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Probability of Brownian particle absorption

  1. Jun 24, 2013 #1
    1. The problem statement, all variables and given/known data

    There is a brownian particle in 3D space and absorbing sphere with radius a. At moment t = 0 the particle was situated at distance l from the sphere. Caluclate the probability of absorbing the particle by the sphere.

    2. Relevant equations

    n is probability densithy for the particle,
    $$\partial _t n = D \Delta n$$

    3. The attempt at a solution
    The equation for probability density for the particle in spherical coordinates is
    $$\partial _t n = D \frac 1 {r^2} \partial _r \left(r^2 \partial _r n\right)$$
    with initial conditions
    $$n(r,0) = \frac {\delta \left(r - r_0\right)} {4 \pi r_0^2}, \ r_0 = a + l$$

    But what is the right boundary conditions for the equation?

    Also, what is the right way to calculate the probability of absorbtion?
     
  2. jcsd
  3. Jun 25, 2013 #2

    haruspex

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    Can you obtain a generic solution of the PDE using e.g. separation of variables?
     
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