ISSN:
1572-9613
Schlagwort(e):
Fractals
;
Cayley trees
;
chemical distance
;
diffusion on trees
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Physik
Notizen:
Abstract We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, 〈M(l)〉∼l dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d l s , can be expressed in terms ofd l asd l s = 1,d l ⩽ d l c = 2;d l s = d l −1,d 1 ⩾d l c = 2, which implies that the tree is finitely ramified ford l ⩽ 2 and infinitely ramified whend l ⩾ 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01009019
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