Physical Sciences and Mathematics Commons^™

Control And Calibration Strategies For Quantum Simulation, Paul M. Kairys

Doctoral Dissertations

The modeling and prediction of quantum mechanical phenomena is key to the continued development of chemical, material, and information sciences. However, classical computers are fundamentally limited in their ability to model most quantum effects. An alternative route is through quantum simulation, where a programmable quantum device is used to emulate the phenomena of an otherwise distinct physical system. Unfortunately, there are a number of challenges preventing the widespread application of quantum simulation arising from the imperfect construction and operation of quantum simulators. Mitigating or eliminating deleterious effects is critical for using quantum simulation for scientific discovery. This dissertation develops strategies …

Assessing The Economic Tradeoffs Between Prevention And Suppression Of Forest Fires, Elizabeth Trulia Heines

Doctoral Dissertations

The number of large-scale, high-severity forest fires occurring in the United States is increasing, as is the cost to suppress these fires. These trends have prompted investigations into alternative fuels methods to help prevent these large wildfires. One of the key challenges in studying the costs and benefits of forest fire prevention management is the incorporation of risk and uncertainty surrounding management decisions. We use a technique developed by William Reed to incorporate the stochasticity of the time of a forest fire into our optimal control problems. The goal of these problems is to determine the optimal fire prevention management …

Investigating Advection Control In Competitive Pde Systems And Environmental Transmission In Johne's Disease Ode Models, Kokum Rekha De Silva

Doctoral Dissertations

We extend the work on optimal control of advective direction in a reaction-diffusion population model to a system representing two competing populations. We investigate the choice of movement direction to benefit a population. First, the advective direction in one of the populations in a competition model is the control. Next, we extend the work by taking the advective directions of both populations as controls. In both these cases the objective is to maximize a weighted combination of the two populations while minimizing the cost involved in the species movement. Mathematical analysis is completed to derive the optimality system and numerical …

Population Modeling For Resource Allocation And Antimicrobial Stewardship, Jason Bintz

Doctoral Dissertations

This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship.

In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the …

Models Linking Epidemiology With Immunology And Ecology, Eric Shu Numfor

Doctoral Dissertations

Optimal control can be used to design intervention strategies for the control of infectious diseases and predator-prey systems. In this dissertation, we studied models encapsulating two relatively new areas of mathematical biology, which combine epidemiology with immunology and ecology.

We formulated immuno-epidemiological models of coupled within-host model of ordinary differential equations and between-host model of ordinary differential equations and partial differential equations, using the Human Immunodeficiency Virus (HIV) for illustration, and set a framework for optimal control of immuno-epidemiological models. By constructing an iterative sequence from a representation formula for a solution to the linked model and using the fixed-point …

Optimal Control For Management In Gypsy Moth Models, Marco Vinisio Martinez

Doctoral Dissertations

The gypsy moth, Lymantria dispar (L.), is an invasive species and the most destructive forest defoliator in North America. Gypsy moth outbreaks are spatially synchronized over areas across hundreds of kilometers. Outbreaks can result in loss of timber and other forestry products. Greater losses tend to occur to the ecosystem services that forests provide, such as wildlife habitat, carbon sequestration, and nutrient cycling. The United States can be divided in three different areas: a generally infested area (populations established), an uninfested area (populations not established), and a transition zone between the two. There are different management programs matching these different …

Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong

Doctoral Dissertations

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior.

Cholera remains a public health threat in many parts of the world and improved …

A Method To Accomplish The Optimal Control Of Continuous Dynamical Systems With Impulse Controls Via Discrete Optimal Control And Utilizing Optimal Control Theory To Explore The Emergence Of Synchrony., Rachel Natalie Graves

Doctoral Dissertations

This research concerns the development of new optimal control methodologies and applications. In the first chapter we consider systems of ordinary differential equations subject to a restricted number of impulse controls. Examples of such systems include tumor growth, in which case the impulsive control is the administration of medication, and ecological invasion, in which case the impulse control is the release of predator species. Impulse control problems are typically solved via related partial differential equations known as quasi-variational inequalities. We show that these types of impulse control problems can be formulated as a discrete optimal control problems. Furthermore, this formulation …