An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, 2015 Universidad de la Republica Oriental del Uruguay

#### An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, Martin Egozcue, Luis Fuentes García

*Martin Egozcue*

No abstract provided.

Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, 2015 Auckland University of Technology

#### Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, Reza Moosavi Mohseni Dr., Wenjun Zhang Dr., Jiling Cao Prof.

*Reza Moosavi Mohseni*

The aim of the present study is to detect the chaotic behavior in the monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase the complexity of the system and leads to more chaotic behavior.

Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, 2015 University of Bucharest

#### Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu

*UNLV Gaming Research & Review Journal*

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of mathematical modeling, arguing that such non-standard knowledge ...

Transition Orbits Of Walking Droplets, 2015 California Polytechnic State University - San Luis Obispo

#### Transition Orbits Of Walking Droplets, Joshua Parker

*Physics*

It was recently discovered that millimeter-sized droplets bouncing on the surface of an oscillating bath of the same fluid can couple with the surface waves it produces and begin walking across the fluid bath. These walkers have been shown to behave similarly to quantum particles; a few examples include single-particle diffraction, tunneling, and quantized orbits. Such behavior occurs because the drop and surface waves depend on each other to exist, making this the first and only known macroscopic pilot-wave system. In this paper, the quantized orbits between two identical drops are explored. By sending a perturbation to a pair of ...

Hydrodynamic Analogues Of Hamiltonian Systems, 2015 University of Massachusetts Boston

#### Hydrodynamic Analogues Of Hamiltonian Systems, Francisco J. Jauffred

*Graduate Masters Theses*

A one-dimensional Hamiltonian system can be modeled and understood as a two-dimensional incompressible fluid in phase space. In this sense, the chaotic behavior of one-dimensional time dependent Hamiltonians corresponds to the mixing of two-dimensional fluids. Amey (2012) studied the characteristic values of one such system and found a scaling law governing them. We explain this scaling law as a diffusion process occurring in an elliptical region with very low eccentricity. We prove that for such a scaling law to occur, it is necessary for a vorticity field to be present. Furthermore, we show that a conformal mapping of an incompressible ...

Multiphysics Modeling To Enhance Understanding Of Microwave Heating Of Food In Domestic Ovens, 2015 University of Nebraska-Lincoln

#### Multiphysics Modeling To Enhance Understanding Of Microwave Heating Of Food In Domestic Ovens, Jiajia Chen

*Biological Systems Engineering--Dissertations, Theses, and Student Research*

Nonuniform heating is the biggest issue in the microwave heating of prepared meals. Multiphysics based models are promising tools to improve microwave heating uniformity by properly designing the food product. However, limited availability of accurate temperature-dependent material properties, inadequate model prediction accuracy, and high computational power and complexity in model development are three gaps that greatly limited the application of these models in the food industry.

To fill in the gaps, firstly, we developed a multitemperature calibration protocol to measure temperature-dependent dielectric properties (dielectric constant and loss factor). The temperature-dependent dielectric and thermal (thermal conductivity and specific heat capacity) properties ...

Using Community Structure Networks To Model Heterogeneous Mixing In Epidemics, And A Potential Application To Hiv In Washington, D.C., 2015 Bates College

#### Using Community Structure Networks To Model Heterogeneous Mixing In Epidemics, And A Potential Application To Hiv In Washington, D.C., Katherine Ragland Paulson

*Honors Theses*

Using models, mathematicians can better understand and analyze the factors that influence the dynamic spread of infectious disease through a population. The most fundamental epidemiological model is the SIR model, originally proposed by Kermack and McKendrick. In this model individuals in a population are categorized as Susceptible (S), Infected (I), or Removed (R), and differential equations are used to analyze the flow of people from one compartment to another. Many epidemiological models use the SIR model as a foundation, building complexities into it. Modeling HIV, for example, is complex because not all people in a population are at equal risk ...

Entropy Vs. Energy Waveform Processing: A Comparison Based On The Heat Equation, 2015 Washington University in St Louis

#### Entropy Vs. Energy Waveform Processing: A Comparison Based On The Heat Equation, Michael S. Hughes, John E. Mccarthy, Paul J. Bruillard, Jon N. Marsh, Samuel A. Wickline

*Mathematics Faculty Publications*

Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information”, as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined ...

A Model For Mountain Pine Beetle Outbreaks In An Age-Structured Forest: Predicting Severity And Outbreak Recovery Cycle Period, 2015 Utah State University

#### A Model For Mountain Pine Beetle Outbreaks In An Age-Structured Forest: Predicting Severity And Outbreak Recovery Cycle Period, Jacob P. Duncan

*Jacob P Duncan*

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years,warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations. Stability of fixed points is analyzed as a function of (thermally controlled) MPB population growth rates and indicates the existence of periodic outbreaks that intensify as growth rates increase. We devise ...

