Physical Sciences and Mathematics Commons^™

The Structure And Stability Of Expanding And Converging Near-Stoichiometric Flames, Raymond Addabbo

Dissertations

The stability of expanding and converging premixed flames is investigated theoretically. These configurations are inherently unsteady and represent simple examples of positively (expanding) and negatively (converging) stretched flames. A new model is employed in this study that incorporates both hydrodynamic and diffusional-thermal effects. The model expands earlier works by incorporating variable transport properties, variations in the mixture strength and a more realistic dependence on viscosity.

The expanding flame is shown to remain stable at small radii provided the thermal diffusivity exceeds the mass diffusivity of the deficient reactant. However, once the flame achieves a critical size, a cellular instability appears, …

Asymptotic Methods In Applied Waveguide Problems, Helen Martynov

Dissertations

Some of the most challenging problems in acoustics and electromagnetics involve the study of scattered fields in waveguides caused by targets of elaborate shape. The complexity of the resulting scattered field depends on the geometry of the scatterer, and exact solutions exist only for the simple geometries.

The asymptotic methods developed in this dissertation give the approximate solutions for the scattered fields in two practically important geometries: an object placed inside a stratified waveguide, and a waveguide with multiple abrupt width transitions. The solutions for these geometries are obtained by approximating the field near the target or junction by the …

A Dynamical Model Of The Distributed Interaction Of Intracellular Signals, Adrienne C.N. James

Dissertations

A major goal of modern cell biology is to understand the regulation of cell behavior in the reductive terms of all the molecular interactions. This aim is made explicit by the assertion that understanding a cell's response to stimuli requires a full inventory of details. Currently, no satisfactory explanation exists to explain why cells exhibit only a relatively small number of different behavioral modes.

In this thesis, a discrete dynamical model is developed to study interactions between certain types of signaling proteins. The model is generic and "connectionist" in nature and incorporates important concepts from the biology. The emphasis is …

Efficient Inversion Methods In Underwater Acoustics, Xiaoqun Ma

Dissertations

This dissertation describes efficient methods developed and implemented for source localization and sound speed and bottom depth estimation using sound propagation in the ocean. The proposed inversion techniques are based on the linearization of the generally non-linear inverse problem of parameter estimation in underwater acoustics. These techniques take into account properties of the ocean environment and are accurate in their estimation results without being prohibitively computationally intensive. For the inversion, select ray paths are taken into account: the direct, first surface bounce, and first bottom bounce. Ray travel time derivatives with respect to parameters that affect path arrival times are …

Multi-Mode Cavity Effects In The Microwave Heating Of A Ceramic Slab, Stuart J. Walker

Dissertations

In order to gain insight into hot spot development in microwave heated ceramics, a partially insulated, two dimensional ceramic slab situated in a TE_M01 cavity is modeled in the small Biot number limit. If the electrical conductivity is an exponential function of temperture and E₀ is the strength of the incident mode, then the relationship between the spatially uniform, steady state leading order temperature, v₈, and E₀¹ is characterized by the well known bi-stable, or S shaped, response curve. The steady state second order temperature, v₁, is described by a boundary …

Analysis Of Discrete Dynamical System Models For Competing Species, Jerry J. Chen

Dissertations

A discrete version of the Lotka-Volterra (LV) differential equations for competing population species is analyzed in detail, much the same way as the discrete form of the logistic equation has been investigated as a source of bifurcation phenomena and chaotic dynamics. Another related system, namely, the Exponentially Self Regulating (ESR) population model, is also thoroughly analyzed. It is found that in addition to logistic dynamics - ranging from the very simple to manifestly chaotic regimes in terms of the governing parameters - the discrete LV model and the ESR model exhibit their own brands of bifurcation and chaos that are …