Related papers: Coarsening versus pattern formation
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…
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…
We study the steady states and the coarsening dynamics in a one dimensional driven non-conserved system modelled by the so called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In…
We consider coarsening dynamics associated with a Burgers--Cahn--Hilliard system modeling a two-phase flow in one space dimension. Our emphasis is on the effect that coupling between the phase and fluid dynamics has on coarsening rates, and…
In this paper we focus on crystal surfaces led out of equilibrium by a growth or erosion process. As a consequence of that the surface may undergo morphological instabilities and develop a distinct structure: ondulations, mounds or…
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…
We demonstrate the large scale effects of the interplay between shape and hard core interactions in a system with left- and right-pointing arrowheads ~$\textless ~~ \textgreater$~ on a line, with reorientation dynamics. This interplay leads…
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…
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation…
Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks.…
We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process…
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
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…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Phase separation between two fluids in two-dimensions is investigated by means of Direct Numerical Simulations of coupled Navier-Stokes and Cahn-Hilliard equations. We study the phase ordering process in the presence of an external stirring…
We investigate a model for pattern formation in the presence of Galilean symmetry proposed by Matthews and Cox [Phys.\ Rev.\ E \textbf{62}, R1473 (2000)], which has the form of coupled generalized Burgers and Ginzburg-Landau-type equations.…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular…
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…
An overview of the related topics of anomalous coarsening and glassy dynamics is given. In anomalous coarsening, the typical domain size of an ordered phase grows more slowly with time than the power law dependence that is usually observed,…