Related papers: Annihilation Catastrophe: From Formation to Univer…
We consider a system of q diffusing particle species A_1,A_2,...,A_q that are all equivalent under a symmetry operation. Pairs of particles may annihilate according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the symmetry, and…
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…
There is general agreement that the universe began with an "explosion" of matter and energy at a "singularity", the "Big Bang". This paper analyses the mechanics of that beginning and two alternative theories related to it: - The…
The conventional theory of combustion describes systems where all of the parameters are spatially homogeneous. On the other hand, combustion in disordered explosives has long been known to occur after local regions of the material, called…
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…
A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to…
A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
A scenario for a quantum big crunch to big bang transition is proposed. We first clarify the similarities between this transition and the final stages of black hole evaporation. The black hole and the universe are thought of as quantum…
This paper studies singularity formation for conservation laws with a source term. Motivated by John (1974) and Barlin (2023), we prove finite-time blow-up under initial data conditions weaker than those in Barlin. Moreover, we show that a…
We present a mean field model for coagulation ($A+A\to A$) and annihilation ($A+A\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is…
The main goal of this paper is to show that the blow up phenomenon (the explosion of the $ \rL^{\infty }$-norm) of the solutions of several classes of evolution problems can be controlled by means of suitable global controls $\alpha (t)$…
We consider a diffusion-limited reaction in case the reacting entities are not available simultaneously. Due to the fact that the reaction takes place after a spatiotemporal accumulation of reactants, the underlying rate equation has to be…
I show that de Sitter space disintegrates into an infinite number of copies of itself. This occurs iteratively through a quantum process involving two types of topology change. First a handle is created semiclassically, on which multiple…
It is usually believed that Darwin's theory leads to a smooth gradual evolution, so that mass extinctions must be caused by external shocks. However, it has recently been argued that mass extinctions arise from the intrinsic dynamics of…
We analyze a reaction-diffusion system on $\mathbb{R}^{N}$ which models the dispersal of individuals between two exchanging environments for its diffusive component and incorporates a Fujita-type growth for its reactive component. The…
Naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. We show that explosive radiation is emitted during the formation process of the naked…
We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results…
We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…