相关论文: Front Propagation at the Isotropic Nematic Transit…

We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphas. Flow 19, 589…

Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear…

We develop a long-wavelength theory for the linear stability of a flat interface between an active nematic and an isotropic fluid. Starting from a diffuse-interface Cahn--Hilliard--Landau--de Gennes description coupled to Brinkman-screened…

We investigate experimentally the dynamic phase transition of a two-dimensional active nematic layer interfaced with a passive liquid crystal. Under a temperature ramp that leads to the transition of the passive liquid into a highly…

A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank--Oseen model. The combination of both chemical and geometrical…

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…

Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…

We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…

The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…

We use direct numerical simulation to study the temporal evolution of a perturbation localized on the turbulent layer that typically separates a cloud from the surrounding clear air. Across this shearless layer, a turbulent kinetic energy…

We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the…

This study investigates the droplet coalescence mechanisms and the interplay between various thermodynamic non-equilibrium (TNE) effects under isothermal and non-isothermal conditions kinetically. The main findings include: (1) Coalescence…

We study the steady-state properties as well as the relaxation dynamics of the nonequilibrium interacting resonant level model at finite temperatures. It constitutes the prototype model of a correlated charge fluctuating quantum dot. The…

The isotropic to ferroelectric nematic liquid transition had been theoretically studied over one hundred years ago, but its experimental studies are rare. Here we present polarizing optical microscopy studies and theoretical considerations…

We investigate the Cauchy problem of three-dimensional compressible non-isothermal nematic liquid crystal flows in $\mathbb{R}^3$. We derive the global existence and uniqueness of strong solutions with both interior and far field vacuum…

Dynamics of spreading of small droplets on surfaces has been studied by the molecular dynamics method. Simulations have been performed for mixtures of solvent and dimer, and solvent and tetramer droplets. For solvent particles and dimers,…

In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…

Applying a numerical transfer-matrix formalism, we obtain complex-valued constrained free energies for the two-dimensional square-lattice nearest-neighbor Ising ferromagnet below its critical temperature and in an external magnetic field.…

We study uniaxial energy minimizers within the Landau-de Gennes theory for nematic liquid crystals, subject to dirichlet boundary conditions. Topological defects in such minimizers correspond to the zeros of the corresponding equilibrium…

A phase-field model for three-phase flows is established by combining the Navier-Stokes (NS) and the energy equations, with the Allen-Cahn (AC) and Cahn-Hilliard (CH) equations and is demonstrated analytically to satisfy the energy…