The Open UniversitySkip to content
 

Uniformity transition for ray intensities in random media

Pradas, Marc; Pumir, Alain and Wilkinson, Michael (2018). Uniformity transition for ray intensities in random media. Journal of Physics A: Mathematical and Theoretical, 51(15), article no. 155002.

Full text available as:
[img]
Preview
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (1MB) | Preview
DOI (Digital Object Identifier) Link: https://doi.org/10.1088/1751-8121/aab161
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
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: 01 May 2019 21:29
URI: http://oro.open.ac.uk/id/eprint/54011
Share this page:

Metrics

Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU