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 186.55-186.75-1

Domain boundaries observed between the fine grained and coarse grained sediment. The coarse grained sediment contains lineations.

HG 186.55-186.75-2

Fine grained sediment, quite structure-less.

HG 215.65-215.75 Thin Section

Brown to dark brown sediment with small to medium sized clasts ranging from sub-angular to sub-rounded. This sample contains a coarse grained domain and a fine grained domain. Clear boundaries can be seen. Grain stacking can be seen in the coarse domain, while lineations are the dominant microstructure in the fine grained domain. Minor grain crushing can also be seen. Some of the coarser domain is rich in clay and organics.

HG 230.75-230.85 Thin Section

Coarse grained sediment with fine grained domains, clay material, rotation structures and lineations. Clasts range from sub-angular to sub-rounded. Mainly brown sediment with darker patches of brown throughout. Major amounts of grain crushing can be seen in the coarse grained material.

HG 257.55-257.75 Thin Section

Dark brown sediment with clasts that range from small to large. The clast shape ranges from sub-angular to sub-rounded. Lineations are abundant in this sample. Edge-to-edge grain crushing can also be seen. Darker organic rich domains are also present throughout the sample.

HG 326.65-326.75

Dark brown sediment with clasts ranging from small to large. Grains are sub-angular in shape. Faint water escape structures are present.

HG 354.65-354.75

Grey sediment with clasts ranging from small to medium in size. Clasts are sub-angular to sub-rounded. Rotation structures can be seen throughout. Some clasts have multiple rotation structures surrounding them. Comet structures and lineations are also present.

HG 388.75-388.85

Dark brown sample with clasts that range from small to large. The clast shape ranges from angular to sub-rounded. Grain crushing is present in this sample along with some lineations. Faint water escape structures can also be seen.

HG 445.60-445.75

Coarse grained, light brown sample with clasts ranging from small to medium in size. The clast shape ranges from sub-angular to sub-rounded. Lineations were abundant throughout the sample. A few comet structures were also found.

HG 450.65-450.75

Mainly a coarse brown sediment with a few patches of a finer grained domain. The clasts range from small to large in size and angular to sub-rounded in clast shape. The coarser domain mainly contains grain crushing and stacking, with some rotation structures. The finer domain mainly contains lineations.