Losert-Valiente Kroon, C.M.; (2010) Stochastic population dynamics in astrochemistry and aerosol science. Doctoral thesis , UCL (University College London).

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Abstract

Classical, non-equilibrium systems of diffusing species or entities undergoing depletion, evaporation and reaction processes are at the heart of many problems in Physics, Chemistry, Biology and Financial Mathematics. It is well known that fluctuations and correlations in statistical systems can have a profound influence on the macroscopic properties of the system. However, the traditional rate equations that describe the evolution of mean populations in time and space do not incorporate statistical fluctuations. This becomes an issue of great importance when population densities are low. In order to develop a stochastic description of birth-and-death processes beyond the mean field approximation I employ techniques in classical many-body Physics in a manner analogous to the treatment of quantum systems. I obtain promising results to understand and quantify the exact circumstances of the failure of the mean-field approximation in specific problems in Astrophysics, namely heterogeneous chemical reactions in interstellar clouds, and in Aerosol Science, namely heterogeneous nucleation processes, and deliver the means to manipulate the alternative stochastic framework according to the Doi-Peliti formalism. In this framework the mean population of a species is given by the average of a solution to a set of constraint equations over all realisations of the stochastic noise. The constraint equations are inhomogeneous stochastic partial differential equations with multiplicative real or complex Gaussian noise. In general, these equations cannot be solved analytically. Therefore I resort to the numerical implementation of the Doi-Peliti formalism. The main code is written in the GNU C language, some algebraic calculations are performed by means of the MapleV package. In the case of large population densities the stochastic framework renders the same results as the mean field approximation whereas for low population densities its predictions differ substantially from the calculations using the traditional model.

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