Related papers: Annihilation catastrophe: New critical phenomenon …
Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…
Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding of…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
The collapse of man-made and natural structures is a complex phenomenon that has been studied for centuries. We propose a new approach to understanding catastrophic instabilities, based on the idea that they do not occur at the critical…
At finite concentrations of reacting molecules, kinetics of diffusion-controlled reactions is affected by intra-reactant interactions. As a result, multi-particle reaction statistics cannot be deduced from single-particle results. Here we…
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite…
We discuss the failure dynamics of the Fiber Bundle Model, especially in the equal-load-sharing scheme. We also highlight the "Critical" aspects of their dynamics in comparison with those in standard thermodynamic systems undergoing phase…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
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 diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…
In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena.
The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to…
On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
This study explores the integration of a diffusion control parameter into the chaotic dynamics of a modified bouncing ball model. By extending beyond simple elastic collisions, the model introduces elements that affect the diffusive…
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…