Related papers: Domain Coarsening in Systems Far from Equilibrium
We study the dynamics of 2d spin-ice following a quench from a fully disordered initial condition (equilibrium at infinite temperature) into its disordered, ferromagnetic and antiferromagnetic phases. We analyze the evolution of the density…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
We study the coarsening of strongly microphase separated membrane domains in the presence of recycling of material. We study the dynamics of the domain size distribution under both scale-free and size-dependent recycling. Closed form…
We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry…
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a…
We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing/spectral simulation technique, with a transformation to…
We carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances…
We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
We study the kinetics of domain growth in ferromagnets with random exchange interactions. We present detailed Monte Carlo results for the nonconserved random-bond Ising model, which are consistent with power-law growth with a variable…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A…
Dynamics of ordering in Ising model, following quench to zero temperature, have been studied via Glauber spin-flip Monte Carlo simulations in space dimensions $d=2$ and $3$. One of the primary objectives has been to understand phenomena…
We investigate the dynamics of two-dimensional site-diluted Ising antiferromagnets. In an external magnetic field these highly disordered magnetic systems have a domain structure which consists of fractal domains with sizes on a broad range…
The Chapter is devoted to reviewing the main features of aging in non disordered systems relaxing via domain growth, after an istantaneous temperature quench. Using the autocorrelation and autoresponse functions to gauge the deviation from…
In this paper we present a detailed description of the statistical and computational techniques that were employed to study a driven far-from-equilibrium steady-state Rayleigh-B{\'e}nard system in the non-turbulent regime ($Ra\leq 3500$).…
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,…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
We propose general conditions for the emergence of Turing patterns in a domain that changes size through homogeneous growth/shrinkage based on the qualitative changes of a potential function. For this part of the work, we consider the most…
By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are…