Mathematics Commons^™

Travel Time Theory For Traffic Conservation Laws With Applications, Sergio Contreras

UNLV Theses, Dissertations, Professional Papers, and Capstones

Travel time is an important concept in various intelligent transportation system (ITS) applications. The concept is used in a wide array of applications, such as system planning, system performance, and optimization. Reducing the time required to travel between different points on a network is an important goal. Benefits include reducing time wasted in traveling, and keeping travelers satisfied. Thus, studying and reducing travel time in ITS is beneficial in different applications.

The classic density-based Lighthill Whitman Richards (LWR) equation for modeling traffic flow is the starting point in this dissertation. A more recent travel time dynamics function built on top …

The Zorich Transform And Generalizing Koenigs Linearization Theorem To Quasiregular Maps, Jacob A. Pratscher

Graduate Research Theses & Dissertations

This dissertation investigates the role that a new tool called the Zorich transform plays in quasiregular dynamics as a generalization of the logarithmic transform in complex dynamics. In particular we use the Zorich transform to construct analogues of the logarithmic spiral maps and interpolation between radial stretch maps. These constructions are then used to completely classify the orbit space of a quasiregular map. Also, conditions are given in which a quasiregular map $f:D\to\R^n$, where $D\subset\R^n$ is a domain, that is quasiconformal in a neighborhood of a geometrically attracting fixed point can be conjugated by a quasiconformal map to the asymptotic …

Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan

Doctoral Dissertations

Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed …

Role Of Influence In Complex Networks, Nur Dean

Dissertations, Theses, and Capstone Projects

Game theory is a wide ranging research area; that has attracted researchers from various fields. Scientists have been using game theory to understand the evolution of cooperation in complex networks. However, there is limited research that considers the structure and connectivity patterns in networks, which create heterogeneity among nodes. For example, due to the complex ways most networks are formed, it is common to have some highly “social” nodes, while others are highly isolated. This heterogeneity is measured through metrics referred to as “centrality” of nodes. Thus, the more “social” nodes tend to also have higher centrality.

In this thesis, …

A Spider's Web Of Doughnuts, Daniel Stoertz

Graduate Research Theses & Dissertations

This dissertation studies an interplay between the dynamics of iterated quasiregular map-

pings and certain topological structures. In particular, the relationship between the Julia set

of a uniformly quasiregular mapping f : R 3 → R 3 and the fast escaping set of its associated

Poincaré linearizer is explored. It is shown that, if the former is a Cantor set, then the latter

is a spider’s web. A new class of uniformly quasiregular maps is constructed to which this

result applies. Toward this, a geometrically self-similar Cantor set of genus 2 is constructed.

It is also shown that for any …

Dynamics Of Gene Networks In Cancer Research, Paul Scott

Electronic Theses and Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

Existence Of The Mandelbrot Set In The Parameter Planes Of Certain Rational Functions, Alexander Jay Mitchell

Theses and Dissertations

In complex dynamics we compose a complex valued function with itself repeatedly and

observe the orbits of values of that function. Particular interest is in the orbit of critical

points of that function (critical orbits). One famous, studied example is the quadratic

polynomial Pc(z) = z^2 +c and how changing the value of c makes a difference to the orbit of the critical point z = 0. The set of c values for which the critical orbit is bounded is called

the Mandelbrot set.

This paper studies rational functions of the form Rn;a;c(z) = z^n + a/z^n + c and …

No-Slip Billiards, Christopher Lee Cox

Arts & Sciences Electronic Theses and Dissertations

We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. A general theory of rigid body collisions in is developed, which returns the known dimension two model as a special case but generalizes to higher dimensions. We give new results on periodicity and boundedness of orbits which suggest that a class of billiards (including all polygons) is not ergodic. Computer generated phase portraits demonstrate non-ergodic features, suggesting chaotic no-slip billiards cannot easily be constructed using the common techniques for generating chaos in standard billiards. However, …

Chaos And Learning In Discrete-Time Neural Networks, Jess M. Banks

Honors Papers

We study a family of discrete-time recurrent neural network models in which the synaptic connectivity changes slowly with respect to the neuronal dynamics. The fast (neuronal) dynamics of these models display a wealth of behaviors ranging from simple convergence and oscillation to chaos, and the addition of slow (synaptic) dynamics which mimic the biological mechanisms of learning and memory induces complex multiscale dynamics which render rigorous analysis quite difficult. Nevertheless, we prove a general result on the interplay of these two dynamical timescales, demarcating a regime of parameter space within which a gradual dampening of chaotic neuronal behavior is induced …

Algebraic Aspects Of (Bio) Nano-Chemical Reaction Networks And Bifurcations In Various Dynamical Systems, Teng Chen

Electronic Theses and Dissertations

The dynamics of (bio) chemical reaction networks have been studied by different methods. Among these methods, the chemical reaction network theory has been proven to successfully predicate important qualitative properties, such as the existence of the steady state and the asymptotic behavior of the steady state. However, a constructive approach to the steady state locus has not been presented. In this thesis, with the help of toric geometry, we propose a generic strategy towards this question. This theory is applied to (bio)nano particle configurations. We also investigate Hopf bifurcation surfaces of various dynamical systems.

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

Perturbed Spherical Objects In Acoustic And Fluid Flow Fields, Manmeet Kaur

Dissertations

In this study, the time averaged acoustic radiation force and drag on a small, nearly spherical object suspended freely in a stationary sound wave field in a compressible, low viscosity fluid is to be calculated. This problem has been solved for a spherical object, and it has many important engineering applications related to segregation and separation processes for particles in fluids such as water. Small but significant errors have occurred in the predicted behavior of the particles using the existing approximate solutions based on perfect spheres. The classical approach has been extended in this research to objects that deviate slightly …

Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar

Theses and Dissertations

In this thesis we derive a hydrodynamical kinetic theory to study the orientational response of a mesoscopic system of nematic liquid crystals in the presence of an external flow field. Various problems have been attempted in this direction. First, we understand the steady-state behavior of uniaxial LCPs under an imposed elongational flow, electric and magnetic field respectively. We show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field is parallel to one of the eigenvectors of the second moment tensor, and (3) the steady state probability density function is of the Boltzmann type. …

Dynamics Of Spatial Pattern Formation: Cases Of Spikes And Droplets, Yuya Sasaki

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis studies the gradient system that forms spatial patterns such that the minimum distances of pairs among various points are maximized in the end. As this problem innately involves singularity issues, an extended system of the gradient system is proposed. Motivated by the spatial pattern suggested by a numerical example, this extended system is applied to a three-point problem and then to a two-point problem in a quotient space of ℝ² modulo a lattice.

Bounds On Constraint Weight Parameters Of Hopfield Networks For Stability Of Optimization Problem Solutions, Gursel Serpen

Electrical & Computer Engineering Theses & Dissertations

The purpose of the presented research is to study the convergence characteristics of Hopfield network dynamics. The relation between constraint weight parameter values and the stability of solutions of constraint satisfaction and optimization problems mapped to Hopfield networks is investigated. A theoretical development relating constraint weight parameter values to solution stability is presented. The dependency of solution stability on constraint weight parameter values is shown employing an abstract optimization problem. A theorem defining bounds on the constraint weight parameter magnitudes for solution stability of constraint satisfaction and optimization problems is proved. Simulation analysis on a set of optimization and constraint …

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …