Related papers: Three-dimensional pattern formation, multiple homo…
The effect of superimposed ac and dc electric fields on the formation of electroconvection and flexoelectric patterns in nematic liquid crystals was studied. For selected ac frequencies an extended standard model of the electro-hydrodynamic…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
Patterns are quotidian in nature. Distinct multiscale patterns are generally a consequence of nonequilibrium dynamical processes associated with mechanical or hydrodynamic instabilities. In this thesis, I report experimental investigations…
The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
We construct a new hydrodynamic framework describing plastic deformations in electronic crystals. The framework accounts for pinning, phase, and momentum relaxation effects due to translational disorder, diffusion due to the presence of…
Molecular dynamics simulation has been used to model pattern formation in three-dimensional Rayleigh--Benard convection at the discrete-particle level. Two examples are considered, one in which an almost perfect array of hexagonally-shaped…
Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly…
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The…
One of the most interesting phenomena in the soft-matter realm consists in the spontaneous formation of super-molecular structures (microphases) in condition of thermodynamic equilibrium. A simple mechanism responsible for this…
The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal…
We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
We formulate a theory of dissipative hydrodynamics with spontaneously broken translations, describing charge density waves in a clean isotropic electronic crystal. We identify a novel linear transport coefficient, lattice pressure,…
The main objective of this paper is to describe the dynamic transition of the incompressible MHD equations in a three dimensional (3D) rectangular domain from a perspective of pattern formation.
In this work we consider bubbles that can form spontaneously when a two-dimensional (2D) crystal is transferred to a substrate with gases or liquids trapped at the crystal-substrate interface. The underlying mechanics may be described by a…
From microactuators to biological tissues, non-porous materials with the ability to strongly expand when in contact with a solvent are ubiquitous. Consequently, the swelling of polymer systems such as hydrogel has received recently much…
For the first time the electrohydrodynamic convection (EHC) of nematic liquid crystals is studied via fully nonlinear simulation. As a system of rich pattern-formation the EHC is mostly studied with negative nematic liquid crystals…
Three-dimensional double-diffusive convection in a horizontally infinite layer of an uncompressible fluid interacting with horizontal vorticity field is considered in the neighborhood of Hopf bifurcation points. A family of amplitude…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…