Continuum diffusion on networks: Trees with hyperbranched trunks and fractal branches

Haynes, C. P. and Roberts, A. P. (2009) Continuum diffusion on networks: Trees with hyperbranched trunks and fractal branches. Physical Review E, 79 3: 031111-1-031111-11. doi:10.1103/PhysRevE.79.031111

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Author Haynes, C. P.
Roberts, A. P.
Title Continuum diffusion on networks: Trees with hyperbranched trunks and fractal branches
Journal name Physical Review E   Check publisher's open access policy
ISSN 1539-3755
1550-2376
Publication date 2009-03-18
Sub-type Article (original research)
DOI 10.1103/PhysRevE.79.031111
Open Access Status File (Publisher version)
Volume 79
Issue 3
Start page 031111-1
End page 031111-11
Total pages 11
Editor Gary S. Grest
Margaret Malloy
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2010
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010404 Probability Theory
020304 Thermodynamics and Statistical Physics
Formatted abstract
The probability that a random walker returns to its origin for large times scales as t−d̅ ∕2, where is the spectral dimension. We calculate for a class of tree structures using a renormalization technique on an infinite continued fraction. We consider a wide range of homogeneous networks based on replacing the branches of a self-similar tree with arbitrary fractals and composite fractals. We also consider a new class of inhomogeneous hyperbranched trees.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 7 times in Thomson Reuters Web of Science Article | Citations
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Created: Tue, 30 Mar 2010, 13:22:50 EST by Kay Mackie on behalf of School of Mathematics & Physics