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Iafrate, JR (2014)

Benfordís Law and Power Law Behavior in Fragmentation Processes

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 = {Benfordís 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