Related papers: Instabilities and disorder of the domain patterns …
We investigate the energetic ground states of a model two-phase system with 1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous formation of two kinds of periodic domain structure. A striped domain structure is…
The single-site dynamical mean field theory approximation to the double exchange model is found to exhibit a previously unnoticed instability, in which a well-defined ground state which is stable against small perturbations is found to be…
The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and…
We develop a theory of the domain patterns in systems with competing short-range attractive interactions and long range repulsive Coulomb interactions. We take an energetic approach, in which patterns are considered as critical points of a…
Consider a system of $N$ particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a $\mathcal{C}^2$ smooth potential in any dimension. We prove that in the mean field limit $N \to +…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
Nonequilibrium conditions fundamentally change how systems undergo phase separation. In systems with temperature gradients, attractive particles have been shown to form periodic patterns and steady convective currents, but a clear…
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
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 formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains…
The instabilities triggered when two counter-streaming pair beams collide are analyzed. A guiding magnetic field is accounting for, while both beams are considered identical and cold. The instability analysis is conducted over the full…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical and biological media and to macro-scale vegetation and cloud patterns. Their…
The dynamics of an exciton-polariton superfluid resonantly pumped in a semiconductor microcavity are investigated by mean-field theory. Modulational instability develops into crystalline order and then ordered and disordered states…
There is a growing interest, inspired by advances in technology, in the low temperature physics of thin films. These quasi-2D systems show a wide range of ordering effects including formation of striped states, reorientation transitions,…
The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…
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…