It is plausible that the hydromagnetic flow in the Earth's core which sustains the geomagnetic field is driven by small-scale buoyant blobs, with the buoyancy being of either compositional or thermal origin. The possibility and importance of the $\alpha$-effect, a mean-field induction effect by small-scale flow and field, by blob convection in the Earth's core are studied assuming that the flows driven by blobs do not interact with each other. / In a rotating hydromagnetic system such as the Earth's core, various types of flows are possible due to the effects of Coriolis, Lorentz and viscous forces. With a balance between Coriolis and Lorentz forces and with Coriolis dominant, the wake is a foreshortened Taylor column. With same force balance but with Lorentz dominant, the wake is elongated in the direction of the ambient magnetic field. It is believed that one or both of the wakes having a Lorentz-Coriolis force balance are relevant for the Earth's core. / To dominant order in the magnetic Reynolds number (assumed small), the integral of helicity and electromotive force over all space, produced by any buoyancy field which decays to zero at infinity, is zero. Analyses of distribution of leading order helicity and electromotive force are carried out in detail for a spherically symmetric blob. The electromotive force integrated over the plane perpendicular to the rotation direction is found to be parallel to the ambient magnetic field, as modeled by the $\alpha$-effect. If there are enough blobs (of order $10\sp7$), this electromotive force contributes significantly to the geodynamo. / The constraint of symmetry must be broken to have non-zero net helicity. Four symmetry breakers are considered: non-linear effect, the effect of rigid non-conducting boundary, the effect of large-scale geostrophic flow, and the effect of non-uniform ambient magnetic field. Order of magnitude of helicities are estimated and found to be either zero or very small. Some other effect is necessary to get significant non-zero helicity. / Source: Dissertation Abstracts International, Volume: 57-06, Section: B, page: 3621. / Major Professor: David E. Loper. / Thesis (Ph.D.)--The Florida State University, 1996.

Flow was created in freely suspended liquid crystal films in the smectic C phase using gradients in the surface tension to drive the motion. The director field was distorted into a pattern of vortices which wind upon themselves while the gradient was being applied. The dependence of the pattern in the director field for topological defects of index S = +1,0, or $-$1 are reported. The flow pattern for the S = $-$1 defect has not been observed in other flow fields. The diffusion constant for the c-director orientation is extracted from the orientation field patterns under flow and are compared to other independent measurements. / Source: Dissertation Abstracts International, Volume: 57-02, Section: B, page: 1172. / Major Professor: David van Winkle. / Thesis (Ph.D.)--The Florida State University, 1995.

Source: Dissertation Abstracts International, Volume: 38-04, Section: B, page: 1774. / Thesis (Ph.D.)--The Florida State University, 1976.

We derived the unidirectional shear flows appropriate for Hele Shaw cell when there is no buoyancy driving force. Using the Galerkin spectral method, the linear stability of Hele Shaw convection in shear flows has been analyzed. The results show that all shear flows stabilize the convection. / Using a modified perturbation method with a two parameter expansion and a strained time coordinate, we successfully obtained the oscillatory (steady) finite amplitude solutions with (without) imposed shear flows. The two parameters are $\epsilon$ Pe, where $\epsilon$ is the amplitude of the stream function to leading order, and Pe is the Peclet number. It has been found that the flow pattern in Couette flow tilted more strongly with the stream as the Prandtl number was decreased. The temperature pattern was symmetric about the vertical axis when the Prandtl number is large. As the Prandtl number is decreased the temperature pattern becomes an intense narrow hot center and relatively weak broad cold center and then the cold center splits into a cats-eyes pattern and the hot center remains narrow and intense. This kind of pattern change has also been observed as the Peclet number is increased. / The generated mean flow and the momentum flux in both shear flows were derived analytically and were increased whereas the Prandtl number decreases. The momentum flux in all shear flows is found to be always up the gradient of the mean flow and results in the energy transformation from the the convective kinetic energy into the mean kinetic energy. / The study reported here might be very helpful for understanding the porous medium convection in shear flows. Therefore, the consequence of these results to ground water transport as well as industrial processes might be significant. / Source: Dissertation Abstracts International, Volume: 52-04, Section: B, page: 1926. / Major Professor: Ruby Krishnamurti. / Thesis (Ph.D.)--The Florida State University, 1991.

