Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/8356
Title: | The resistance of randomly grown trees |
Authors: | Rodgers, GJ |
Keywords: | Electrical network;Random tree;Vertex;Random Fibonacci sequence;Identical resistors |
Issue Date: | 2011 |
Publisher: | IOP Publishing Ltd |
Citation: | Journal of Physics A: Mathematical and Theoretical, 44(50): 505001, Dec 2011 |
Abstract: | An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 − p. With each edge having a resistance equal to 1 omega, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value (Rn) for this system approaches (1 + p)/(1 − p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with |(Rn) − (1 + p)/(1 − p)| ∼ n−1/2. |
Description: | Copyright @ 2011 IOP Publishing Ltd. This is a preprint version of the published article which can be accessed from the link below. |
URI: | http://iopscience.iop.org/1751-8121/44/50/505001/ http://bura.brunel.ac.uk/handle/2438/8356 |
DOI: | http://dx.doi.org/10.1088/1751-8113/44/50/505001 |
ISSN: | 1751-8113 |
Appears in Collections: | Publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Preprint.pdf | 482.01 kB | Adobe PDF | View/Open |
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.