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Solution of a diffusion equation of smoke molecules due to constant point source in gravitational field

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Abstract

From both the Langevin equation, including a gravitational term, the Fokker-Planck equation based on the dynamical behavior of Brownian particles, and equation of smoke molecular diffusion due to a constant point source is introduced and is solved by applying the Laplace transformation with the convolution theorem.

The solution is expressed by the complementary error function with a mean pathway of smoke molecules affected by gravity and is proved to be reduced to conventional forms by a certain restriction neglecting gravity without any forced term.

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Authors and Affiliations

  1. Department of Applied Physics, Faculty of Engineering, Miyazaki University, 889-21, Miyazaki, Japan

    Kanji Etori

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  1. Kanji Etori
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Etori, K. Solution of a diffusion equation of smoke molecules due to constant point source in gravitational field. Lett Math Phys 26, 271–275 (1992). https://doi.org/10.1007/BF00420236

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