相关论文: Reaction-diffusion system with self-organized crit…
We show that large, slowly driven systems can evolve to a self-organized critical state where long range temporal correlations between bursts or avalanches produce low frequency $1/f^{\alpha}$ noise. The avalanches can occur instantaneously…
The propagator for the activity in a broad class of self-organized critical models obeys an imaginary-time Schr\"odinger equation with a nonlocal, history-dependent potential representing memory. Consequently, the probability for an…
We develop a dynamical system approach for the Zhang's model of Self-Organized Criticality, for which the dynamics can be described either in terms of Iterated Function Systems, or as a piecewise hyperbolic dynamical system of skew-product…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
A mean-field sandpile model that exhibits self-organized criticality (SOC) despite violation of the grain-transfer conservation law during avalanches is proposed. The sandpile consists of $N$ agents and possesses background activity with…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…
We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an…
We study global-in-time behavior of the solution to a reaction-diffusion system with mass conservation, as proposed in the study of cell polarity, particularly, the second model of \cite{oi07}. First, we show global-in-time existence of…
Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
We employ the eigen microstate approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely, the BTW model and the Manna model. In both models, phase transitions from the absorbing-state to the critical…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…