Related papers: Scaling in dynamical Turing pattern formation: den…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
Kibble-Zurek scaling is the scaling of the density of the topological defects formed via the Kibble-Zurek mechanism with respect to the rate at which a system is cooled across a continuous phase transition. Recently, the density of the…
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…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
This study examines how patterns on mammal body surfaces change as they transition from juveniles to adults and with seasonal variations. Our previous research suggests that patterns formed in infancy may fade due to the growing domain…
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…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
The experiments on verification of the Kibble-Zurek mechanism showed that topological defects are formed most efficiently in the systems of small size or low (quasi-)dimensionality, whereas in the macroscopic two- and three-dimensional…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently,…
The surface pattern formation on a gelation surface is analyzed using an effective surface roughness. The spontaneous surface deformation on DiMethylAcrylAmide (DMAA) gelation surface is controlled by temperature, initiator concentration,…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We introduce a model for the turbulent energy cascade aimed at studying the effect of dynamical scaling on intermittency. In particular, we show that by slowing down the energy transfer mechanism for fixed energy flux, intermittency…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz…