Short-time regime propagator in fractals

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 5, 1998, Pages 5160-5167

  Acedo, L ^a   Yuste, S Bravo ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010445031     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.5160     Document Type: Article

References (21)

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9. The function P̂(r,t), defined as the (configurational averaged) density probability of finding the random walker at r at time t, is sometimes called propagator or Green function. The two functions, P and P̂, are related by P̂(r,t)=(Ω/Ωd)rdf-dP(r,t), where df is the fractal dimension of the fractal substrate, d is the Euclidean dimension in which the fractal is embedded and Ωrdf-1dr (Ωdrd-1dr) is the fractal (Euclidean) volume between r and r+dr. It should be noted that in this paper P(r,t) is defined in a slightly different way from that used in Ref. 7, where it was defined as P̂(r,t)/rdf-d, thus differing by the factor Ω/Ωd from the definition of this paper.
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