Physical Sciences and Mathematics Commons^™

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 …

Active Feedback Control Of A Wake Flow Via Forced Oscillations Based On A Reduced Model, Fu Li

Dissertations

As it is well known, the flow past a cylinder consists of a symmetric recirculation bubble of vortices at small Reynolds numbers. As Reynolds number increases, the bubble becomes unstable and develops into a Karman vortex street of alternating vortices. This instability is responsible for the occurrence of large amplitude oscillations in the lift and an increase in the mean drag. It was previously shown by numerical simulation that the mechanism driving the bubble instability is well mimicked by Foppl's four dimensional potential flow model where the bubble is represented by a saddle point. In this work, we design two …

A Study Of Droplet Burning In The Nearly Adiabatic Limit, Juan C. Gomez

Dissertations

We consider a small drop of liquid fuel that burns in an oxidizing gaseous environment and translates slowly (relative to flow 'at infinity') under the action of gravity. Practical applications include the burning of liquid fuels as sprays in domestic and industrial oil-fired burners, diesel engines, and liquid-propellant rocket motors. More relevant to the simple physical set-up of the present study are wellcharacterized laboratory experiments on the burning of a single, isolated fuel drop.

The drop burns in a nearly spherical, diffusion flame, flame sheet regime. We consider a specific example, or limit, referred to as 'nearly adiabatic burning', in …

Numerical Study Of Particle Dynamics In A Falling-Ball Viscometer, Peiwen Hou

Dissertations

The falling-ball viscometer is a device where a spherical particle falls along the axis of a circular cylinder filled with viscous fluid. The various classical results for this device are developed under the assumption that the Reynolds number of the flow is zero, i.e., Stoke's flow. Inertial effects are not taken into account. To better understand the dynamics of the particle sedimentation process and the role of inertia in this process, we implemented a numerical simulation.

The ADI (Alternating Direction Implicit) scheme is widely used to solve the vorticity-stream function formulation of the Navier-Stokes equation in axisymmetric geometries. However, a …

A Mathematical Model Of Wheelchair Racing, Susan J. Schenk

Dissertations

Wheelchair racing strokes are very complicated movements, which involve a coupling between the athlete and his or her racing chair. Each body segment, as well as the wheel, follows a distinct trajectory as the motion is performed. Understanding the kinematics and kinetics of various stroke techniques would provide the athletes and their coaches with information, which could help guide the racers toward improved performances.

In this thesis, a mathematical model is developed, which is capable of providing such valuable kinematic and kinetic information. This two-dimensional model represents the body segments as a coupled pendulum system of point masses and the …

Flame Dynamics In Steady Strained Flows, Zili Huang

Dissertations

In this dissertation, the response of a premixed flame to time-dependent strained flow fields is investigated. Because of the potential application to turbulent combustion modeling, the main focus is on the particular case of a flame in stagnation point flow with an imposed oscillatory strain rate. The flame is modeled as a hydrodynamic discontinuity separating burned from unburned gasses. To complete the formulation of the problem, conditions relating the fluid variables across the flame front are needed, as is a flame speed equation that determines the evolution of the discontinuity. These conditions are derived through asymptotic analysis of the flame …

A Theoretical Study Of Bubble Motion In Surfactant Solutions, Yanping Wang

Dissertations

We examine the effect of surfactants on a spherical gas bubble rising steadily in an infinite fluid at low and order one Reynolds number with order one and larger Peclet numbers. Our mathematical model is based on the Navier-Stokes equations coupled with a convection-diffusion equation together with appropriate interfacial conditions. The nonlinearity of the equations and boundary conditions, and the coupling between hydrodynamics and surfactant transport make the problem very challenging.

When a bubble rises in a fluid containing surface-active agents, surfactant adsorbs onto the bubble surface at the leading edge, convects to the trailing edge by the surface flow …