Related papers: Phase Transition With Rapini-Papoular Surface Anch…
We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes equation for the fluid velocity with a transported heat flow…
We study critical properties of the relaxation time at a threshold point in switching processes between bistable states under change of external fields. In particular, we investigate the relaxation processes near the spinodal point of the…
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…
We investigate existence and regularity of weak solutions of a 1-dimensional parabolic differential equation with a non-constant H\"older diffusion coefficient and a rough forcing term. Such an equation appears in studying the 1-dimensional…
By means of a molecular model, we examine hybrid nematic films with antagonistic anchoring angles where one of the surfaces is in the strong anchoring regime. If anchoring at the other surface is weak, and in the absence of wetting by the…
A nonlinear model due to Soddemann et al. [37] and Stewart [38] describing incompressible smectic-A liquid crystals under flow is studied. In comparison to previously considered models, this particular model takes into account possible…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
We discuss the generalization of a classical problem involving an $N$-step ideal polymer adsorption at a sticky boundary (potential well of depth $U$). It is known that as $N$ approaches infinity, the path undergoes a 2nd-order localization…
Lamellar or smectic phases often have an intricate intralamellar structure that remains scarcely understood from a microscopic viewpoint. In this work, we use molecular dynamics simulations to study the effect of volume exclusion and…
We present the linear theory of two-dimensional incompressible magneto-Rayleigh-Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and…
In search for novel nematic materials, a laterally linked H-shaped liquid crystal dimer have been synthesized and characterized. The distinct feature of the material is a very broad temperature range (about 50 oC) of the nematic phase,…
We clarify topology of $^3P_2$ superfluids which are expected to be realized in the inner cores of neutron stars and cubic odd-parity superconductors. $^3P_2$ phases include uniaxial/biaxial nematic phases and nonunitary ferromagnetic and…
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a…
In this paper, we study the long-time behavior of full Ericksen-Leslie system modeling the hydrodynamics of nematic liquid crystals between two dimensional unit spheres. Under a weaker assumption for Leslie's coefficients, we give the key…
Space-filling assemblies of athermal hydrophobic particles floating at an air-water interface, called particle rafts, are shown to undergo an unusual phase transition between two i.e., a low density `less-rigid and a high density…
By Monte Carlo simulations of a soft ellipsoid model for liquid crystals, we study whether a layer of grafted liquid-crystalline chain molecules can induce tilt in a nematic fluid. The chains are fairly short (four monomers) and made of the…
We consider the dynamics of a layer of an incompressible electrically conducting fluid interacting with the magnetic field in a two-dimensional horizontally periodic setting. The upper boundary is in contact with the atmosphere, and the…
For any bounded smooth domain $\Omega\subset\mathbb R^3$, we establish the global existence of a weak solution $u:\Omega\times (0,+\infty)\to\mathbb R^3\times\mathbb S^2$ of the initial-boundary value (or the Cauchy) problem of the…
This paper presents a mathematical analysis of the evolution of a mixture of two incompressible, isothermal fluids flowing through a porous medium in a three dimensional bounded domain. The model is governed by a coupled system of…
The glass transition can simply be viewed as the point at which the viscosity of a structurally disordered liquid reaches 10^{13} Poise [1]. This definition is operational but it sidesteps fundamental controversies about the glass: Is the…