Related papers: Nearest pattern interaction and global pattern for…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Magnetic domain patterns under an oscillating field is studied theoretically by using a simple Ising-like model. We propose two ways to investigate the effects of the oscillating field. The first one leads to a model in which rapidly…
In this paper we present a study of pattern formation in bidimensional systems with competing short-range attractive and long-range repulsive interactions. The interaction parameters are chosen in such a way to analyse two different…
Motivated by the observation of localized circular excitations (`oscillons') in vertically vibrated granular layers (P.B. Umbanhowar, F. Melo and H.L. Swinney, Nature 382 (1996) 793), we numerically investigate an extension of a…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…
We report three-dimensional particle mechanics static calculations that predict the microstructure evolution during die-compaction of elastic spherical particles up to relative densities close to one. We employ a nonlocal contact…
It is proposed that the spatial (and temporal) patterns spontaneously appearing in dissipative systems maximize the energy flow through the pattern forming interface. In other words - the patterns maximize the entropy growth rate in an…
By using cosmological simulations, we studied the effects of galaxy interactionson the star formation activity in the local Universe. We selected galaxy pairs from the 3D galaxy distribution according to a proximity criterion. The 2D galaxy…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
We analyze the spatio-temporal patterns of two competing species in the presence of two white noise sources: an additive noise acting on the interaction parameter and a multiplicative noise which affects directly the dynamics of the species…
We study interactions between shocks and standing-wave patterns in vertically oscillated layers of granular media using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order. We simulate a layer…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
This contribution reports on numerical simulations of 2D granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibits spontaneous oscillatory motion in generic flow conditions, and…
Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the…