 (10) ◽  
pp. 968-975 ◽  
Author(s):  
Albert Rapini
Keyword(s):  
Free Surface ◽  
Liquid Crystals ◽  
Diffusion Process ◽  
Layered Structure ◽  
Elastic Energy ◽  
Nematic Liquid Crystals ◽  
Simple Liquids ◽  
Theoretical Predictions ◽  
Surface Fluctuation

Theoretical predictions are given concerning the spectrum of the free surface fluctuation modes in liquid crystals such as smectics and cholesterics. We find drastic differences with simple liquids and nematic liquid crystals. These differences came from two new properties: the elastic energy associated with the layered structure and the permeation, that is the diffusion process of the fluid through the layers.

scholarly journals Sphere-valued harmonic maps with surface energy and the K13 problem

2019 ◽  
Vol 12 (4) ◽  
pp. 363-392
Author(s):  
Stuart Day ◽  
Arghir Dani Zarnescu
Keyword(s):  
Liquid Crystals ◽  
Surface Energy ◽  
Boundary Conditions ◽  
Critical Point ◽  
Partial Regularity ◽  
Harmonic Maps ◽  
Nematic Liquid Crystals ◽  
Energy Functional ◽  
Dirichlet Energy ◽  
Surface Term

AbstractWe consider an energy functional motivated by the celebrated {K_{13}} problem in the Oseen–Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an additional surface term. It is known that this energy is unbounded from below and our aim has been to study the local minimisers. We show that even having a critical point in a suitable energy space imposes severe restrictions on the boundary conditions. Having suitable boundary conditions makes the energy functional bounded and in this case we study the partial regularity of the global minimisers.

Poiseuille flow of nematic liquid crystals

2000 ◽  
Vol 38 (9-10) ◽  
pp. 1007-1022 ◽  
Author(s):  
M.Carme Calderer ◽  
Chun Liu
Keyword(s):  
Liquid Crystals ◽  
Poiseuille Flow ◽  
Nematic Liquid Crystals

Surface Energy for Nematic Liquid Crystals: A New Point of View

1992 ◽  
Vol 47 (12) ◽  
pp. 1235-1240 ◽  
Author(s):  
A. L. Alexe-Ionescu ◽  
R. Barberi ◽  
G. Barbero ◽  
T. Beica ◽  
R. Moldovan
Keyword(s):  
Liquid Crystals ◽  
Surface Energy ◽  
Order Parameter ◽  
Nematic Liquid Crystals ◽  
Point Of View ◽  
Tensor Order ◽  
Tensor Order Parameter ◽  
Surface Tensor ◽  
The One ◽  
Phenomenological Point

The surface energy of nematic liquid crystals is deduced from a phenomenological point of view. The idea of an easy surface tensor order parameter is proposed. An expression similar to a Landau expansion for the free energy of a system characterized by two order parameters is deduced and analysed. An interpretation similar to the one usually accepted for magnetic materials is given. The possibility of surface transitions induced by temperature is discussed.

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