The dynamics of propagation fronts on sets with a negative fractal dimension

Alfred Hubler, Josey Nance

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In sets with a fractal dimension greater than 1, the average number of neighbors increases with distance. For that reason spherical pulses propagate outward in systems with nearest neighbor interactions. In sets with a negative fractal dimension, such as the set of individual coordinates of a population of a small city, the average number of neighbors decreases with distance in a precise way relating the number of neighbor to the fractal dimension of the set. We study the propagation of diffusive pulses and waves on such sets. We find that on sets with negative fractal dimension, the velocity of pulse peak is negative (i.e. the median radius of circular pulses decreases as a function of time). Eventually the pulse broadens and disappears. We discuss applications in physical systems, such as the spreading of heat and sound, as well as applications in social systems, such as the spread of infectious diseases and the spread of rumors.

Original languageEnglish (US)
Title of host publicationComplex Sciences - 2nd International Conference, COMPLEX 2012, Revised Selected Papers
EditorsKristin Glass, Richard Colbaugh, Jeffrey Tsao, Paul Ormerod
PublisherSpringer-Verlag
Pages152-158
Number of pages7
ISBN (Print)9783319034720
StatePublished - Jan 1 2013
Event2nd International Conference on Complex Sciences, COMPLEX 2012 - Santa Fe, United States
Duration: Dec 5 2012Dec 7 2012

Publication series

NameLecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST
Volume126 LNICST
ISSN (Print)1867-8211

Other

Other2nd International Conference on Complex Sciences, COMPLEX 2012
CountryUnited States
CitySanta Fe
Period12/5/1212/7/12

Keywords

  • Diffusion
  • Negative fractal dimension
  • Propagation front

ASJC Scopus subject areas

  • Computer Networks and Communications

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