Measuring shape with topology

作者:MacPherson Robert*; Schweinhart Benjamin
来源:Journal of Mathematical Physics, 2012, 53(7): 073516.
DOI:10.1063/1.4737391

摘要

We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks.

  • 出版日期2012-7