@inproceedings{21f2098cf26a4c609c80f6eb86b02ace,

title = "The dynamics of propagation fronts on sets with a negative fractal dimension",

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.",

keywords = "Diffusion, Negative fractal dimension, Propagation front",

author = "Alfred Hubler and Josey Nance",

year = "2013",

month = jan,

day = "1",

language = "English (US)",

isbn = "9783319034720",

series = "Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST",

publisher = "Springer-Verlag",

pages = "152--158",

editor = "Kristin Glass and Richard Colbaugh and Jeffrey Tsao and Paul Ormerod",

booktitle = "Complex Sciences - 2nd International Conference, COMPLEX 2012, Revised Selected Papers",

note = "2nd International Conference on Complex Sciences, COMPLEX 2012 ; Conference date: 05-12-2012 Through 07-12-2012",

}