Related papers: Phase separation patterns from directional quenchi…
We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules…
We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general,…
A simple model for an interface moving in a disordered medium is presented. The model exhibits a transition between the two universality classes of interface growth phenomena. Using this model, it is shown that the application of…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We study post-quench dynamics of charge-density-wave (CDW) order in the square-lattice $t$-$V$ model. The ground state of this system at half-filling is characterized by a checkerboard modulation of particle density. A generalized…
We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte-Carlo simulations for times up to $10^9$ and system sizes up to $10^7$ sites. In agreement with…
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…
An electric-field-induced phase transition and pattern formation in a binary dielectric fluid layer are studied using a coarse-grained free energy functional. The electrostatic part of the free energy is a nonlinear functional of the…
Mixing of two fluids can lead to the formation of a precipitate. If one of the fluids is injected into a confined space filled with the other, a created precipitate disrupts the flow locally and forms complex spatiotemporal patterns. The…
Phase separation in complex systems is a ubiquitous phenomenon. While simple theories predict coarsening until only macroscopically large phases remain, concrete models often exhibit patterns with finite length scales. To unify such models,…
A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell…
Within the framework of the frozen temperature approximation we develop a strongly-nonlinear theory of one-dimensional pattern formation during directional solidification of binary mixture under nonequilibrium segregation. In the case of…
In this paper, the effects of disorder on the dynamical quantum phase transitions (DQPTs) in the transverse-field anisotropic XY chain are studied by numerically calculating the Loschmidt echo after quench. We obtain the formula for…
We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel type models. The evolution of small perturbations is studied analytically in the linear regime complemented by…
The velocity of dislocations is derived analytically to incorporate and predict the intriguing effects induced by the preferential solute segregation and Cottrell atmospheres in both two-dimensional and three-dimensional binary systems of…
The theory of quantum quenches in near-critical one-dimensional systems formulated in [J. Phys. A 47 (2014) 402001] yields analytic predictions for the dynamics, unveils a qualitative difference between non-interacting and interacting…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
We explore the quench dynamics of a binary Bose-Einstein condensate crossing the miscibility-immiscibility threshold and vice versa, both within and in particular beyond the mean-field approximation. Increasing the interspecies repulsion…
We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a…
We obtain analytical results for the time evolution of local observables in systems undergoing quantum quenches in $d$ spatial dimensions. For homogeneous systems we show that oscillations undamped in time occur when the state produced by…