Mean exit time

Exercise. The mean exit time from the interval L, R is the average time the particle survives without hitting either boundary. It is given by... 

Exercise. Compute the mean exit time from the interval (L, R). 

As was shown in Chapter 3, the mean exit time of any reactor is the space time, t. 

The mean exit time from the well should be actually obtained by averaging t(x) over the steady-state distribution... 

In order to categorize the obtained Markovian model for the effective dynamics more precisely, let us denote the typical (mean) exit time from Dj to Dk by Tjk, and the typical relaxation timescale within Dj by Tj (that is, when the system enters Dj at t = 0 it has lost almost all of its memory tt = Tj). 

The probability of exit through the other boundary, x = a, and the corresponding mean exit time taixo)) are given by the same equations as above by interchanging the labels a and b. Naturally,... 

The mean exit time r+(xo) through the downstream boundary at x = L follows from Equation 6.107 as... 

Similarly, Equation 6.109 yields the mean exit time through the upstream boundary as... 

Figure 6.11 (a) Dependence of the mean exit time r+(xo) to reach the down-... 

Situation 1 Mean Exit Time Between Slices for Neutral Species... 

The Slice simulation package relies on generating exit times from the centre of each overlapping slice and the respective probability of exit at either the upper or lower ends of the slice. In this section the generation of the mean exit time is presented which extends the functionality of Slice for ionic systems. The time dependent diffusion equation for charged species is known to be... 

Integrating Eq. (4.149) using the required boundary conditions finally yields an expression for the mean exit time as... 

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