Related papers: Nearest pattern interaction and global pattern for…
In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically.…
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Climate models exhibit an approximately invariant surface warming pattern in typical end-of-century projections. This observation has been used extensively in climate impact assessments for fast calculations of local temperature anomalies,…
We consider a generalization of the FKPP equation for the evolution of the spatial density of a single-species population where all the terms are nonlocal. That is, the spatial extension of each process (growth, competition and diffusion)…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
One of the most interesting phenomena in the soft-matter realm consists in the spontaneous formation of super-molecular structures (microphases) in condition of thermodynamic equilibrium. A simple mechanism responsible for this…
Active matter systems provide fascinating examples of pattern formation and collective motility without counterparts in equilibrium systems. Here, we employ Brownian dynamics simulations to study the collective motion and self-organization…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered micro-crystallites, time-periodic structures, and chaotic…
Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where the cascade is eventually arrested by dissipation. In this article, we show how to harness these…
We numerically examine a binary system of particles with repulsive interactions, where one species is driven by a rotating drive and the other is subjected either to a constant drive in a fixed direction or to a rotating drive that is out…
Three-wave interactions (or resonant triads) are the lowest-order nonlinear interaction in pattern formation and arise between waves with different orientations when the sum of two wavevectors equals a third one. When a pattern has only one…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
We study the concentration field in a prescribed 2D Cahn-Hilliard Navier-Stokes (CHNS) system. We formulate a description for the target pattern formation and pattern merging processes, and compare this description with simulation results.…
Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the…
In the standard picture of cosmological structure formation, the Universe we see today is evolved under the gravitational instability from tiny random fluctuations. In this talk I discuss the onset of non-linearity in the large scale…
We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…