Applied Mathematics Commons^™

Swarm Control Through Symmetry And Distribution Characterization, Georgi Dinolov

HMC Senior Theses

Two methods for control of swarms are described. The first of these methods, the Virtual Attractive-Repulsive (VARP) method, is based on potentials defined between swarm elements. The second control method, or the abstraction method, is based on controlling the macroscopic characteristics of a swarm. The derivation of a new control law based on the second method is described. Numerical simulation and analytical interpretation of the result is also presented.

Verification Of Solutions To The Sensor Location Problem, Chandler May

HMC Senior Theses

Traffic congestion is a serious problem with large economic and environmental impacts. To reduce congestion (as a city planner) or simply to avoid congested channels (as a road user), one might like to accurately know the flow on roads in the traffic network. This information can be obtained from traffic sensors, devices that can be installed on roads or intersections to measure traffic flow. The sensor location problem is the problem of efficiently locating traffic sensors on intersections such that the flow on the entire network can be extrapolated from the readings of those sensors. I build on current research …

Simulations Of Surfactant Spreading, Jeffrey Wong

HMC Senior Theses

Thin liquid films driven by surface tension gradients are studied in diverse applications, including the spreading of a droplet and fluid flow in the lung. The nonlinear partial differential equations that govern thin films are difficult to solve analytically, and must be approached through numerical simulations. We describe the development of a numerical solver designed to solve a variety of thin film problems in two dimensions. Validation of the solver includes grid refinement studies and comparison to previous results for thin film problems. In addition, we apply the solver to a model of surfactant spreading and make comparisons with theoretical …

Generalized Bathtub Hazard Models For Binary-Transformed Climate Data, James Polcer

Masters Theses & Specialist Projects

In this study, we use a hazard-based modeling as an alternative statistical framework to time series methods as applied to climate data. Data collected from the Kentucky Mesonet will be used to study the distributional properties of the duration of high and low-energy wind events relative to an arbitrary threshold. Our objectiveswere to fit bathtub models proposed in literature, propose a generalized bathtub model, apply these models to Kentucky Mesonet data, and make recommendations as to feasibility of wind power generation. Using two different thresholds (1.8 and 10 mph respectively), results show that the Hjorth bathtub model consistently performed better …

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

Operator Splitting Method And Applications For Semilinear Parabolic Partial Differential Equations, R. Corban Harwood

Faculty Publications - Department of Mathematics

This dissertation presents a redefined operator splitting method used in solving semilinear parabolic partial differential equations. As one such form, the reaction-diffusion equation is highly prevalent in mathematical modeling. Besides being physically meaningful as a separation of two distinct physical processes in this equation, operator splitting simplifies the solution method in several ways. The super-linear speed-up of computations is a rewarding simplification as it presents great benefits for large-scale systems. In solving these semilinear equations, we will develop a condition for oscillation-free methods, a condition independent of the usual stability condition. This numerical consideration is important to fully embody our …

Color Image Noise Reduction With The Total Variation Model And Proximity Operators, Aaron Katchen

Renée Crown University Honors Thesis Projects - All

The following paper discusses how efficient and effective color image noise reduction may be achieved through the use of mathematic numerical analysis. Digital image noise is a longstanding problem for which efficient and effective solutions are critical to the advancement of the field of digital imaging. Micchelli-Shen-Xu [3] used the Total Variation Model in conjunction with proximity operators to propose a set of algorithms to effectively and efficiently solve for noisy grayscale images. They proposed the use of the proximity operator in anisotropic and isotropic total variation in fixed point algorithms. The following paper will discuss their algorithms as well …

New Algorithms For Computing Groebner Bases, Frank Volny

All Dissertations

In this thesis, we present new algorithms for computing Groebner bases. The first algorithm, G2V, is incremental in the same fashion as F5 and F5C. At a typical step, one is given a Groebner basis G for an ideal I and any polynomial g, and it is desired to compute a Groebner basis for the new ideal , obtained from I by joining g. Let (I : g) denote the colon ideal of I divided by g. Our algorithm computes Groebner bases for I, g and (I : g) simultaneously. In previous algorithms, S-polynomials that reduce to zero are useless, …

Energy Efficient Compressed Sensing In Wireless Sensor Networks Via Random Walk, Robert Brian Fletcher

Masters Theses and Doctoral Dissertations

In this paper, we explore the problem of data acquisition using compressive sensing (CS) in wireless sensor networks. Unique properties of wireless sensor networks require we minimize communication cost for efficient power usage. At first, a compressive distributed sensing (CDS) algorithm is proposed but is then modified to decrease communication costs. The final algorithm presented is compressive distributed sensing with random walk CDS(RW); an algorithm that combines the data gathering and projection generation process of CDS.CDS(RW) uses rateless encoding, graph algorithms, and belief propagation decoding to improve upon the communication cost associated with CDS. In the end, we show that …

Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He

Scholarship

We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences. Using a new polynomial sequence transformation technique presented in [12], we give a method to evaluate the measures and their supports of some orthogonal generalized Gegenbauer-Humbert polynomial sequences.

