Physical Sciences and Mathematics Commons^™

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

Portfolio Optimization Analysis In The Family Of 4/2 Stochastic Volatility Models, Yuyang Cheng

Electronic Thesis and Dissertation Repository

Over the last two decades, trading of financial derivatives has increased significantly along with richer and more complex behaviour/traits on the underlying assets. The need for more advanced models to capture traits and behaviour of risky assets is crucial. In this spirit, the state-of-the-art 4/2 stochastic volatility model was recently proposed by Grasselli in 2017 and has gained great attention ever since. The 4/2 model is a superposition of a Heston (1/2) component and a 3/2 component, which is shown to be able to eliminate the limitations of these two individual models, bringing the best out of each other. Based …

A Molecular Dynamics Study Of Polymer Chains In Shear Flows And Nanocomposites, Venkat Bala

Electronic Thesis and Dissertation Repository

In this work we study single chain polymers in shear flows and nanocomposite polymer melts extensively through the use of large scale molecular dynamics simulations through LAMMPS. In the single polymer chain shear flow study, we use the Lattice Boltzmann method to simulate fluid dynamics and also include thermal noise as per the \emph{fluctuation-dissipation} theorem in the system. When simulating the nanocomposite polymer melts, we simply use a Langevin thermostat to mimic a heat bath. In the single polymer in shear flow study we investigated the margination of a single chain towards solid surfaces and how strongly the shear flow …

Algorithms For Regular Chains Of Dimension One, Juan P. Gonzalez Trochez

Electronic Thesis and Dissertation Repository

One of the core commands in the RegularChains library inside Maple is Triangularize. The underlying decomposes the solution set of a polynomial system into geometrically meaningful components represented by regular chains. This algorithm works by repeatedly calling a procedure, called Intersect, which computes the common zeros of a polynomial p and a regular chain T .

As the number of variables of p and T , as well as their degrees, increase, the call to the function Intersect(p, T ) becomes more and more computationally expensive. It was observed in that when the input polynomial system is zero-dimensional and T …

Statistical Applications To The Management Of Intensive Care And Step-Down Units, Yawo Mamoua Kobara

Electronic Thesis and Dissertation Repository

This thesis proposes three contributing manuscripts related to patient flow management, server decision-making, and ventilation time in the intensive care and step-down units system.

First, a Markov decision process (MDP) model with a Monte Carlo simulation was performed to compare two patient flow policies: prioritizing premature step-down and prioritizing rejection of patients when the intensive care unit is congested. The optimal decisions were obtained under the two strategies. The simulation results based on these optimal decisions show that a premature step-down strategy contributes to higher congestion downstream. Counter-intuitively, premature step-down should be discouraged, and patient rejection or divergence actions should …