In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
Phase transitions occur in such diverse and important systems as ferromagnets, liquid crystals and the early Universe. The dynamics of phase transitions such as these have been studied for decades, but the analytical models still need a great deal...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Ζ[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
Motivated by the goal of investigating the dynamics of the electroweak phase transition in the early Universe, a study of dynamical aspects of nonlinear field-theoretical systems is performed. Symmetric and asymmetric double-well potentials in the...
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....
Manifolds (Mathematics) Geodesics (Mathematics) Space and time.
We investigate weak and strong refocusing of light rays in a space-time and related concepts. A strongly causal space-time ( X^ n +1 , g ) is emphstrongly refocusing at x ∈ X if there is a point y ≠ x such that all null-geodesics through y pass...
In this thesis, the dynamics of long-lived, time-dependent, coherent field configurations, known as oscillons, are investigated in the presence of an expanding background. In a (1+1)-dimensional expanding spacetime, scalar-field oscillon lifetimes...
Core-binding factors (CBFs) are a small family of transcription factors that play important roles in several developmental processes and in human disease. CBFs consist of CBFα (Runx1, Runx2, or Runx3) and CBFβ. The CBFα subunit binds DNA in a...
Microwave spectroscopy. Imaging systems -- Design and construction. Diagnostic imaging -- Digital techniques. Breast -- Cancer -- Diagnosis. Microwave imaging in medicine.
Microwave spectroscopy has been investigated as a possible modality for breast imaging because of the significant contrast in electrical properties between normal and malignant tissue over the microwave spectrum. A liquid-coupled, non-contacting...
Shape modeling is an important area in computer vision and medical imaging. Shape models have proved valuable in the tasks of object representation, recognition, and classification. This thesis focuses on shape models of 3D surfaces extracted from...
One of the important challenges facing image-guided neurosurgery is the fact that the brain deforms significantly over the course of an operation during open-cranial procedures. This results in a loss of registration between the brain and the...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
The processes by which nonlinear physical systems approach thermal equilibrium is of great importance in many areas of science. Central to this is the mechanism by which energy is transferred between the many degrees of freedom comprising these...
Experimental and theoretical aspects of macroscopic and mesoscopic elastic instability are investigated in this thesis. For the theoretical investigations we utilize a Lagrangian formulation of nonlinear continuum elasticity theory, the novel...
Self-reconfiguring (SR) robots are modular systems that can autonomously change shape, or reconfigure , for increased versatility and adaptability in unknown environments. In this thesis, we investigate planning and control for systems of...
This thesis presents two-fluid simulations of forced magnetic reconnection with finite electron inertia in two and three dimensional periodic systems. Reconnection in the system is driven by a spatially localized forcing function, added to the ion...
Electric generators -- Windings. Electric inductors -- Design and construction -- Mathematical models. Electric current converters -- Design and construction -- Mathematical models. Energy dissipation -- Mathematical models.
Magnetic components for high-frequency power conversion applications can have significant losses that compromise the performance of the converter. In particular, winding losses can be large due to high-frequency effects that are difficult to model...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
Prostacyclin (PGI 2 ) is a major product of COX-2 catalyzed metabolism of arachidonic acid in the endothelium and has been shown to be atheroprotective. PGI 2 signals though its G-coupled protein receptor (GPCR) the human Prostacyclin receptor...
Van Allen radiation belts -- Mathematical models. Electrons -- Diffusion -- Mathematical models. Magnetohydrodynamic waves -- Mathematical models.
It is becoming increasingly important to understand the dynamics of radiation belt energetic particles given their potentially hazardous effects on satellites and our ever-increasing dependence on those satellites. There is a need to determine...
This thesis presents technologies for the design, fabrication, operation, and control of electrostatic MEMS micro-robots. It describes prototype micro-robots, with dimensions of 60 μm by 250 μm by 10 μm, that are capable of controllable...
We present results from a modeling effort of simple shock phenomena in the Cygnus Loop and Cassiopeia A. Using multi-epoch MDM observations of a small, isolated cloud in the southwest region of the Cygnus Loop, we measure the velocity of the...
Eddy currents (Electric) -- Mathematical models. Electric generators -- Windings. Finite element method.
Magnetic components, such as transformers and inductors, are essential parts of most power electronics circuits. They usually are the largest components in the circuit, and also account for a large portion of the power loss. Reducing the volume of...
Despite being cloned over twenty years ago, many regulatory mechanisms of the β-globin genes have yet to be fully elucidated. The regulation of the β-globin locus in erythroid cells requires chromatin structural changes before the genes can be...
Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
Multisensor data fusion. Sensor networks. Plumes (Fluid dynamics). Automatic tracking. Signal processing -- Digital techniques -- Mathematics.
The work in this thesis deals with a novel approach for detecting and tracking chemical plumes in distributed sensor networks. The ultimate objective is solving the inverse location problem: given unknown sources released at unknown times, the...
We present designs, theory and the results of fabrication and testing for a novel parallel microrobotic assembly scheme using stress-engineered MEMS microrobots. The robots are 240-280 μm × 60 μm × 7-20 μm in size, each robot consist of a...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
G proteins -- Receptors. Cardiovascular system -- Diseases -- Genetic aspects. Medical Term Receptors, G-Protein-Coupled -- genetics.
Single-nucleotide polymorphisms (SNPs), particularly non-synonymous variants, provide opportunities for deciphering pathophysiological protein influence. An ideal group for realizing these opportunities is the GPCR-superfamily. Principles from...
Subject Protein kinases. Aldosterone -- Physiological effect. Sodium -- Physiological transport. Sodium channels. Epithelial cells. Glucocorticoids. Medical Term Sgk protein.
It is well established that SGK1 plays a role in aldosterone mediated sodium transport. The intracellular localization of SGK1 has recently been demonstrated as mitochondrial. The studies described here evaluate the hypothesis that SGK1...
Metal powders -- Extrusion. Metal powders -- Microstructure. Shear flow.
The manufacture of bulk parts from metastable powder materials requires new approaches to cold consolidation. One potential technique is equal-channel angular extrusion (ECAE), a simple shear process. This thesis describes an investigation into the...
Ovaries -- Cancer -- Photochemotherapy.
Ovaries -- Cancer -- Treatment -- Evaluation.
Ovaries -- Cancer -- Treatment -- Mathematical models.
The translational potential of new therapeutic strategies for cancer is limited, in part, by a lack of biological models that capture important aspects of tumor growth and treatment response. It is also becoming increasingly evident that no single...
The ability to forecast the weather of the geospace environment depends critically on the ability to accurately model the dynamics of the coupled magnetosphere-ionosphere (MI) system. The MI interaction involves a set of electrodynamic and plasma...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...