Related papers: Defect Relaxation and Coarsening Exponents
We theoretically and numerically investigate a two-dimensional O(2) model where an order parameter is convected by shear flow. We show that a long-range phase order emerges in two dimensions as a result of anomalous suppression of phase…
Numerical simulations of phase ordering under dissipative dynamics in a (2+1)-dimensional 3-vector model with O(3) symmetry are reported. The energy functional includes terms which stabilize the size of extended topological defects. They…
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
The basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large $N$ model through the exact separation of the order parameter into the sum of thermal and condensation…
In the conceptual framework of phase ordering after temperature quenches below transition, we consider the underdamped Bales-Gooding-type 'momentum conserving' dynamics of a 2D martensitic structural transition from a square-to-rectangle…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in…
We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by…
Systems far from equilibrium approach stability slowly due to "anti-mixing" characterized by regions of the phase-space that remain disconnected after prolonged action of the flow. We introduce the Optimal Growth Mode (OGM) to capture this…
This Article is a brief review of coarsening phenomena occurring in systems where quenched features - such as random field, varying coupling constants or lattice vacancies - spoil homogeneity. We discuss the current understanding of the…
We investigate, via numerical simulations, the phase ordering kinetics of a two- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible mode cou- pling is included via the conserved conjugate momentum of the spin order parameter…
Understanding the relaxation of a system towards equilibrium is a longstanding problem in statistical mechanics. Here we address the role of long-range interactions in this process by considering a class of two-dimensional or geophysical…
We find a breakdown of the critical dynamic scaling in the coarsening dynamics of an antiferromagnetic {\em XY} model on the kagome lattice when the system is quenched from disordered states into the Kosterlitz-Thouless ({\em KT}) phases at…
A consistent perturbation theory expansion is presented for phase-ordering kinetics in the case of a nonconserved scalar order parameter. At zeroth order in this expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At…
We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of…
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…
A consistent perturbation theory expansion is presented for phase ordering kinetics in the case of a nonconserved scalar order parameter. At lowest order in this formal expansion one obtains the theory due to Ohta, Jasnow and Kawasaki…
Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to…
We investigate the nonequilibrium coarsening dynamics in two-dimensional overdamped superconducting arrays under zero external current, where ohmic dissipation occurs on junctions between superconducting islands through uniform resistance.…