Nonlinear pattern formation in parametric surface waves in weakly viscous fluids is studied by using both analytical and numerical means. The investigation is based on a quasi-potential approximation valid for weakly viscous incomprehensible fluids. The three-dimensional quasi-potential equations are then written in a two-dimensional nonlocal form (2D-QPEs). Standing wave and traveling wave amplitude equations are derived by using a multiple scale perturbation method. The 2D-QPEs are also solved numerically by using a pseudospectral method. In addition, analytical and numerical studies are also performed on a two-dimensional order parameter model to further describe the nonlinear dynamics of parametric surface waves away from onset. On the conceptual level, the findings of our investigation include (i) an amplitude-limiting effect by the driving force in parametrically forced systems; (ii) the importance of three-wave resonant interactions among capillary-gravity waves to pattern selection. Our results provide explanations to a number of recent experimental observations, as well as a number of predictions that await experimental verification. The main results include: (1) We explain why standing wave patterns of square symmetry are observed experimentally near onset of capillary Faraday waves with a sinusoidal forcing. (2) We predict that hexagonal or triangular patterns, and patterns of quasicrystalline symmetry can be stabilized in certain mixed capillary-gravity waves with a sinusoidal forcing. (3) Analytical results for a bicritical line for two-frequency forced Faraday waves are obtained. The results are in qualitative agreement with the available experimental results. (4) The triad resonant condition for capillary-gravity waves is modified for two-frequency forced Faraday waves of frequency ratio 1:2 compared to the case of single frequency forcing. / As a result, square patterns can be unstable for subharmonic responses of the fluid surface even in the capillary wave limit. (5) An order parameter equation (OPE) for a two-dimensional complex field is proposed for weakly damped Faraday waves. Stationary solutions of this OPE become unstable to transverse amplitude modulation (TAM) at a finite value of the reduced driving amplitude. For larger values of the driving force, TAM defects appear, and the system appears to be spatiotemporally chaotic due to the erratic motions of TAM defects. / Source: Dissertation Abstracts International, Volume: 55-11, Section: B, page: 4910. / Co-Major Professors: Jorge Vinals; Dennis W. Duke. / Thesis (Ph.D.)--The Florida State University, 1994.

This thesis describes theoretical studies of adiabatic motion of relativistic charged particles in the radiation belts and numerical modeling of multi-dimensional diffusion due to interactions between electrons and plasma waves. A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space (which includes energy and time as independent coordinates) for all three adiabatic invariants. First, the guiding-center equations of motion for a relativistic particle are derived from the particle Lagrangian. Covariant aspects of the resulting relativistic guiding-center equations of motion are discussed and contrasted with previous works. Next, the second and third invariants for the bounce motion and drift motion, respectively, are obtained by successively removing the bounce phase and the drift phase from the guiding-center Lagrangian. First-order corrections to the second and third adiabatic invariants for a relativistic particle are derived. These results simplify and generalize previous works to all three adiabatic motions of relativistic magnetically-trapped particles. Interactions with small amplitude plasma waves are described using quasi-linear diffusion theory, and we note that in previous work numerical problems arise when solving the resulting multi-dimensional diffusion equations using standard finite difference methods. In this thesis we introduce two new methods based on stochastic differential equation theory to solve multi-dimensional radiation belt diffusion equations. We use our new codes to assess the importance of cross diffusion, which is often ignored in previous work, and effects of ignoring oblique waves, which are omitted in the parallel-propagation approximation of calculating diffusion coefficients. Using established wave models we show that ignoring cross diffusion or oblique waves may produce large errors at high energies. Results of this work are useful for understanding radiation belt dynamics, which is crucial for predictability of radiation in space.

In this thesis we show that the entropy parameter PV5/3 , where P is the pressure and V is the volume of a flux tube with unit magnetic flux, plays a central role in the earthward plasma convection from the near- and middle-Earth plasma sheet to the inner magnetosphere. This work presents a series of numerical simulations, investigating the relationship between the value of PV5/3 and the different features of plasma earthward transport that occur during different types of events in geomagnetic active times. The simulations are conducted using the Rice-Convection-Model (RCM) and the Rice-Convection-Model-Equilibrium (RCM-E) that have carefully designed boundary conditions to simulate the effect of various values of PV 5/3. In Chapter 3 we present results of an RCM simulation of a sawtooth event where it is found that a dramatic reduction of PV5/3 on the boundary along a wide range of local times produces interchange convection in the inner magnetosphere and drives spatially quasi-periodic Birkeland currents that suggest an explanation for the finger-like aurora usually observed during this type of event. In Chapter 4 we present results of an RCM-E simulation of an isolated substorm, which is done by imposing depleted PV5/3 (a bubble) in the expansion phase. The results of this simulation reproduce typical features of a substorm and agree fairly well with multipoint observations. Chapter 6 presents a detailed analysis of the RCM-E expansion phase simulation which indicates that the reconfigurations of PV5/3, plasma pressure and magnetic field in an idealized bubble injection event can be quite complicated. Chapter 7 presents results of a superposed epoch study using Geotail data showing that the time variations of PV 5/3 are different in isolated substorms, pseudo-breakups and convection bay events, suggesting that bubbles have different characteristics in different modes of earthward transport. We follow this up with three corresponding RCM-E simulations by representing a sustained bubble, a transient bubble and sustained low PV5/3 plasma along the boundary. The simulations are roughly consistent with theoretical suggestions, superposed epoch results and some other observations. These simulations provide a systematic description of inner magnetospheric configuration during various active events, suggesting the temporal and spatial characteristics of PV5/3 in the plasma sheet as a key in the magnetospheric convection.

