On the spectral theory of Rayleigh's piston. III. Exact solution of the absorbing barrier problem ( =1)
| Autor: | M R Hoare, M Rahman |
|---|---|
| Rok vydání: | 1976 |
| Předmět: |
Spectral theory
Continuous spectrum Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics law.invention symbols.namesake Piston Unit mass Exact solutions in general relativity law symbols Rayleigh test Rayleigh scattering Mathematical Physics Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 9:77-85 |
| ISSN: | 0305-4470 |
| DOI: | 10.1088/0305-4470/9/1/013 |
| Popis: | For pt.II see ibid., vol.7, p.1070 (1974). The authors derive an exact solution for the evolution of a one-dimensional ensemble of Rayleigh test particles at unit mass ratio ( gamma =1) in the presence of a speed absorbing barrier. The result, which entails an Arrhenius-law dependence of mean first-passage time on barrier height, appears to be a hitherto unique example of a singular passage-time problem exactly soluble through a continuous spectrum of eigenvalues and their associated eigen distributions. |
| Databáze: | OpenAIRE |
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