Mathematical aspects of coagulation and fragmentation processes

  • Damien Allen

Student thesis: Doctoral Thesis

Abstract

In this thesis, we develop a number of approaches to investigate coagulation and fragmentation processes. We initially use visibility graphs as a tool to analyse the results of kinetic Monte Carlo (kMC) simulations of submonolayer deposition in a one dimensional point island model. We introduce an effcient algorithm for the computation of the visibility graph resulting from a kMC simulation and show that from the properties of the visibility graph one can determine the critical island size, thus demonstrating that the visibility graph approach, which combines island size and spatial distribution data, can provide insights into island nucleation and growth mechanisms. We then consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption. Finally, we demonstrate the versatility of the coagulation-fragmentation framework by considering the asymptotics of the average Erdos number. We also compare our results with those obtained by using a Gillespie type algorithm.
Date of Award9 Jun 2020
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SupervisorMichael Grinfeld (Supervisor) & Paul Mulheran (Supervisor)

Cite this

'