A Thermodynamic Analysis of the Al-C-Fe System (original) (raw)

A note on random catalytic branching processes

Journal of theoretical biology, 2018

A variety of evolutionary processes in biology can be viewed as settings where organisms 'catalyse' the formation of new types of organisms. One example, relevant to the origin of life, is where transient biological colonies (e.g. prokaryotes or protocells) give rise to new colonies via lateral gene transfer. In this short note, we describe and analyse a simple random process which models such settings. By applying theory from general birth-death processes, we describe how the survival of a population under catalytic diversification depends on interplay of the catalysis rate and the initial population size. We also note how such process can also be viewed within the framework of 'self-sustaining autocatalytic networks'.

Individuals at the origin in the critical catalytic branching random walk

2008

A continuous time branching random walk on the lattice is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove a conditional limit theorem for the number of individuals at the origin. Keywords: catalytic branching random walk; critical two-dimensional Bellman-Harris process 1 Statement of problem and main results We consider the following modification of a standard branching random walk on ¡. Consider a population of individuals evolving as follows. The population is initiated at time t ¢ 0 by a single particle. Being outside the origin the particle performs a continuous time random walk on ¡ with infinitesimal transition matrix A ¢¤ £ a ¥ x ¦ y§¨ £ x © y�� � ¦ a ¥ 0 ¦ 0§� � 0¦ until the moment when it hits the origin. At the origin it spends an exponentially distributed time with parameter 1 and then either jumps to � ¢ a point y �� ¥ 0 � α § a ¥ 0 ¦ y §...