We begin with a result on the refocussing of null geodesics in space-times. We show that all oriented refocussing 2-dimensional Lorentz manifolds are also strongly refocussing. We also introduce a theory of virtual Legendrian knots. We show that...
This thesis reports work on a new device to detect changes in spatially nonuniform intensity distributions, and shows how this device can be applied to the particular problem of optical vibration detection. The phase of optical radiation is very...
Laser speckle monitoring is a way to measure the motion of an optically rough surface without making physical contact to that surface. Laser speckle is inherently sensitive to motion in the plane of the reflecting surface, which gives speckle...
Continual improvements to clinical breast imaging technologies have led to ever earlier detections and increasingly accurate localizations of female breast cancers. While these advancements have certainly improved the prognoses of many patients,...
The purpose of this thesis is to describe methods for detecting hidden crevasses on glaciers in Polar regions. Crevasses form in ice sheets as a result of forces imposed upon the brittle ice. The crevasses are hidden from view by bridges of soft...
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...
While Cherenkov emission was discovered more than eighty years ago, the potential applications of imaging this during radiation therapy have just recently been explored. With approximately half of all cancer patients being treated by radiation at...
Van Allen radiation belts -- Mathematical models. ; Magnetosphere -- Mathematical models. ; Magnetohydrodynamics -- Mathematical models.
The physics of geomagnetically-trapped radiation has been a topic of interest since the discovery of the Van Allen belts in 1958. As the energetic particles comprising these belts can pose a hazard to human activity in space, considerable effort...
The Cerenkov Maser radiation is examined using linear and nonlinear theory. Linear theories for the gain in the single particle and the collective limits have been given previously. In this work, we show the connections between these two operating...
In an undercooled environment any protuberance or bump on a planar solid/liquid interface that extends into the melt enhances its growth since the surrounding temperature gradient is greater than that about the planar surface. Consequently, the...
A method for the reconstruction of a spectrum of mechanical properties from phase-contrast, MR displacement data is developed and implemented via the finite element method. To overcome the significant computational load associated with...
Many of today's communication and imaging technologies share the common challenge of signal deterioration due to water's large absorption coefficient. As an example, it is water molecules that contaminate the fused silica of optical fibers and...
Macrocyclic tetrapyrroles are essential to life. In nature, they play important roles in living organisms, such as oxygen transportation and photosynthesis. Pentynoic acids are versatile precursors for preparing pyrrolines and higher homologues....
Earth's high latitude ionosphere, highly disturbed by particle and energy inputs and associated aurora, is the stage for plasma wave activity across a wide range of frequencies. These waves often exhibit strikingly distinct time-frequency structure...
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...
Magnetic resonance elastography (MRE) is a recently developed imaging modality that measures and visualizes the mechanical properties of tissue in vivo. One of the essential reconstruction procedures in MRE is motion estimation. For dynamic...