Exact results on diffusion in a piecewise linear potential with a time-dependent sink


The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

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Diwaker, Chakraborty, A. Exact results on diffusion in a piecewise linear potential with a time-dependent sink. J. Exp. Theor. Phys. 122, 384–388 (2016). https://doi.org/10.1134/S1063776116020035

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  • Probability Distribution Function
  • Exact Result
  • Sink Term
  • Smoluchowski Equation
  • Exponential Variation