A Statistical Model For Long-Term Forecasting Of Strong Sand Dust Storms, Siqi Tan

UNLV Theses, Dissertations, Professional Papers, and Capstones

Dust elevated into the atmosphere by dust storms has numerous environmental consequences. These include contributing to climate change; modifying local weather conditions; producing chemical and biological changes in the oceans; and affecting soil formation, surface water, groundwater quality, crop growth, and survival (Goudie and Middleton, 1992). Societal impacts include disruptions to air, road and rail traffic; interruption of radio services; the myriad effects of static-electricity generation; property damage; and health effects on humans and animals (Warner, 2004).

In this thesis, we extend the idea of empirical recurrence rate (ERR), developed by Ho (2008), to model the temporal trend of the …

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …

A Restarted Homotopy Method For The Nonsymmetric Eigenvalue Problem, Brandon Hutchison

Graduate Theses and Dissertations

The eigenvalues and eigenvectors of a Hessenberg matrix, H, are computed with a combination of homotopy increments and the Arnoldi method. Given a set, Ω, of approximate eigenvalues of H, there exists a unique vector f = f(H,Ω) in Rn where λ(H-e_{1ft)=Ω. A diagonalization of the homotopy H(t)=H−(1−t)e1ft at $t=0$ provides a prediction of the eigenvalues of H(t) at later times. These predictions define a new Ω that defines a new homotopy. The correction for each eigenvalue has an O(t2) error estimate, enabling variable step size and efficient convergence tests. Computations are done primarily in real arithmetic, and …}

Global Well-Posedness For A Nonlinear Wave Equation With P-Laplacian Damping, Zahava Wilstein

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation deals with the global well-posedness of the nonlinear wave equation
u_tt − Δu − Δ_pu_t = f (u) in Ω × (0,T),
{u(0), u_t(0)} = {u₀,u₁} ∈ H¹₀ (Ω) × L ² (Ω),
u = 0 on Γ × (0, T ),
in a bounded domain Ω ⊂ ℜ ⁿ with Dirichlét boundary conditions. The nonlinearities f (u) acts as a strong source, which is allowed to …

On Morrey Spaces In The Calculus Of Variations, Kyle Fey

Department of Mathematics: Dissertations, Theses, and Student Research

We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫_Ω f(x, u, ∇u)dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(|·|)^α(x), where h is an N-function.

Following this, we provide a characterization of the class of Young measures that can be generated by a sequence …

The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates, Xuzhou Chen, Jun Ji

Faculty Articles

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

Implementation Of Hidden Semi-Markov Models, Nagendra Abhinav Dasu

UNLV Theses, Dissertations, Professional Papers, and Capstones

One of the most frequently used concepts applied to a variety of engineering and scientific studies over the recent years is that of a Hidden Markov Model (HMM). The Hidden semi-Markov model (HsMM) is contrived in such a way that it does not make any premise of constant or geometric distributions of a state duration. In other words, it allows the stochastic process to be a semi-Markov chain. Each state can have a collection of observations and the duration of each state is a variable. This allows the HsMM to be used extensively over a range of applications. Some of …

Mathematical Modeling Of Metamaterials, Valjean Elizabeth Elander

UNLV Theses, Dissertations, Professional Papers, and Capstones

Metamaterials are artificially structured nano materials with negative refraction index. The successful construction of such metamaterials in 2000 triggered a great interest in study of metamaterials by researchers from different areas. The discovery of metamaterials opened a wide potential for applications in diverse areas such as cloaking, sub-wavelength imaging, solar cell design and antennas.

In this thesis, we investigate the most popular Drude metamaterial model. More specifically, we first present a brief overview of metamaterials and their potential applications, then we discuss the well-posedness of this model, and develop several numerical schemes to solve it. We implement our schemes using …

Biologically Relevant Classes Of Boolean Functions, Lori Layne

All Dissertations

A large influx of experimental data has prompted the development of
innovative computational techniques for modeling and reverse
engineering biological networks. While finite dynamical systems,
in particular Boolean networks, have gained attention as relevant
models of network dynamics, not all Boolean functions reflect the
behaviors of real biological systems. In this work, we focus on two
classes of Boolean functions and study their applicability as
biologically relevant network models: the nested and partially nested
canalyzing functions.
We begin by analyzing the nested canalyzing functions} (NCFs),
which have been proposed as gene regulatory network models due to
their stability properties. We …

K-Hyponormality Of Powers Of Multivariable Weighted Shifts, Mayra O. Martinez

Theses and Dissertations - UTB/UTPA

In mathematics, weighted shifts, also known as shift operators or translation operators, are examples of linear operators. Single and multivariable weighted shifts have played an important role in the study of (joint) k-hyponormality to LPCS. They have also played a significant role in the study of cyclicity and reflexivity, in the study of C*-algebras generated by multiplication operators on Bergman spaces, as fertile ground to test new hypotheses, and as canonical models for theories of dilation and positivity. We will first consider the hyponormality of powers of commuting multivariable weighted shifts. Specifically, if we let W(α,β) := (T1, T2) denote …