Related papers: Scale invariance and dynamic phase transitions in …
We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model…
We revisit the problem of deriving the mean-field values of avalanche critical exponents in systems with absorbing states. These are well-known to coincide with those of an un-biased branching process. Here, we show that for at least 4…
We study diffusion-reaction processes on periodic square planar lattices and simple cubic (sc) lattices. Considered first is a single diffusing reactant undergoing an irreversible reaction upon first encounter with a stationary co-reactant…
We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is…
The pair contact process with diffusion (PCPD) with modulo 2 conservation (\pcpdt) [$2A\to 4A$, $2A\to 0$] is studied in one dimension, focused on the crossover to other well established universality classes: the directed Ising (DI) and the…
We investigate the critical behavior of systems exhibiting a continuous absorbing phase transition in the presence of a conserved field coupled to the order parameter. The results obtained point out the existence of a new universality class…
One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an…
Scale-invariant avalanches -- with events of all sizes following power-law distributions -- are considered critical. Above the upper critical dimension of four, the mean-field solution with a robust $3/2$ size exponent describes the…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
A conserved generalized zero range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability $p$. The steady state particle distribution function $P(n)$ is…
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…
We consider the probability $P(t)$ that a given site remains unvisited by any of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$ when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a universal…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…