In this paper, we provide a thorough proof of most of Bertrand's Theorem. Using Arnold's book "Mathematical methods of classical mechanics" as a backbone and calculus methods demonstrated by Jovanović in his article "A note on the proof of Bertrand's theorem," we show that for masses in a central field...
In this paper, we discuss two possible modifications to a numerical solution method for a model of microbiologically induced calcite precipitation (MICP). MICP provides a means to seal cracks in the surfaces of geological structures. From a mathematical and computational point of view MICP has very interesting features which make...
I had to write again. My research lay in science, and it was a science of three parts. The first part made a careful, introductory chapter, begged for by things that were lacking. It summarizes the von Neumann measurement model, derived from the Stern-Gerlach experiment, and it explains how weak...
Aggregation equations have been used to model phenomena such as insect swarming and chemotaxis. Previous work on aggregation equations in the area of analysis applied to PDE has proven well-posedness of certain classes of aggregation equations in Lebesgue spaces. We will prove local existence of solutions in H^1 to an...
This paper concerns a question that frequently occurs in various applications: Is any dispersal coupling of stable discrete linear systems, also stable? Although it has been known this is not the case, we shall identify a reasonably diverse class of systems for which it is true. We shall employ the...
There are three chapters of manuscripts in this dissertation and all of them are talking about a specific theme: stochastic control, but with completely different perspectives.
In the first manuscript, we solve the optimal barrier strategy for dividend distribution in a complicated Lévy system. In this system, the capital of...
In this work, we provide a detailed analysis of a discrete time regime switching financial market model with jumps. We consider the model under two different scenarios: known and unknown initial regime. For each scenario we investigated conditions that guarantee the model's completeness. We find that the model under consideration...
In this work we consider a model for pattern-producing vegetation in semi-arid regions of the world proposed by Klausmeier. It is a coupled nonlinear diffusion-advection evolutionary PDE system describing the vegetation density and water amount. The model was studied extensively by J.Sherratt who took into consideration the field data for...
This thesis consists of extensions of results on a perpetual American swaption problem. Companies routinely plan to swap uncertain benefits with uncertain costs in the future for their own benefits. Our work explores the choice of timing policies associated with the swap in the form of an optimal stopping problem....
The complexity of numerical ocean circulation models requires careful checking with a variety of test problems. The purpose of this paper is to develop a test problem involving Rossby and gravity waves in a two-layer fluid in a channel. The goal is to compute very accurate solutions to this test...
Agricultural revenues, the product of stochastic prices and yields, lead to markets which are
incomplete, thereby entreating and complicating economic inquiry. The following three essays
explore the incomplete nature of agricultural markets and consider the implications of
incompleteness for a range of policy questions and economic tools.
The first essay,...
This research explores the viability and effectiveness of using an inertial navigation system (INS) to control a beamforming array of microstrip patch antennas with the aim of reducing users' exposure to electromagnetic radiation. The system reduces radiated power directed toward a cellular phone user to below 10% of the total...
Two forest management objectives being debated in the context of federally managed landscapes in the US Pacific Northwest involve a perceived trade-off between fire restoration and C sequestration. The former strategy would reduce fuel (and therefore C) that has accumulated through a century of fire suppression and exclusion that has...
Concentrically arranged multiple-tube reactors with different dimensions were
built for synthesizing nano-sized silicon nitride powder via the ammonolysis of SiO
vapor. The reaction was operated at temperatures ranging from 1350 to 1400°C and
pressure slightly above atmospheric pressure. Silicon monoxide (SiO) vapor was
generated by charging argon gas through a...
A fully-saturated poroelastic medium is confined by the sides of a cylinder, and the regions below and above the medium are filled with fluid at respective constant pressures. The filtration flow of fluid through the poroelastic medium and the small deformations of the medium are described by a quasi-static Biot...
Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on...
Stein's method initially introduced in 1970 by C. Stein is a powerful technique for bounding the distance between the laws of two real-valued random variables. Stein's method has been used to prove distributional convergence to many standard probability distributions such as normal, multivariate normal, Poisson and Brownian motion approximation. In...
