Related papers: Function spaces for liquid crystals
This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global…
Some recent analytical papers have explored limiting behaviors of Landau-deGennes models for liquid crystals in certain extreme ranges of the model parameters: limits of "vanishing elasticity" (in the language of some of these papers) and…
Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the…
We use nematic Multi-particle Collision Dynamics (N-MPCD) simulations to study confined nematic liquid crystals in square domains, with three distinct mean-field potentials: the classical Maier-Saupe and Marrucci-Greco models, and a more…
A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows.…
We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in the co-rotational…
We present a lattice Boltzmann algorithm for liquid crystal hydrodynamics. The coupling between the tensor order parameter and the flow is treated consistently allowing investigation of a wide range of non-Newtonian flow behavior. We…
We investigate the local structural fluctuations of a model equilibrium fluid with an aim of better understanding the structural basis of locally heterogeneous dynamics identified in recent simulations and experimental studies of…
A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
In the Landau-de Gennes theory on nematic liquid crystals, the well-known Landau-de Gennes energy depends on four elastic constants; $L_1$, $L_2$, $L_3$, $L_4$. For the general case of $L_4\neq 0$, Ball-Majumdar \cite {BM} found an example…
In this paper we prove the existence of global in time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible…
We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by…
The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…
Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the…
We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order…
We present a large-scale (36000-particle) computational study of the "inherent structures" (IS) associated with equilibrium, two-dimensional, one-component Lennard-Jones systems. Our results provide strong support both for the…
In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…
Riemann's non-differentiable function is one of the most famous examples of continuous but nowhere differentiable functions, but it has also been shown to be relevant from a physical point of view. Indeed, it satisfies the Frisch-Parisi…