Related papers: Ordering kinetics of stripe patterns
The growth of striped order resulting from a quench of the two-dimensional Swift-Hohenberg model is studied in the regime of a small control parameter and quenches to zero temperature. We introduce an algorithm for finding and identifying…
Spatio-temporal pattern formation in complex systems presents rich nonlinear dynamics which leads to the emergence of periodic nonequilibrium structures. One of the most prominent equations for the theoretical and numerical study of the…
The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of…
We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or…
We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very…
We introduce a model for describing the defected growth of striped patterns. This model, while roughly related to the Swift-Hohenberg model, generates a quite different mixture of defects during phase ordering. We find two characteristic…
We study the coarsening of two-dimensional smectic polycrystals characterized by grains of oblique stripes with only two possible orientations. For this purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close enough…
We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we analyze how the orientation of stripes changes depending on…
We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic…
The dynamical mechanisms underlying the grain evolution and growth are of fundamental importance in controlling the structural properties of large-scale polycrystalline materials, but the effects of lattice ordering and distinct atomic…
We have studied the ordering kinetics of a two-dimensional anisotropic Swift-Hohenberg (SH) model numerically. The defect structure for this model is simpler than for the isotropic SH model. One finds only dislocations in the aligned…
The dynamics of dislocations confined to grain boundaries in a striped system are studied using electroconvection in the nematic liquid crystal N4. In electroconvection, a striped pattern of convection rolls forms for sufficiently high…
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in…
We study stripe formation in two-dimensional systems under directional quenching in a phase-diffusion approximation including non-adiabatic boundary effects. We find stripe formation through simple traveling waves for all angles relative to…
A characterization of textured patterns, referred to as the disorder function \bar\delta(\beta), is used to study properties of patterns generated in the Swift-Hohenberg equation (SHE). It is shown to be an intensive,…
Numerical simulations of the time-dependent Swift-Hohenberg equation are used to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that Rayleigh-Benard convection in the form of straight rolls or of an array of dislocations may…
We study the phase-ordering kinetics of the one-dimensional Heisenberg model with conserved order parameter, by means of scaling arguments and numerical simulations. We find a rich dynamical pattern with a regime characterized by two…
We describe numerical solutions of two non potential models of pattern formation in nonequilibrium systems to address the motion and decay of grain boundaries separating domains of stripe configurations of different orientations. We first…
Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical and biological media and to macro-scale vegetation and cloud patterns. Their…
We study kinetic theories for isotropic, two-dimensional grain boundary networks which evolve by curvature flow. The number densities $f_s(x,t)$ for $s$-sided grains, $s =1,2,\ldots$, of area $x$ at time $t$, are modeled by kinetic…