Related papers: Liquid Crystals on Deformable Surfaces
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle.…
We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal con- strained on a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural…
Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…
We study the disordered, multi-spiral solutions of two-dimensional homogeneous oscillatory media for parameter values at which the single spiral/vortex solution is fully stable. In the framework of the complex Ginzburg-Landau (CGLE)…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…
Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts.…
See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the…
Liquids in contact with solids are submitted to intermolecular forces making liquids heterogeneous and, in a mechanical model, the stress tensor is not any more spherical as in homogeneous bulks. The aim of this article is to show that a…
In this paper we study the dynamics of a layer of incompressible viscous fluid bounded below by a rigid boundary and above by a free boundary, in the presence of a uniform gravitational field. We assume that a mass of surfactant is present…
Nematic liquid crystal (LC) molecules adsorbed on two dimensional materials are aligned along the crystal directions of the hexagonal lattice. It was demonstrated that short electric pulses can reorient the aligned LC molecules in the…
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex, or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…
Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet thus encodes a pattern of contraction on heating,…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in…
A theoretical analysis is presented of a nematic liquid crystal confined between substrates pat- terned with squares that promote vertical and planar alignment. Two approaches are used to eluci- date the behavior across a wide range of…