Laboratory experiments on wave propagation through saturated and partially saturated porous media have often been conducted on porous cylinders that were initially fully saturated and then allowed to dry while continuing to acquire data on the wave behavior. Since it is known that drying typically progresses from outside to inside, a sensible physical model of this process is concentric cylinders having different saturation levels--the simplest example being a fully dry outer cylindrical shell together with a fully wet inner cylinder. We use this model to formulate the equations for wave dispersion in porous cylinders for patchy saturation (i.e. drainage) conditions. In addition to multiple modes of propagation obtained numerically from these dispersion relations, we find two distinct analytical expressions for torsional wave modes. We solve the dispersion relation for torsional waves for two examples: Massillon sandstone and Sierra White granite. The drainage analysis appears to give improved agreement with the data for both these materials.

The objectives of this work include automatic recovery and visualization of a 3D chromosome structure from a sequence of 2D tomographic reconstruction images taken through the nucleus of a cell. Structure is very important for biologists as it affects chromosome functions, behavior of the cell and its state. Chromosome analysis is significant in the detection of deceases and in monitoring environmental gene mutations. The algorithm incorporates thresholding based on a histogram analysis with a polyline splitting algorithm, contour extraction via active contours, and detection of the 3D chromosome structure by establishing corresponding regions throughout the slices. Visualization using point cloud meshing generates a 3D surface. The 3D triangular mesh of the chromosomes provides surface detail and allows a user to interactively analyze chromosomes using visualization software.