A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain.
We introduce a new formulation from regularizing the classical Un-Split...
3D vector tomography has been explored and results have been achieved in the last few decades. Among these was a reconstruction formula for the solenoidal part of a vector field from its Doppler transform with sources on a curve. The Doppler transform of a vector field is the line integral...
Integral representations provide a useful framework of study and simulation of fractional Browian motion, which has been used in modeling of many natural situations. In this thesis we extend an integral representation of fractional Brownian motion that is supported on a bounded interval of ℝ to integral representation that is...
The flow of incompressible, viscous fluids in R³ is governed by the non-linear Navier-Stokes equations. Two common linearizations of the Navier-Stokes equations, the Stokes equations and the Oseen equations, are studied in this thesis using probabilistic methods.
The incompressibility condition presents new challenges for the well known theory relating partial...
The degenerate nature of the metric on null hypersurfaces creates many difficulties
when attempting to define a covariant derivative on null submanifolds. This dissertation
investigates these challenges and provides a technique for defining a connection on null
hypersurfaces in some cases. Recent approaches using decomposition to define a covariant
derivative...
Due to age, original design that is deficient by modern standards, inadequate maintenance, environmental conditions, and increasing loads, large numbers of bridges in United States and elsewhere are classified as deficient and in need of rehabilitation or replacement. According to a national bridge inventory established by the Federal Highway Administration,...
X-ray computed tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects. Computed tomography machines are deployed across the world to provide doctors with an image that reveals more detail than a standard x-ray image. We investigate algorithms based on exact computed tomography reconstruction formulas...
Long-term durability of surface-bonded carbon fiber-reinforced polymer (CFRP) U-wraps for shear strengthening of reinforced concrete (RC) bridge members remains uncertain due to the limited field experience with these materials. This paper provides experimental results from the testing of full-scale RC bridge girder specimens after exposure to prolonged freeze-thaw cycling. CFRP...
Cellular sets in the Hilbert cube are the intersection of nested sequences of normal
cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert
cube into cellular sets and using a quotient map. By using a cellular decomposition of the
Hilbert cube, an example...