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DC Field | Value | Language |
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dc.contributor.author | Rodgers, GJ | - |
dc.date.accessioned | 2014-04-29T13:59:30Z | - |
dc.date.available | 2014-04-29T13:59:30Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | Journal of Physics A: Mathematical and Theoretical, 44(50): 505001, Dec 2011 | en_US |
dc.identifier.issn | 1751-8113 | - |
dc.identifier.uri | http://iopscience.iop.org/1751-8121/44/50/505001/ | en |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/8356 | - |
dc.description | Copyright @ 2011 IOP Publishing Ltd. This is a preprint version of the published article which can be accessed from the link below. | en_US |
dc.description.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. | en_US |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_US |
dc.language | English | - |
dc.language.iso | en | en_US |
dc.publisher | IOP Publishing Ltd | en_US |
dc.subject | Electrical network | en_US |
dc.subject | Random tree | en_US |
dc.subject | Vertex | en_US |
dc.subject | Random Fibonacci sequence | en_US |
dc.subject | Identical resistors | en_US |
dc.title | The resistance of randomly grown trees | en_US |
dc.type | Article | en_US |
dc.identifier.doi | http://dx.doi.org/10.1088/1751-8113/44/50/505001 | - |
pubs.organisational-data | /Brunel | - |
pubs.organisational-data | /Brunel/Brunel Active Staff | - |
pubs.organisational-data | /Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths | - |
pubs.organisational-data | /Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths/Maths | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Information Systems, Computing and Mathematics - URCs and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Information Systems, Computing and Mathematics - URCs and Groups/Brunel University Random Systems Research Centre | - |
Appears in Collections: | Publications |
Files in This Item:
File | Description | Size | Format | |
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Preprint.pdf | 482.01 kB | Adobe PDF | View/Open |
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