Properties of the skeleton of aggregates grown on a Cayley tree |
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Authors: | Shlomo Havlin James E Kiefer George H Weiss Daniel Benavraham Yehoshua Glazer |
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Institution: | (1) National Institutes of Health, 20205 Bethesda, Maryland;(2) Department of Physics, Bar-Ilan University, 52100 Ramat Gan, Israel |
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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. |
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Keywords: | Fractals Cayley trees chemical distance diffusion on trees |
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