A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Real-Time Automatic Object Classification and Tracking using Genetic Programming and NVIDIA R CUDA TM

Genetic Programming (GP) is a widely used methodology for solving various computational problems. GP's problem solving ability is usually hindered by its long execution times. In this thesis, GP is applied toward real-time computer vision. In particular, object classification and tracking using a parallel GP system is discussed. First, a study of suitable GP languages for object classification is presented. Two main GP approaches for visual pattern classification, namely the block-classifiers and the pixel-classifiers, were studied. Results showed that the pixel-classifiers generally performed better. Using these results, a suitable language was selected for the real-time implementation. Synthetic video data was used in the experiments. The goal of the experiments was to evolve a unique classifier for each texture pattern that existed in the video. The experiments revealed that the system was capable of correctly tracking the textures in the video. The performance of the system was on-par with real-time requirements.

HG 187.45-187.65 Thin Section

Coarse grained sediment with fine grained domains throughout. The clasts in the coarse grained domain range from sub-angular to sub-rounded. Short distance lineations are present throughout the sample. Organic rich domains (darker) are prevalent alongside fractured grains.

HG 195.45-195.55 Thin Section

Dark brown sediment with clasts ranging from small to large. The grains are sub-angular. Two main domains can be seen. Both are coarse grained, but one contains larger grains and potentially more clay material. Lineations are present throughout the sample in multiple directions. Minor rotation around a few larger clasts can be seen, as well as comet structures.

HG 216.35-216.45

Brown, coarse grained sample. Clasts range from small to medium in size and sub-angular to angular. Patched of clay rich domains can be seen throughout the sample. Rotation with and without a central grain can be seen throughout the sample. Edge-to-edge grain crushing and grain stacking can be seen throughout the sample.

HG 246.30-246.45 Thin Section

Generally coarse grained, with a few different fine grained domains. Clasts range from small to large, ranging from sub-angular to sub-rounded in shape. Domain boundaries are clear, and the sample also contains rotation structures and lineations.

HG 264.30-264.45

Coarse grained sample with clasts that range from small to large in size. The clast shape ranges from angular to rounded, and many grains are fractured. Grain crushing is present in large amounts. This includes edge-to-edge crushing as well as grains that are crushed into one another. Rotation structures are also common among the clasts that are sub-rounded to rounded. Areas of finer sediment can also be seen.

HG 290.45-290.55 Thin Section

Two main domains can be seen in this sample. One is coarse grained with clasts ranging from small to medium in size. The other is very fine grained, and a very dark brown, potentially influenced by organic material. Grain crushing and lineations can be seen in the coarser domain.

HG 364.45-364.55

Dark grey sediment with clasts that are large in size. The shape of the clasts range from angular to sub-rounded. Grain stacking can be seen throughout the sample. Minor amounts of rotation structures can also be seen.

HG 427.45-427.55

Brown sediment with grains ranging from small to large. The clast shape of this sample ranges from sub-angular to sub-rounded. Grain crushing can be seen in large amounts, and commonly involves the larger grains. Many of the larger grains are also fractured. Lineations and comet structures can also be seen.

HG 473.45-473.55

Light brown, coarse grained sediment with a few patches of a finer grained domain. Clasts range from small to medium in size. The finer grained domain mainly contains small sized grains that are very well dispersed. Clast shape ranges from angular to sub-rounded. Edge-to-edge grain crushing is common in the coarser domain, with a few grain stacks. The finer grained domain contains a few lineations.

HG 36.45-36.55

Dark brown sediment with areas of darker organic material. The clasts range from small to medium in size and angular to sub-rounded in shape. Lineations were abundant in this sample along with some rotation structures and common structures. A few grain stacks were also present.

HG 69.45-69.65

Dark brown sediment with clasts ranging from small to medium in size. The clast shape ranges from angular to sub-rounded. Lineations are abundant throughout the sample. Comet structures and grain crushing/stacking are also present in minor amounts.

HG 75.45-75.60

Dark brown sediment with clasts ranging from small to medium in size. The clast shape ranges from angular to sub-rounded. Lineations are commonly seen throughout the sample. Grain crushing/stacking can also be seen along with varying amounts of rotation structures and comet structures.