Related papers: Growth Kinetics in the $\Phi ^6$ N-Component Model…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
We discuss the possibility of the spontaneous symmetry breaking characterized by order parameters with higher dimensionful composite fields. By analyzing general Ginzburg-Landau potential for a complex scalar field \phi=\phi_1 + i \phi_2…
We consider the large-N $\Phi^4$ theory with spontaneously broken symmetry at finite temperature. We study, in the large-N limit, quantum states which are characterized by a time dependent, spatially homogenous expectation value of one of…
We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in…
We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with and 4 on graphs. By means of extensive simulations, we show that the global pattern of scaling behaviours is analogous to the one…
A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized…
We numerically study the metastable states of the 2d Potts model. Both of equilibrium and relaxation properties are investigated focusing on the finite size effect. The former is investigated by finding the free energy extremal point by the…
We study phase ordering dynamics in the three-dimensional nonconserved XY model, via Monte Carlo simulations, for quenches from paramagnetic phase to certain final temperatures $T_f$ within the ferromagnetic region of the phase diagram. The…
A Ginzburg-Landau model for the macroscopic behaviour of a shape memory alloy is proposed. The model is one-dimensional in essence, in that we consider the effect of the martensitic phase transition in terms of a uniaxial deformation along…
This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved…
The influence of the initial fluctuations on the onset of scaling in the quench to zero temperature of a two dimensional system with conserved order parameter, is analyzed in detail with and without topological defects. We find that the…
Results for the late-time regime of phase ordering in three dimensions are reported, based on numerical integration of the time-dependent Ginzburg-Landau equation with nonconserved order parameter at zero temperature. For very large systems…
The $\phi^4$ model has been the "workhorse" of the classical Ginzburg--Landau phenomenological theory of phase transitions and, furthermore, the foundation for a large amount of the now-classical developments in nonlinear science. However,…
This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed,…
The order parameter correlation function of the nonconserved, continuum $q$-state clock model is evaluated in the asymptotic scaling limit, during the phase ordering process after a temperature quench. The short distance behavior of the…
We study analytically the aging dynamics of the O(n) model in the large-n limit, with conserved and with non-conserved order parameter. While in the non-conserved dynamics, the autocorrelation function scales in the usual way C(t,tw) =…
We study the nonequilibrium dynamics of the $q$-state Potts model following a quench from the high temperature disordered phase to zero temperature. The time dependent two-point correlation functions of the order parameter field satisfy…
The quench dynamics of systems exhibiting cooperative or almost competitive orders in equilibrium are explored using Ginzburg-Landau theory plus fluctuations. We show that when the renormalization of the free energy by fluctuations is taken…
The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical…
We present a comprehensive picture of (non-critical) domain growth in model C systems where a non-conserved scalar order parameter is coupled to a conserved concentration field. For quenches into the region where the ordered and disordered…