Document Detail

Percolation in sign-symmetric random fields: topological aspects and numerical modeling
MedLine Citation:
PMID:  11088458     Owner:  NLM     Status:  Publisher    
The topology of percolation in random scalar fields psi(x) with sign symmetry [i.e., that the statistical properties of the functions psi(x) and -psi(x) are identical] is analyzed. Based on methods of general topology, we show that the zero set psi(x)=0 of the n-dimensional (n>/=2) sign-symmetric random field psi(x) contains a (connected) percolating subset under the condition |nablapsi(x)| not equal0 everywhere except in domains of negligible measure. The fractal geometry of percolation is analyzed in more detail in the particular case of the two-dimensional (n=2) fields psi(x). The improved Alexander-Orbach conjecture [Phys. Rev. E 56, 2437 (1997)] is applied analytically to obtain estimates of the main fractal characteristics of the percolating fractal sets generated by the horizontal "cuts," psi(x)=h, of the field psi(x). These characteristics are the Hausdorff fractal dimension of the set, D, and the index of connectivity, straight theta. We advocate an unconventional approach to studying the geometric properties of fractals, which involves methods of homotopic topology. It is shown that the index of connectivity, straight theta, of a fractal set is the topological invariant of this set, i.e., it remains unchanged under the homeomorphic deformations of the fractal. This issue is explicitly used in our study to find the Hausdorff fractal dimension of the single isolevels of the field psi(x), as well as the related geometric quantities. The results obtained are analyzed numerically in the particular case when the random field psi(x) is given by a fractional Brownian surface whose topological properties recover well the main assumptions of our consideration.
Milovanov; Zimbardo
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Publication Detail:
Journal Detail:
Title:  Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics     Volume:  62     ISSN:  1063-651X     ISO Abbreviation:  Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics     Publication Date:  2000 Jul 
Date Detail:
Created Date:  2000-11-28     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  9887340     Medline TA:  Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics     Country:  UNITED STATES    
Other Details:
Languages:  Eng     Pagination:  250-60     Citation Subset:  -    
Department of Space Plasma Physics, Space Research Institute, 117810 Moscow, Russia.
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