Related papers: Equivalent theories of liquid crystal dynamics
We study the global existence of weak solutions to a multi-dimensional simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain $\Omega\subset \mathbb{R}^N$, where N=2…
For any smooth domain $\Omega\subset \mathbb{R}^3$, we establish the existence of a global weak solution $(\mathbf{u},\mathbf{d}, \theta)$ to the simplified, non-isothermal Ericksen-Leslie system modeling the hydrodynamic motion of nematic…
The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of…
We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all…
Successful realization of ferromagnetic nematic liquid crystals has opened up the possibility to experimentally study a completely new set of fundamental physical phenomena. In this contribution we present a detailed investigation of some…
In this note we prove the existence and uniqueness of local maximal smooth solution of the stochastic simplified Ericksen-Leslie systems modelling the dynamics of nematic liquid crystals under stochastic perturbations.
Ericksen and Leslie established a theory to model the flow of nematic liquid crystals. This paper is devoted to the Cauchy Problem of a simplified version of their system, which retains most of the properties of the original one. We…
If a static perturbation is applied to a liquid crystal, the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, one might ask: Does the director configuration change to minimize any…
We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight…
We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is…
Expressions are obtained for force and couple densities and stress tensors in macroscopic models for nematic liquid crystals subjected to electric fields. The coupling between the liquid crystal orientational properties and the electric…
We investigate, numerically, the effects of externally imposed material flows on the structure and temporal evolution of liquid crystal skyrmions. The dynamics of a 2D system of skyrmions is modeled using the Ericksen-Leslie theory, which…
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified…
The exchange of mass, momentum and energy between a membrane of liquid crystal and its surroundings of stokesian fluids is added to the dynamic equations of membranes which were deduced from the Ericksen-Leslie's theory of liquid crystals…
We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three…
This paper establishes the global well-posedness and long-time dynamics of the general Ericksen--Leslie system for isotropic nematic liquid crystals under a constant magnetic field. On the two-dimensional torus $\mathbb{T}^2$, a liquid…
Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analysed. We derive the thin-film Ericksen-Leslie equations that govern…
In this work, we study the Cauchy problem of Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of two partial differential equations: One is a quasi-linear wave equation for the…
Recent numerical simulations of lid-driven cavity flow of a nematic liquid crystal have found dynamical behavior where topological defects rotate about the center of the fluid vortex induced by the lid motion. By considering a simpler…
Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting from this model, we use a Poisson-bracket formalism to derive the equations governing the dynamics of nematic liquid crystals. We treat the spin angular momentum…