Physical Sciences and Mathematics Commons^™

Adaptation Reshapes The Distribution Of Fitness Effects, Diego Tenoch Morales Lopez

Electronic Thesis and Dissertation Repository

The process of adaptation has been of interest since the XIX century, when Darwin first proposed the idea of natural selection. Since then, there has been a myriad of theoretical and empirical works that have expanded the field. From the many evolutionary insights these works have produced, a foundational idea is that spontaneous mutations in the genome of organisms can produce changes to their reproductive success that might confer an advantage for the mutant organisms with respect to their peers. Therefore, mutations drive adaptive evolution by virtue of their heritable effects on fitness. Empirical measures of the distribution of these …

Study Of Behaviour Change And Impact On Infectious Disease Dynamics By Mathematical Models, Tianyu Cheng

Electronic Thesis and Dissertation Repository

This thesis uses mathematical models to study human behaviour changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behaviour response evolves during epidemics and the effects of adaptive precaution behaviour on epidemics. The second topic is how to build general framework models incorporating human behaviour response in epidemiological modelling.

In the first project, based on the fact that a fraction of the epidemiologically susceptible population is actually susceptible due to precautions, we present a novel perspective on understanding the infection force, incorporating human protection behaviours. This view explains many existing infection force …

Complex-Valued Approach To Kuramoto-Like Oscillators, Jacqueline Bao Ngoc Doan

Electronic Thesis and Dissertation Repository

The Kuramoto Model (KM) is a nonlinear model widely used to model synchrony in a network of oscillators – from the synchrony of the flashing fireflies to the hand clapping in an auditorium. Recently, a modification of the KM (complex-valued KM) was introduced with an analytical solution expressed in terms of a matrix exponential, and consequentially, its eigensystem. Remarkably, the analytical KM and the original KM bear significant similarities, even with phase lag introduced, despite being determined by distinct systems. We found that this approach gives a geometric perspective of synchronization phenomena in terms of complex eigenmodes, which in turn …

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …