Document Type


Date of Award


Degree Name

Master of Science in Computer Science - (M.S.)


Computer and Information Science

First Advisor

Rajesh N. Dave

Second Advisor

James A. McHugh

Third Advisor

Daochuan Hung


This work investigates techniques to analyze and characterize the presence of microstructure in moderately dilute three-dimensional shear flows. In three dimensional shear flows, a distinct structure develops as the coefficient of restitution is lowered with the particles exhibiting a strong tendency towards the formation of clusters. There exists a need to automatically detect and characterize this microstructure in the given flow. Several methods are examined for effective characterization of the microstructure. The techniques employed are based on the classification of the data based on the properties of the Voronoi diagram constructed from the positional parameters of the two-dimensional slices of the 3d shear flows and on the extraction of quantitative descriptors from determining the fractal dimension.

The fractal nature of the microstructure in three-dimensional shear flows lends itself to the application of several measures of the fractal dimension. The self-similarity property of fractals makes the fractal dimension particularly effective in distinguishing between nuances in the structure. The geometrical properties of Voronoi and Delaunay tessellations help describe the neighborhood of particles. In such a scheme, the statistics gathered from the properties involving the proximity relationships between particles is particularly significant because of the proven tendency of the particles to form clusters. The scheme involves discriminating between the statistical parameters obtained from the measures of the Voronoi polygons and Delaunay triangles.

Methods such as the Fourier Transform techniques and variance analysis, shown by other researchers have suffered from either being severely computationally intensive or being relatively weak in discriminating between nuances in the miscrostructure. The techniques discussed are shown to be computationally efficient and to be successful in characterizing the microstructure. Thus a potentially effective set of methods are introduced that may be adapted to better detect and characterize the microstructure and may also be extendible to other spatial data analysis situations.



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