Spectra Of Quantum Trees And Orthogonal Polynomials, 2018 Louisiana State University and Agricultural and Mechanical College

#### Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang

*LSU Doctoral Dissertations*

We investigate the spectrum of regular quantum-graph trees, where the edges are endowed with a Schr\"odinger operator with self-adjoint Robin vertex conditions. It is known that, for large eigenvalues, the Robin spectrum approaches the Neumann spectrum. In this research, we compute the lower Robin spectrum. The spectrum can be obtained from the roots of a sequence of orthogonal polynomials involving two variables. As the length of the quantum tree increases, the spectrum approaches a band-gap structure. We find that the lowest band tends to minus infinity as the Robin parameter increases, whereas the rest of the bands remain positive ...

Generation Of Nonlinear-Differential-Equations System From A Model Of Boolean Relationships In Arabidopsis Salt Stress Network, 2018 Louisiana State University and Agricultural and Mechanical College

#### Generation Of Nonlinear-Differential-Equations System From A Model Of Boolean Relationships In Arabidopsis Salt Stress Network, Renee Dale

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Modeling Hcv Interactions With P53: Implications For Carcinogenesis, 2018 Florida State University

#### Modeling Hcv Interactions With P53: Implications For Carcinogenesis, Harsh Jain

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Disruption Of Synchronous Behavior In Pancreatic Islets Via Hub Cells, 2018 University of Maryland - Baltimore County

#### Disruption Of Synchronous Behavior In Pancreatic Islets Via Hub Cells, Janita Patwardhan

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Quantifying Effects Of Neutrophil Memory On Migration Patterns Using Microfluidic Platforms And Ode Modeling Of The Mechanistic Molecular Pathways, 2018 Virginia Polytechnic Institute and State University

#### Quantifying Effects Of Neutrophil Memory On Migration Patterns Using Microfluidic Platforms And Ode Modeling Of The Mechanistic Molecular Pathways, Brittany P. Boribong, Mark J. Lenzi, Mirjam Sarah Kadelka, Stanca Ciupe, Liwu Li, Caroline N. Jonea

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Modeling Pharmaceutical Inhibition Of Glucose-Stimulated Renin-Angiotensin System In Kidneys, 2018 Oklahoma State University - Main Campus

#### Modeling Pharmaceutical Inhibition Of Glucose-Stimulated Renin-Angiotensin System In Kidneys, Ashlee N. Ford Versypt, Minu R. Pilvankar, Hui Ling Yong

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Staged Hiv Transmission And Treatment In A Dynamic Model With Concurrency, 2018 Howard University

#### Staged Hiv Transmission And Treatment In A Dynamic Model With Concurrency, Katharine Gurski, Kathleen Hoffman

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Physical Applications Of The Geometric Minimum Action Method, 2018 The Graduate Center, City University of New York

#### Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

*All Dissertations, Theses, and Capstone Projects*

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...

The Pope's Rhinoceros And Quantum Mechanics, 2018 Bowling Green State University

#### The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

*Honors Projects*

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time ...

Analyzing Lagrangian Statistics Of Eddy-Permitting Models, 2018 University of Colorado, Boulder

#### Analyzing Lagrangian Statistics Of Eddy-Permitting Models, Amy Chen

*Applied Mathematics Graduate Theses & Dissertations*

Mesoscale eddies are the strongest currents in the world oceans and transport properties such as heat, dissolved nutrients, and carbon. The current inability to effectively diagnose and parameterize mesoscale eddy processes in oceanic turbulence is a critical limitation upon the ability to accurately model large-scale oceanic circulations. This investigation analyzes the Lagrangian statistics for four faster and less computationally expensive eddy-permitting models --- Biharmonic, Leith, Jansen & Held Deterministic, and Jansen & Held Stochastic --- and compares them against each other and an eddy-resolving quasigeostrophic Reference model. Results from single-particle climatology show that all models exhibit similar behaviour in large-scale movement over long times ...

Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, 2018 Pomona College

#### Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, Ami Radunskaya, Ruby Kim, Timothy Woods Ii

*Spora: A Journal of Biomathematics*

Monoclonal antibodies have shown promising results as a form of cancer immunotherapy used either alone or in combination with another treatment. We model a monoclonal antibody in combination with a dendritic cell (DC) vaccine in order to study treatment optimization. Certain proteins on tumor cells allow the tumor cells to bind to specific receptors on immune cells, rendering the immune cells ineffective. Experiments using mouse models show that a combination of antibodies to these proteins with tumor suppressing drugs improves the effectiveness of cancer vaccines. We create independent models of each of the two treatments in combination with DC therapy ...

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, 2018 University of North Florida

#### Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, Mahbubur Rahman 6203748

*Showcase of Faculty Scholarly & Creative Activity*

Approximation of stochastic differential equations (SDEs) with parametric noise plays an important role in a range of application areas, including engineering, mechanics, epidemiology, and neuroscience. A complete understanding of SDE theory with perturbed noise requires familiarity with advanced probability and stochastic processes. In this paper, we derive an asymptotic estimate of variance, and it is shown that numerical method gives a useful step toward solving SDEs with perturbed noise. Our goal is to diffuse the results to an audience not entirely familiar with functional notations or semi-group theory, but who might nonetheless be interested in the practical simulation of dynamical ...

Theoretical Analysis Of Nonlinear Differential Equations, 2018 Stephen F Austin State University

#### Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

*Electronic Theses and Dissertations*

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy ...

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, 2018 Augsburg College

#### Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz

*Spora: A Journal of Biomathematics*

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model ...

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, 2018 Augsburg University

#### Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz

*Faculty Authored Articles*

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model ...

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, 2018 Nanjing University of Science and Technology

#### Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

*SIUE Faculty Research, Scholarship, and Creative Activity*

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between local strong ...

Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, 2018 The University of Akron

#### Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans

*Honors Research Projects*

The spreading behavior of spherical and cylindrical water droplets between 30Å and 100Å in radius on a sapphire surface is investigated using all-atom molecular dynamics simulations for durations on the order of tens of nanoseconds. A monolayer film develops rapidly and wets the surface, while the bulk of the droplet spreads on top of the monolayer, maintaining the shape of a spherical cap. Unlike previous simulations in the literature, the bulk radius is found to increase to a maximum value and receed as the monolayer continues to expand. Simple time and droplet size dependence is observed for monolayer radius and ...

Modeling Public Opinion, 2018 Rollins College

#### Modeling Public Opinion, Arden Baxter

*Honors Program Theses*

The population dynamics of public opinion have many similarities to those of epidemics. For example, models of epidemics and public opinion share characteristics like contact rates, incubation times, and recruitment rates. Generally, epidemic dynamics have been presented through epidemiological models. In this paper we adapt an epidemiological model to demonstrate the population dynamics of public opinion given two opposing viewpoints. We find equilibrium solutions for various cases of the system and examine the local stability. Overall, our system provides sociological insight on the spread and transition of a public opinion.

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, 2018 Michigan Technological University

#### A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

*Dissertations, Master's Theses and Master's Reports*

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty ...

Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, 2018 The University of Akron

#### Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones

*Honors Research Projects*

In Dunn County, Wisconsin the lakes suffer from algae blooms due to excess phosphorus runoff. A coupled bio-economic model is studied with the intent of finding the optimal level of phosphorus that should be allowed into the lake depending on certain biologic and economic parameters. We model the algae and phosphorus concentration in the lake over time based off the phosphorus input. Community welfare is modeled by comparing the costs and benefits of phosphorus fertilizer. This model is proposed to find the phosphorus level that maximizes community welfare and then determine how certain environmental and social change initiatives will affect ...