Spatially Random Processes In One-Dimensional Maps: The Logistic Map And The Arnold Circle Map, 2015 University of Colorado Boulder

#### Spatially Random Processes In One-Dimensional Maps: The Logistic Map And The Arnold Circle Map, An T. Le

*Applied Mathematics Graduate Theses & Dissertations*

One way to model in-situ remediation of contaminated groundwater is to consider spatially random processes in nonlinear systems. Groundwater remediation often requires injecting an aquifer with treatment solution, where degradation reactions break down the toxins. As the treatment solution and contaminated water flow through the aquifer, their movement is limited by the types of sediment found in the aquifer, which act as spatial barriers to mixing. The onset of chaos in this system implies the two solutions are well mixed, and thus the contaminants are rendered inert. The spatially random processes explored in this thesis are meant to mimic the ...

A Hierarchical Graph For Nucleotide Binding Domain 2, 2015 East Tennessee State University

#### A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

*Electronic Theses and Dissertations*

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2 ...

Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, 2015 Western Kentucky University

#### Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik

*Masters Theses & Specialist Projects*

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental ...

Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, 2015 Western Kentucky University

#### Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, Stephen Guffey

*Masters Theses & Specialist Projects*

In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the ...

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, 2015 University of Nebraska-Lincoln

#### Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

*Dissertations, Theses, and Student Research Papers in Mathematics*

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to ...

Boundary Problems For One And Two Dimensional Random Walks, 2015 Western Kentucky University

#### Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

*Masters Theses & Specialist Projects*

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with ...

On Mikhailov's Reduction Group, 2015 Dublin Institute of Technology

#### On Mikhailov's Reduction Group, Tihomir I. Valchev

*Articles*

We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.

A Mechanistic Model Of Multidecadal Climate Variability, 2015 University of Wisconsin-Milwaukee

#### A Mechanistic Model Of Multidecadal Climate Variability, Tyler J. Plamondon

*Theses and Dissertations*

This thesis addresses the problem of multidecadal climate variability by constructing and analyzing the output of a mechanistic model for the Northern Hemisphere’s multidecadal climate variability. The theoretical backbone of our modeling procedure is the so-called “stadium-wave” concept, in which interactions between regional climate subsystems are thought to result in a phase-space propagation of multidecadal climate anomalies across the hemispheric and global scales. The current generation of comprehensive climate models do not appear to support the “stadium wave,” which may indicate that either the models lack the requisite physics, or that the “stadium wave” itself is an artifact of ...

Modeling Enrollment At A Regional University Using A Discrete-Time Markov Chain, 2015 East Tennessee State University

#### Modeling Enrollment At A Regional University Using A Discrete-Time Markov Chain, Zachary T. Helbert

*Undergraduate Honors Theses*

A discrete time Markov Chain is used to model enrollment at a regional university. A preliminary analysis is conducted on the data set in order to determine the classes for the Markov chain model. The semester, yearly, and long term results of the model are examined thoroughly. A sensitivity analysis of the probability matrix entries is then conducted to determine the overall greatest influence on graduation rates.

Flexible Memory Allocation In Kinetic Monte Carlo Simulations, 2015 University of Tennessee - Knoxville

#### Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig

*Masters Theses*

We introduce two new algorithms for Kinetic Monte Carlo simulations: the minimal and flexible allocation algorithms. The theory and computational challenges associated with K.M.C. simulations are briefly discussed. We outline the simple cubic, solid-on-solid model of epitaxial growth and analyze four methods for its simulation: the linear search, standard inverted list, minimal allocation, and flexible allocation algorithms. We then implement these algorithms, analyze their performances, and discuss implications of the results.

Numerical Analysis Of Convex Splitting Schemes For Cahn-Hilliard And Coupled Cahn-Hilliard-Fluid-Flow Equations, 2015 University of Tennessee - Knoxville

#### Numerical Analysis Of Convex Splitting Schemes For Cahn-Hilliard And Coupled Cahn-Hilliard-Fluid-Flow Equations, Amanda Emily Diegel

*Doctoral Dissertations*

This dissertation investigates numerical schemes for the Cahn-Hilliard equation and the Cahn-Hilliard equation coupled with a Darcy-Stokes flow. Considered independently, the Cahn-Hilliard equation is a model for spinodal decomposition and domain coarsening. When coupled with a Darcy-Stokes flow, the resulting system describes the flow of a very viscous block copolymer fluid. Challenges in creating numerical schemes for these equations arise due to the nonlinear nature and high derivative order of the Cahn-Hilliard equation. Further challenges arise during the coupling process as the coupling terms tend to be nonlinear as well. The numerical schemes presented herein preserve the energy dissipative structure ...