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Ergodic Theorem in the Solution of the Scalar Wave Equation with Statistical Boundary Conditions*
- Source :
- Journal of the Optical Society of America (1917-1983); November 1961, Vol. 51 Issue: 11 p1246-1251, 6p
- Publication Year :
- 1961
-
Abstract
- By assuming the random, time-varying boundary conditions for the scalar wave equation to be ergodic, we can associate with the time-varying boundary conditions an ensemble of strictly monochromatic boundary conditions. Formally solving and comparing the solutions for each type of boundary condition, we conclude that the time-averaged and ensemble-averaged powers (squares of the field) are the same at all points where the path difference to any two points on the boundary is small compared to c/Δν, where c is the free-space speed of light and Δν is the frequency spread of the time-varying boundary conditions. That is, if the boundary conditions are ergodic, the solutions are ergodic.
Details
- Language :
- English
- ISSN :
- 00303941
- Volume :
- 51
- Issue :
- 11
- Database :
- Supplemental Index
- Journal :
- Journal of the Optical Society of America (1917-1983)
- Publication Type :
- Periodical
- Accession number :
- ejs38009287