ISSN:
1572-9613
Keywords:
Fokker-Planck equation
;
shock wave
;
Brownian motion
;
eigentheory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract An eigenexpansion solution of the time-independent Brownian motion Fokker-Planck equation is given for a situation in which the external acceleration is a step function. The solution describes the heavy-species velocity distribution function in a binary mixture undergoing a shock wave, in the limit of high dilution of the heavy species and negligible width of the light-gas internal shock. The diffusion solution is part of the eigenexpansion. The coefficients of the series of eigenfunctions are obtained analytically with transcendentally small errors of order exp(−1/M), whereM ≪ 1 is the mass ratio. Comparison is made with results from a hypersonic approximation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01019701
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