Date Awarded
1988
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Virginia Institute of Marine Science
Abstract
Shape analysis methods based on the concept of the fractal dimension are emerging as a new method of quantifying complex particle shapes. The concept of the fractal dimension stems from the approximately linear relationship between the logarithm of the particle perimeter and the logarithm of the step length or unit of measure. as step length is shortened, the resulting particle perimeter is lengthened. The fractal dimension (D) is defined as 1 {dollar}-{dollar} b, where b is the slope of the log/log plot of perimeter against step length. Using two dimensional projected particle outlines measured by a video image digitizing system, the fractal dimensions of at least 400 randomly chosen quartz particles are calculated and used to characterize a specific sediment sample. The shape population from which these samples have been drawn is characterized via a fractal dimension density histogram. These histograms are used to make statistical comparisons of particle shape information contained in different samples. The fractal shape method has several advantages over the more widely used Fourier shape method. The fractal method has greater precision and sensitivity with particle shape discriminative power approximately 4.5 times that of the Fourier method. The fractal and Fourier methods were used in two applied shape analysis studies in order to compare shape method performance and recognize potential interpretive differences arising from the use of one method over the other. The first application investigated contrasting sediment sources and their distribution in Twofold Bay, New South Wales, Australia. These results correspond well with the conclusions of other independent sedimentological investigations of Twofold Bay. The Fourier method did not distinguish clearly between the terrestrial and marine compartments. The second application tested the resolution of shape change which occurs during the process of abrasion. The fractal method proved to be highly sensitive to small scale changes in particle roughness that occur initially as the result of particle to particle collisions, whereas the Fourier method did not. The fractal method detected far greater changes in overall shape than the Fourier method which appeared insensitive to fine-scale changes in particle shape. (Abstract shortened with permission of author.)
DOI
https://dx.doi.org/doi:10.25773/v5-z8pt-q243
Rights
© The Author
Recommended Citation
Frisch, Adam Arthur, "Development, test and application of a new method of particle shape analyses based on the concept of the fractal dimension" (1988). Dissertations, Theses, and Masters Projects. William & Mary. Paper 1539616650.
https://dx.doi.org/doi:10.25773/v5-z8pt-q243
