Situation 1 Mean Exit Time Between Slices for Neutral Species

1 Situation 1 Mean Exit Time Between Slices for Neutral Species 

To generate the required exit times on diffusing from one slice to the next (Fig. 4.6), the backward diffusion equation must be solved for the survival probability S2(r, t) subject to an absorbing inner and outer boundary. The complete derivation is presented in the Sect. A.2 of the Appendix, with the final expression for (r, s) found to be 

Unfortunately analytically inverting Eq. (4.105) in order to generate a reaction time is not possible. However, by letting r reside halfway between the boundary A and B which is always the case if the slices are separated by a constant 3 the expression for the density of first passage times (Eq. 4.103) can be simplified to  

The cumulative distribution function of the survival probability in the Laplace domain 

The last term in Eq. (4.107) arising from the identity sinh(2x) = 2sinh(x) cosh(x). 

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