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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…
The incompressible Navier-Stokes equations currently represent the primary model for describing stratified turbulent fluid flows at low Mach number. The validity of the incompressible assumption, however, has so far only been rigorously…
We discuss in this short note the local-in-time strong well-posedness of the compressible Navier-Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, M\'{a}cha, and…
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…
We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in…
We construct global smooth solutions to the incompressible Navier--Stokes equations in $\mathbb{R}^3$ for initial data in $L^2$ satisfying some smallness condition. The high-frequency part is assumed to be small in $BMO^{-1}$, while the…
In this paper, we consider the model describing viscous incompressible liquid crystal flows, called the Beris-Edwards model, in the half-space.This model is a coupled system by the Navier-Stokes equations with the evolution equation of the…
We study the immersion of a ferromagnetic nanowire within a nematic liquid crystal using a lattice Boltzmann algorithm to solve the full three-dimensional equations of hydrodynamics. We present an algorithm for including a moving boundary,…
In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for…
In spite of the large number of papers appeared in the past which are devoted to the lattice Boltzmann (LB) methods, basic aspects of the theory still remain unchallenged. An unsolved theoretical issue is related to the construction of a…
We derive the Schwinger-Keldysh effective field theories for diffusion including the lowest non-hydrodynamic degree of freedom from holographic Gubser-Rocha systems. At low temperature the dynamical non-hydrodynamic mode could be either an…
This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the…
Consider the (simplified) Leslie-Erickson model for the flow of nematic liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$. This article develops a complete dynamic theory for these equations, analyzing the system…
An interesting issue in fluid dynamics is represented by the possible existence of inverse kinetic theories (IKT) which are able to deliver, in a suitable sense, the complete set of fluid equations which are associated to a prescribed…
We introduce several new models whose common feature is to take into account effects from topological vorticity. The macroscopic unknown is driven by a dissipative anomalous diffusion (of SQG-type) and is coupled with the orientation of the…
The paramagnetic phase of the two-channel Kondo lattice model is examined with a Quantum Monte Carlo simulation in the limit of infinite dimensions. We find non-Fermi-liquid behavior at low temperatures including a finite low-temperature…
The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved…
A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng equations for the evolution of the velocity and tensor order-parameter…
In this paper, we consider the numerical approximations for a hydrodynamical model of smectic-A liquid crystals. The model, derived from the variational approach of the modified Oseen-Frank energy, is a highly nonlinear system that couples…