Abstract

We study uncertainty bounds and statistics of wave solutions through a random waveguide which possesses certain random inhomogeneities. The waveguide is composed of several homogeneous media with random interfaces. The main focus is on two homogeneous media which are layered randomly and periodically in space. Solutions of stochastic and deterministic problems are compared. The waveguide media parameters pertaining to the latter are the averaged values of the random parameters of the former. We investigate the eigenmodes coupling due to random inhomogeneities in media, i.e. random changes of the media parameters. We present an efficient numerical method via Legendre Polynomial Chaos expansion for obtaining output statistics including mean, variance and probability distribution of the wave solutions. Based on the statistical studies, we present uncertainty bounds and quantify the robustness of the solutions with respect to random changes of interfaces.

Original languageEnglish (US)
Pages (from-to)147-159
Number of pages13
JournalDiscrete and Continuous Dynamical Systems
Volume28
Issue number1
DOIs
StatePublished - Sep 2010

Fingerprint

Wave propagation
Wave Propagation
Waveguide
Waveguides
Statistics
Inhomogeneity
Chaos theory
Probability distributions
Numerical methods
Chaos Expansion
Uncertainty
Polynomial Chaos
Random Parameters
Polynomials
Legendre polynomial
Random Media
Quantify
Probability Distribution
Numerical Methods
Robustness

Keywords

  • Evolution of probability distribution
  • Monte carlo simulation
  • Random interface
  • Random media
  • Stochastic partial differential equation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Wave propagation in random waveguides. / Jung, Chang Yeol; Mahalov, Alex.

In: Discrete and Continuous Dynamical Systems, Vol. 28, No. 1, 09.2010, p. 147-159.

Research output: Contribution to journalArticle

Jung, Chang Yeol ; Mahalov, Alex. / Wave propagation in random waveguides. In: Discrete and Continuous Dynamical Systems. 2010 ; Vol. 28, No. 1. pp. 147-159.
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