Related papers: Phase Separation Kinetics in a Model with Order-Pa…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier--Stokes equations, nonlinearly…
A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We…
We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only…
We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and…
We elucidate the effects of chiral quenched disorder on the scaling properties of pure systems by considering a reduced model that is a variant of the quenched disordered cubic anisotropic O(N) model near its second order phase transition.…
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…
We consider a phenomenological continuum model for an active nematic fluid and show a universal, model independent, instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools…
We extend the early time ordering theory of Cahn, Hilliard, and Cook (CHC) so that our generalized theory applies to solid-to-solid transitions. Our theory involves spatial symmetry breaking (the initial phase contains a symmetry not…
Phase separation dynamics with an initially non-uniform concentration are studied. Critical and off-critical behavior is observed simultaneously. A mechanism for an expanding phase separated region is demonstrated and the time dependence of…
The present note deals with a nonstandard systems of differential equations describing a two-species phase segregation. This system naturally arises in the asymptotic analysis carried out recently by the same authors, as the diffusion…
Many materials quenched into their ordered phase undergo ageing and there show dynamical scaling. For any given dynamical exponent z, this can be extended to a new form of local scale-invariance which acts as a dynamical symmetry. The…
We study the dynamics of phase ordering of a non-conserved, scalar order parameter in one dimension, with long-range interactions characterized by a power law $r^{-d-\sigma}$. In contrast to higher dimensional systems, the point nature of…
We investigate time-independent disorder on several two-dimensional discrete-time quantum walks. We find numerically that, contrary to claims in the literature, random onsite phase disorder, spin-dependent or otherwise, cannot localise the…
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…
This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…