Pradas, Marc; Pumir, Alain and Wilkinson, Michael
(2018).
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| DOI (Digital Object Identifier) Link: | https://doi.org/10.1088/1751-8121/aab161 |
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| Google Scholar: | Look up in Google Scholar |
Abstract
This paper analyses a model for the intensity of distribution for rays propagating without absorption in a random medium. The random medium is modelled as a dynamical map. After N iterations, the intensity is modelled as a sum S of N contributions from different trajectories, each of which is a product of N independent identically distributed random variables xk, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: N=ΛN, for some Λ>1. We investigate the probability distribution of S. We find a phase transition as parameters of the model are varied. There is a phase where the fluctuations of S are suppressed as N → ∞, and a phase where the S has large fluctuations, for which we provide a large deviation analysis.
| Item Type: | Journal Item |
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| Copyright Holders: | 2018 IOP Publishing Ltd |
| ISSN: | 1751-8121 |
| Extra Information: | 15 pp. |
| Keywords: | random media; intensity fluctuations; phase transition; large deviations |
| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 54011 |
| Depositing User: | Marc Pradas |
| Date Deposited: | 09 Apr 2018 10:02 |
| Last Modified: | 25 May 2019 23:22 |
| URI: | http://oro.open.ac.uk/id/eprint/54011 |
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