Physical Sciences and Mathematics Commons^™

The Effects Of Periodic And Non-Periodic Inputs On The Dynamics Of A Medial Entorhinal Cortex Layer Ii Stellate Cell Model, Dongwook Kim

Dissertations

Various neuron types exhibit sub-threshold and firing frequency resonance in which the sub-threshold membrane potential or firing frequency responses to periodic inputs peak at a preferred frequency (or frequencies). Previous experimental work has shown that medial entorhinal cortex layer II stellate cells (SCs) exhibit sub-threshold and firing frequency resonance in the theta frequency band (4 - 10 Hz). In this thesis we seek to understand the biophysical and dynamic mechanism underlying these phenomena and how they are related. We studied the effects of sinusoidal current and synaptic conductance inputs at various frequencies, with and without noise, on the supra-threshold dynamics …

Energy Propagation In Jammed Granular Matter, Xiaoni Fang

Dissertations

The systems built from dense granular materials are very important due to their relevance to a number of technological and other fields. However, they are difficult to study in particular due to a lack of accurate continuum description. In this work, studies on these systems are presented using discrete element simulations that model the granular particles as soft, elastic, and frictional disks which interact when in contact. These simulations are used for the purpose of analyzing a few granular systems with the main emphasis on understanding phenomena of energy and force propagation.

Analysis of energy propagation in a two-dimensional disordered …

Some Contributions To Modeling Usage Sensitive Warranty Servicing Strategies And Their Analyses, Rudrani Banerjee

Dissertations

Providing a warranty as a part of a product's sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization …

Using Feed-Forward Networks To Infer The Activity Of Feedback Neuronal Networks, Xinxian Huang

Dissertations

The nervous system is one of the most important organ systems in a multicellular body. Animals, including human beings perceive, learn, think and deliver motion instructions through their nervous system. The basic structural units of the nervous system are individual neurons which constitute different neuronal networks with distinct functions. In each network, constituent neurons are coupled with different connection patterns, for example, some neurons send feed-forward information to the coupling neurons while others are mutually coupled. Because it is often difficult to analyze large interconnected feedback neuronal networks, it is important to derive techniques to reduce the complexity of the …

Confidence Bands For Survival Functions Under Semiparametric Random Censorship Models, Peixin Zhang

Dissertations

In medical reports point estimates and pointwise confidence intervals of parameters are usually displayed. When the parameter is a survival function, however, the approach of joining the upper end points of individual interval estimates obtained at several points and likewise for the lower end points would not produce bands that include the entire survival curve with a given confidence. Simultaneous confidence bands, which allow confidence statements to be valid for the entire survival curve,would be more meaningful

This dissertation focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model- …

High-Order Adaptive Methods For Computing Invariant Manifolds Of Maps, Jacek K. Wrobel

Dissertations

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the …

Markovian And Stochastic Differential Equation Based Approaches To Computer Virus Propagation Dynamics And Some Models For Survival Distributions, Lianzhe Xu

Dissertations

This dissertation is divided in two Parts. The first Part explores probabilistic modeling of propagation of computer 'malware' (generally referred to as 'virus') across a network of computers, and investigates modeling improvements achieved by introducing a random latency period during which an infected computer in the network is unable to infect others. In the second Part, two approaches for modeling life distributions in univariate and bivariate setups are developed.

In Part I, homogeneous and non-homogeneous stochastic susceptible-exposed-infectious- recovered (SEIR) models are specifically explored for the propagation of computer virus over the Internet by borrowing ideas from mathematical epidemiology. Large computer …

Sequential Bayesian Filtering For Spatial Arrival Time Estimation, Rashi Jain

Dissertations

Locating and tracking a source in an ocean environment as well as estimating environmental parameters of a sound propagation medium is of utmost importance in underwater acoustics. Matched field processing is often the method of choice for the estimation of such parameters. This approach, based on full field calculations, is computationally intensive and sensitive to assumptions on the structure of the environment. As an alternative, methods that use only select features of the acoustic field for source localization and environmental inversion have been proposed. The focus here is on inversion using arrival times of identified paths within recorded time-series. After …

Numerical And Asymptotic Modeling Of Evolving Nonlinear Ocean Surface Wave Fields, Matt Malej

Dissertations

The main focus of this dissertation is the asymptotic and numerical modeling of nonlinear ocean surface wave fields. In particular, a development of an accurate numerical model for the evolution of nonlinear ocean waves, including extreme waves known as Rogue/Freak waves. Due to their elusive and destructive nature, the media often portrays Rogue waves as unimaginatively huge and unpredictable monsters of the sea. To address these concerns, derivations of asymptotically reduced models, based on the small wave steepness assumption, are presented and their corresponding numerical simulations via a Fourier pseudo-spectral method are discussed. The simulations are initialized with a well-known …

Uniform Heating Of Thin Ceramic Slabs In A Multimode Microwave Cavity, Shuchi Agrawal

Dissertations

Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled in the small Biot number limit and a thin silicon wafer situated in a TM101 cylindrical cavity modeled in the small fineness ratio limit are studied to gain insight into the dynamics of the heating process. The evolution of temperature is governed by a two-dimensional reaction diffusion equation and a spatially non-homogeneous reaction term. Numerical methods …

Asymptotic And Numerical Analysis Of Time-Dependent Wave Propagation In Dispersive Dielectric Media That Exhibit Fractional Relaxation, Matthew Frank Causley

Dissertations

This dissertation addresses electromagnetic pulse propagation through anomalously dispersive dielectric media. The Havriliak-Negami (H-N) and Cole-Cole (C-C) models capture the non-exponential nature of such dielectric relaxation phenomena, which is manifest in a variety of dispersive dielectric media. In the C-C model, the dielectric polarization is coupled to the time-dependent Maxwell's equations by a fractional differential equation involving the electric field. In the H-N case, a more general pseudo-fractional differential operator describes the polarization.

The development and analysis of a robust method for implementing such models is presented, with an emphasis on algorithmic efficiency. Separate numerical schemes are presented for C-C …

Pattern Formation In Oscillatory Systems, Hui Wu

Dissertations

Synchronization is a kind of ordinary phenomenon in nature, the study of it includes many mathematical branches. Phase space is one of the most powerful inventions of modern mathematical science. There are two variables, the position and velocity, that can describe the 2-dimensional phase space system. For example, the state of pendulum may be specified by its position and its velocity, so its phase space is 2-dimensional. The state of the system at a given time has a unique corresponding point in the phase space. In order to describe the motion of an oscillator, we can talk about its motion …