Physical Sciences and Mathematics Commons^™

The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion

Electronic Thesis and Dissertation Repository

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.

I distinguish three forms of the …

Incomplete Market Models Of Carbon Emissions Markets, Walid Mnif

Electronic Thesis and Dissertation Repository

New regulatory frameworks have been developed with the aim of decreasing global greenhouse gas emissions over both short and long time periods. Incentives must be established to encourage the transition to a clean energy economy. Emissions taxes represent a "price" incentive for this transition, but economists agree this approach is suboptimal. Instead, the "quantity" instrument provided by cap-and-trade markets are superior from an economic point of view. This thesis focuses on the cap-and-trade instrument. Carbon emissions markets have recently been implemented in different countries. We summarize the state of world cap-and-trade schemes. We also provide a literature review of existing …

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

Molecular Dynamics Studies Of Water Flow In Carbon Nanotubes, Alexander D. Marshall

Electronic Thesis and Dissertation Repository

We present classical molecular dynamics (MD) simulations providing insight into the behaviour of water. We focus on confined water, the properties of which are often significantly different from the properties of bulk water.

First, we performed several simulations investigating the handling of long-range interactions in GROMACS [1], a MD simulation package. Selection of simulation protocols such as handling of long-range interactions is often overlooked, sometimes to the significant detriment of the final result [2, 3, 4]. Ensuring that the chosen simulation protocols are appropriate is a critical step in computer simulation.

Second, we performed MD simulations where water flowed between …

Preoperative Planning Of Robotics-Assisted Minimally Invasive Cardiac Surgery Under Uncertainty, Hamidreza Azimian

Electronic Thesis and Dissertation Repository

In this thesis, a computational framework for patient-specific preoperative planning of Robotics-Assisted Minimally Invasive Cardiac Surgery (RAMICS) is developed. It is expected that preoperative planning of RAMICS will improve the rate of success by considering robot kinematics, patient-specific thoracic anatomy, and procedure-specific intraoperative conditions. Given the significant anatomical features localized in the preoperative computed tomography images of a patient's thorax, port locations and robot orientations (with respect to the patient's body coordinate frame) are determined to optimize characteristics such as dexterity, reachability, tool approach angles and maneuverability. In this thesis, two approaches for preoperative planning of RAMICS are proposed that …

Pricing And Trading American Put Options Under Sub-Optimal Exercise Policies, William Wei Xing

Electronic Thesis and Dissertation Repository

No analytical expression has been found for the optimal exercise boundary of finite maturity American put options. This thesis evaluates the performance of approximating the optimal boundary with a class of analytically tractable sub-optimal exercise boundaries which admit known first passage time density functions. The performance is evaluated in two steps, first by computing and comparing the value of the put option under the sub-optimal exercise policy to existing numerical approximation methods such as the binomial price, then by examining the profit/loss of a trader that would result from hedging and trading strategies based on the sub-optimal exercise policy. We …

Further Applications Of Higher-Order Markov Chains And Developments In Regime-Switching Models, Xiaojing Xi

Electronic Thesis and Dissertation Repository

We consider a higher-order hidden Markov models (HMM), also called weak HMM (WHMM), to capture the regime-switching and memory properties of financial time series. A technique of transforming a WHMM into a regular HMM is employed, which in turn enables the development of recursive filters. With the use of the change of reference probability measure methodology and EM algorithm, a dynamic estimation of model parameters is obtained. Several applications and extensions were investigated. WHMM is adopted in describing the evolution of asset prices and its performance is examined through a forecasting analysis. This is extended to the case when the …

A Real Options Valuation Of Renewable Energy Projects, Natasha Burke

Electronic Thesis and Dissertation Repository

Due to climate change concerns, high oil prices and nuclear dangers there is increasing support for renewable energy. At the forefront of the debate for government support of renewable energy are wind energy and biofuels. Used primarily for power generation and transportation, respectively, there have been many debates surrounding the reliability and efficiency of these resources. These debates often address the uncertainty in the economic value of the resource through time, however it is often difficult to quantify this uncertainty, which stems from the random behavior of prices and the unpredictable nature of the resource itself.

In this thesis we …

Phase Field Crystal Approach To The Solidification Of Ferromagnetic Materials, Niloufar Faghihi

Electronic Thesis and Dissertation Repository

The dependence of the magnetic hardness on the microstructure of magnetic solids is investigated, using a field theoretical approach, called the Magnetic Phase Field Crystal model. We constructed the free energy by extending the Phase Field Crystal (PFC) formalism and including terms to incorporate the ferromagnetic phase transition and the anisotropic magneto-elastic effects, i.e., the magnetostriction effect. Using this model we performed both analytical calculations and numerical simulations to study the coupling between the magnetic and elastic properties in ferromagnetic solids. By analytically minimizing the free energy, we calculated the equilibrium phases of the system to be liquid, non-magnetic …

Molecular Dynamics Simulations Of Peptide-Mineral Interactions, Susanna Hug

Electronic Thesis and Dissertation Repository

We present molecular dynamics (MD) simulations providing information about the mechanisms of biomineralization. We focus on osteopontin-related peptides, which inhibit the growth of calcium oxalate monohydrate (COM) the primary constituent of kidney stones.

First, we performed two ab initio MD simulations: aspartic acid (Asp) and the dimer of aspartic acid and phosphoserine (Asp-pSer) interacting with a fully hydrated COM crystal slab exposing the {100} face. For Asp we found that one of the carboxyl and the amine group both interact with the crystal surface but neither forms a stable contact during the simulation. Asp-pSer interacts preferably with its carboxyl groups …