<p> Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. </p><p> First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. </p><p> Second, further extensions to enable the modeling of fluids in vessels with smaller diameters and a method for introducing the deformational forces exerted on the arterial flows from the movement of the heart by borrowing concepts from cosmodynamics are presented. These additional forces have a great impact on the endothelial shear stress. Third, the fluid model is extended to not only recover Navier-Stokes hydrodynamics, but also a wider range of Knudsen numbers, which is especially important in micro- and nano-scale flows. The tradeoffs of many optimizations methods such as the use of deep halo level ghost cells that, alongside hybrid programming models, reduce the impact of such higher-order models and enable efficient modeling of extreme regimes of computational fluid dynamics are discussed. Fourth, the extension of these models to other research questions like clogging in microfluidic devices and determining the severity of co-arctation of the aorta is presented. Through this work, a validation of these methods by taking real patient data and the measured pressure value before the narrowing of the aorta and predicting the pressure drop across the co-arctation is shown. Comparison with the measured pressure drop in vivo highlights the accuracy and potential impact of such patient specific simulations. </p><p> Finally, a method to enable the simulation of longer trajectories in time by discretizing both spatially and temporally is presented. In this method, a serial coarse iterator is used to initialize data at discrete time steps for a fine model that runs in parallel. This coarse solver is based on a larger time step and typically a coarser discretization in space. Iterative refinement enables the compute-intensive fine iterator to be modeled with temporal parallelization. The algorithm consists of a series of prediction-corrector iterations completing when the results have converged within a certain tolerance. Combined, these developments allow large fluid models to be simulated for longer time durations than previously possible.</p>

<p> The use of two magnetised plasma waves as electron temperature diagnostics for the Maryland centrifugal ecperiment (MCX) are explored. First, microwave emission in the whistler mode is examined and ultimately found to be a poor candidate for diagnostic purposes owing to reflections from elsewhere in the plasma confusing the signal. Second, the electron Bernstein wave is found to offer promise as means to measure the radial electron temperature profile. Several numeric codes are developed to analyze the observed microwave emission and calculate the electron temperature profile. Measurements of electron Bernstein wave emission indicate that the electrons in the plasma attain temperatures close to 100 eV. Clear evidence is shown that the measurements are not influenced by reflections or emission from hot (<i>T^e</i> > 1keV) superthermal electrons. The measured electron temperature is shown to be in reasonable agreement with recent measurements of the plasma ion temperature. </p>

High-power solar arrays for satellite power systems are presently being planned with dimensions of kilometers, and with tens of kilovolts distributed over their surface. Such systems will face many plasma interaction problems, such as power leakage to the plasma, enhanced surface damage due to particle focusing, and anomalous arcing to name a few. In most cases, these effects cannot be adequately modeled without detailed knowledge of the plasma-sheath structure and space charge effects. A computer program (PANEL) has been developed to model the solar power satellite (SPS)-plasma interaction by an iterative solution of the coupled Poisson and Vlasov equations. PANEL uses the "inside-out" method and a finite difference scheme to calculate densities and potentials at selected points on either a two or three dimensional grid. PANEL was originally developed by Dr. Lee W. Parker to solve the Laplace equation for the potential distribution about a planar spacecraft and to calculate the plasma currents to the spacecraft surface. After some improvements, this version was tested and used to model the plasma interaction of the MSFC/Rockwell design for the SPS. Those results are presented in chapter three. More recently, with the aid of Dr. Parker, charge density calculation routines have been added to PANEL to include space charge effects. These routines along with some necessary improvements have been installed, resulting in the present version of PANEL. Among these improvements are: selectable boundary conditions, stop and start capability, a grid cell division technique to improve trajectory accuracy, and a method of phase space boundary tracking that greatly increases program efficiency by avoiding the repeated tracing of most trajectories. In this thesis, the history of the spacecraft charging problem is reviewed, the theory of the plasma screening process is discussed and extended, program theory is developed, and a series of models is presented. These models are primarily two-dimensional (2-D) for two reasons; one being that large 3-D models require more computing time than I have been able to afford, and the other being that most analytic models suitable for testing PANEL are 1-D and the 3-D capabilities were not required. These models include PANEL's predictions for two variations on the Child-Langmuir diode problem and two models of the interaction of an infinitely long one meter wide solar array with a dense 10 eV plasma. These models are part of an ongoing effort to adapt PANEL to augment the laboratory studies of a 1 x 10 meter solar array in a simulated low Earth orbit plasma being conducted in the Chamber A facilities at the NASA/Johnson Space Center. Also included are two 3-D test models. One is a "point potential" in a hot plasma and is compared to the Debye theory of plasma screening. The other is a flat disc in charge free space. For the Child-Langmuir diode problem, a good agreement is obtained between PANEL results and the classical theory. This is viewed as a confirming test of PANEL. Conversely, in the solar array models, the agreement between the PANEL and Child-Langmuir predictions for the plasma sheath thickness is presented as a numerical confirmation of the use of the Child-Langmuir diode theory to estimate plasma sheath thickness in the spacecraft charging problem.