Browsing Applied Mathematics by Title
Now showing items 253-272 of 491
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Mathematical Modeling of Secondary Malignancies and Associated Treatment Strategies
(University of Waterloo, 2014-05-21)Several scientific and technological advancements in radiation oncology have resulted in dramatic improvements in dose conformity and delivery to the target volumes using external beam radiation therapy (EBRT). However, ... -
Mathematical Modeling of the Vaporization of Encapsulated Perfluorocarbon Nanodroplets using Chirp Ultrasound
(University of Waterloo, 2023-08-29)Ultrasound imaging is the use of sound waves beyond the human frequency range to construct images of human tissue. This is carried out through the measurement of reflected and scattered waves from the interfaces between ... -
Mathematical Modelling and Numerical Simulation of Marine Ecosystems With Applications to Ice Algae
(University of Waterloo, 2013-07-26)Sea-ice ecosystem modelling is a novel field of research. In this thesis, the main organism studied is sea-ice algae. A basic introduction to algae and its importance in the aquatic food web is given first. An introduction ... -
Mathematical Modelling of Cancer Stem Cells
(University of Waterloo, 2009-08-06)The traditional view of cancer asserts that a malignant tumour is composed of a population of cells, all of which share the ability to divide without limit. Within the last decade, however, this notion has lost ground ... -
Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs
(University of Waterloo, 2019-08-19)Cancer is one of the world's deadliest diseases despite immense investments into oncological research in recent years. Although great strides have been made in our understanding of cancer, much remains unknown regarding ... -
Mathematical Modelling of Social Factors in Decision Making Processes at the Individual and Population Levels
(University of Waterloo, 2016-08-11)In this thesis we apply mathematical modelling techniques to investigate the implications of social influence on decision making processes in two related contexts. The first problem concerns the mathematical modelling ... -
Mathematical modelling of supraglacial meltwater production and drainage
(University of Waterloo, 2021-08-30)Mountain glaciers and the polar ice sheets exert a critical control on water resource availability, drive sea level change, and impact global ocean circulation. These and other impacts are controlled by surface meltwater ... -
Mathematical Modelling of the Intrarenal Renin Angiotensin System in Hypertension
(University of Waterloo, 2023-04-24)Hypertension is the leading cause of cardiovascular disease and premature death world-wide. It is a highly multi-factorial disease associated with multiple risk factors and patho-physiological changes, including impaired ... -
Mathematical models for angiogenic, metabolic and apoptotic processes in tumours
(University of Waterloo, 2014-08-15)This doctoral thesis outlines a body of research within the field of mathematical oncology that focusses on the inclusion of microenvironmental factors in mathematical models for solid tumour behaviour. These models primarily ... -
Mathematical Models of Mitochondria in the Kidney and Liver
(University of Waterloo, 2022-03-24)Mitochondria are key players in several kinds of tissue injury, and are even the site of mechanism of certain diseases. In this work we introduce new models of mitochondrial ATP generation in multiple tissues, including ... -
Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons
(BioMed Central, 2014-07-21)Large networks of integrate-and-fire (IF) model neurons are often used to simulate and study the behaviour of biologically realistic networks. However, to fully study the large network behaviour requires an exploration of ... -
Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons
(Frontiers Media, 2017-12-27)We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential ... -
Measurements of quantum fields and the Unruh effect: a particle detector perspective
(University of Waterloo, 2021-11-19)This thesis is devoted to the study of detector models in quantum field theory. A detector model aims to describe a hypothetical physical situation, realistic or not, in which a measurement is performed on a quantum field ... -
Microcolony Dynamics: Motion from Growth, Order, and Incompressibility
(University of Waterloo, 2023-04-27)Rod-shaped bacteria such as E. coli reproduce by expanding along their long axis and splitting into pairs of daughter cells. If conditions are favourable for growth, they will continue in this way, doubling repeatedly until ... -
Microswimmer Propulsion by Two Steadily Rotating Helical Flagella
(MDPI, 2019-01-01)Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrew-shaped flagellum that rotates to propel the body forward. Motivated by ... -
Model for a cortical circuit associated with childhood absence epilepsy
(University of Waterloo, 2019-08-23)Childhood absence epilepsy is suspected to result from mutations in genes which encode ion channels including sodium channels. Our purpose in this thesis is to explore some of the factors that alter the function of neurons ... -
A Model for Shear Response in Swimming Plankton
(University of Waterloo, 2016-08-11)The responses of zooplankton to the hydrodynamic variables of their environment, such as shear, are not well understood. We examine stochastic swimming models of the run and tumble type for plankton moving in a velocity ... -
Model for the RE-TC thalamic circuit with application to childhood absence epilepsy
(University of Waterloo, 2019-08-12)Childhood absence epilepsy (CAE) is an idiopathic neurological disorder affecting roughly 2-8 children per 100,000 children worldwide. It is characterized by absence seizures, or short lapses in consciousness, and the ... -
Model-based Reinforcement Learning of Nonlinear Dynamical Systems
(University of Waterloo, 2022-01-25)Model-based Reinforcement Learning (MBRL) techniques accelerate the learning task by employing a transition model to make predictions. In this dissertation, we present novel techniques for online learning of unknown dynamics ... -
Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid
(University of Waterloo, 2023-01-16)Flagellated bacteria categorized as microorganisms, play vital roles in human life such that their beneficial and detrimental effects on different aspects of the ecosystem are indisputable. Flagellated bacteria propel ...