Doi-Peliti field theory with applications to biologically inspired systems
File(s)
Author(s)
Bothe, Marius
Type
Thesis
Abstract
Statistical mechanics has enjoyed great success in capturing the emergent behaviour of many-particle ensembles in equilibrium, most notably by characterising phase tran- sitions and their universal behaviour. This success has been carried over to non- equilibrium systems, which are free from the constraints of detailed balance, and thus display a wide variety of collective behaviours and phase transitions. Arguably the most important example of a non-equilibrium system is life itself, which constantly consumes energy to maintain a low-entropy state. As such, living systems are a rich source of novel non-equilibrium systems that have received much attention in the liter- ature. This thesis takes some of the tools developed in statistical mechanics, notably Doi-Peliti field theory and the renormalisation group, and applies them to biologically inspired systems.
In Chapter 3 I work on evaluating different field theories by quantifying the degree to which they take into account the discrete nature of the particles making up a system, as neglecting this can lose important information about the process. Chapter 4 then goes on to apply Doi-Peliti field theory to active matter, deriving exact probability dis- tributions for non-interacting active Ornstein-Uhlenbeck particles. In Chapter 5 I move on to interacting systems of active particles: Based on experimental results I explore minimal mechanisms that can explain the cell sorting seen in biological experiments. Finally in Chapter 6 I study the critical behaviour of a branching random-walk model used to describe the morphogenesis of organs in biology.
In Chapter 3 I work on evaluating different field theories by quantifying the degree to which they take into account the discrete nature of the particles making up a system, as neglecting this can lose important information about the process. Chapter 4 then goes on to apply Doi-Peliti field theory to active matter, deriving exact probability dis- tributions for non-interacting active Ornstein-Uhlenbeck particles. In Chapter 5 I move on to interacting systems of active particles: Based on experimental results I explore minimal mechanisms that can explain the cell sorting seen in biological experiments. Finally in Chapter 6 I study the critical behaviour of a branching random-walk model used to describe the morphogenesis of organs in biology.
Version
Open Access
Date Issued
2023-08
Date Awarded
2024-03
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Pruessner, Gunnar
Sponsor
Engineering and Physical Sciences Research Council
Imperial College London
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)