Undergraduate Honors Thesis, Williams College, Williamstown, MA.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: We construct and analyze models for the fragmentation of a conserved quantity. Using a statistical model, we derive an approximation as well as bounds for the restricted partitioning problem, which we ap- ply to the distribution of fragments. We also modify the canonical ensemble from statistical physics. Taken together, we set a thresh- old on the magnitude of the conserved quantity needed to result in power law behavior, as well as a threshold on the number of possible piece sizes in a special case. We also investigate variations on two specific fragmentation procedures, the directed and undirected frag- mentations, for power law behavior. Calculations show that the undi- rected fragmentation exhibits power law behavior. We consider small perturbations to process rates and find that the multi-path fragmen- tation is affected less as the number of piece sizes grows. We confirm this numerical result using first-order perturbation theory.
Bibtex:
@mastersthesis{,
TITLE = {Benford’s Law and Power Law Behavior in Fragmentation Processes},
AUTHOR = {Iafrate, Joseph R},
YEAR = {2014},
SCHOOL = {Williams College},
ADDRESS = {Williamstown, MA},
URL = {http://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/st/JoeIafrate.pdf},
TYPE = {Undergraduate Honors Thesis},
NOTE = {Last Viewed: 7/7/2014}
}
Reference Type: Thesis
Subject Area(s): Natural Sciences, Statistics