Many geophysical phenomena exhibit complicated dynamics that, due to a variety of factors, diverge quickly from physical models. The arrival of new observations allows researchers to combine the model estimate with measurements in a statistical process called data assimilation to produce a revised estimate of the phenomenon. This assimilation of...
This dissertation explores mathematical theory of the 3 dimensional incompressible Navier-Stokes equations that consists a set of partial differential equations which govern the motion of Newtonian fluids and can be seen as Newton's second law of motion for fluids. The main interest of this work focuses on how local perturbation...
The topic of statistical mechanics has been studied for over a century, and it is one of the pillars of modern physics. This theory can be applied to the study of the thermodynamic behavior of large systems of interacting particles, in which case it is referred to as equilibrium statistical...
In this thesis I will look at a definition of computable randomness from Algorithmic Information Theory as defined by Andre Nies through the lens of Computable Analaysis asdefined by Klaus Weihrauch. I will show that despite the fact that these two paradigmsgenerate distinct classes of computable supermartingales, the class of...
Markov chains have long been used to sample from probability distributions and simulate dynamical systems. In both cases we would like to know how long it takes for the chain's distribution to converge to within varepsilon of the stationary distribution in total variation distance; the answer to this is, called...
The Brownian motion of micron-scale particles reflects the viscoelastic response of the local environment of the medium. Tracking the thermal fluctuations of these particles is a measure of the rheology of the material at the microscopic scale. This technique is called passive microrheology. Microrheology has been developed to assess the...
Observations of the Oregon coast’s physical oceanography over the last few decades have revealed falling dissolved oxygen levels associated with seasonal upwelling, as well as rising water temperatures. In extreme cases, these changes have been associated with die-offs, redistribution, and decreased abundance and diversity of benthic fish and invertebrates. Many...
In order to understand better the defect structure and dynamics associated
with lower valent dopants complexed with native defects in group IV oxides, In/Cd
perturbed angular correlation spectroscopy was performed in ceria and zirconia. Examining
the orientation symmetry axis of defects in ceria single crystals at low temperature
has allowed...
Hydrotreating reaction of vegetable oil is an alternative method for the production of
renewable biodiesel fuel. This reaction involves conversion of triglycerides into
normal alkanes, leads to a deoxygenated and stable product, which is fully compatible
with petroleum derived diesel fuel. The hydrotreating process uses hydrogen to
remove oxygen from...
The asymmetric nature of bit errors in several practical applications provides grounds for efficient error control techniques. The Z-channel model and special classes of codes like asymmetric error detection codes and t-asymmetric error correcting/d-asymmetric error detecting codes can be successfully used in ARQ protocols for feedback error control enhancement. This...
Topological results are applied to boundary value problems modeling nonlinear
beams and dry friction. A classical continuation theorem is used to prove
existence results for nonlinear beams. Unified proofs, where possible, are given for
all the physically relevant boundary conditions. Integration techniques and various
integral inequalities are used to prove...
Ecosystems are highly heterogeneous systems subjected to important levels of environmental variability; however, it is common in terrestrial biogeochemical models to assume homogeneous properties of the elements of the system or constant environmental conditions. For some processes, heterogeneity in these models is treated very simplistically, but there is not much...
The local and remote sources of variability of the South Atlantic Ocean are investigated using a set of numerical experiments and satellite data. A global, eddy-permitting, numerical simulation is analyzed to investigate the dynamical links between the Antarctic Circumpolar Current (ACC) and the Malvinas Current (MC). The model results indicate...
In this work we will analyze branching Brownian motion on a finite interval with oneabsorbing and one reflecting boundary, having constant drift rate toward the absorbingboundary. Similar processes have been considered by Kesten ([12]), and more recently byHarris, Hesse, and Kyprianou ([11]). The current offering is motivated largely by the...
This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for...
The three essays in this dissertation progressively answer the following questions: (a) How important are constraints? (b) Who benefits from removing constraints? (c) When does a constraint for a single market predominantly affect closely related markets? These questions are applied in the context of time, weather, and minimum wage constraints,...
This dissertation's three essays explore the effects of climate change on land use
changes in the U.S., how future land areas in all major land uses change by projecting
land use at the regional scale under two IPCC climate change scenarios. Investigate how
and what role should carbon sequestration plays...