P31: Analysis and Modelling of Bedform Development as an Aggregation & Fragmentation Process
Aggregation and fragmentation processes are known to exhibit interesting non-equilibrium behaviour, such as non-trivial steady states, scaling and phase transitions. The development of ripples on sandy beach surfaces and of dunes in desert sand seas are the examples of a fundamental process of bedform evolution that displays aggregation and fragmentation behaviour in the context of clustering and pattern formation.
In this project we analytically modelled the development of bedforms and pattern coarsening from a set of master equations, and we implemented cellular automaton simulations to explore and test the system in a spatio-temporally explicit domain. We used a combination of aggregation and fragmentation processes to model the development of bedforms and pattern coarsening, including spatial migration (displacement) of the clusters. The starting point of the analysis is a set of master equations describing the time evolution of the fragment mass distribution. The aim of the project was to study the (non-equilibrium) steady states and the scaling properties of a time-dependent solution for different reaction rates, initial distributions, and types of inputs (provision of aggregates in the system). The analysis was underpinned with numerical simulation modelling of bedform evolution over a spatio-temporally explicit domain using a cellular automaton model . The project also provided a novel comparison between analytical and numerical analysis of this process.
Primary Supervisor Andreas Baas (KCL, Faculty of Social Science and Public Policy, Department of Geography) advised on the nature of fundamental bedform development, and processes and mechanisms involved, the context of clustering and pattern formation, and the spatially explicit simulation modelling and exploration of the system using cellular automata approaches.
Secondary Supervisor Dr Alessia Annibale (KCL, Faculty of Natural and Mathematical Sciences, Department of Mathematics) advised on the mathematical analysis of toy models of aggregation and fragmentation processes evolving via master equation, in particular their long time behavior, dependence on reaction rates and initial conditions, their non-equilibrium features.