Reflecting boundary, probability distributions

Furthermore, the initial and outer boundary conditions are effectively identical [eqns. (3), (4) and (165)] as are also the partially reflecting boundary conditions [eqns. (46) and (165)]. This can be shown by substituting p by exp — p p in the boundary conditions (165). Consequently, the relationship between the survival probability of an ion-pair at a time t0 after they were formed at time t and separation r and the density distribution of an initial (time t0) homogeneous distribution of the majority ion species around the minority ionic species, p(r, f f0), is an identity. 

One Absorbing Barrier and One Reflecting Barrier Let the boundary at m = 0 be reflecting and the boundary at m=be absorbing, namely the boundary condition BC2 in Table 6.1. The probability distribution function for the first passage time is given by Equation 6.124 as... 

To generate a reflected distance it is necessary to know the probability distribution function for a pair started at contact subject to the boundary being reflective. Using the renewal theorem, the transition density of reflecting at a and separating to a distance r is... 

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