I simulate the narrow escape problem in a reflective volume, $V$, with a permeable surface $A$, which is either circular or ellipsoid with a semimajor axis $a$. Diffusion coefficient is $D$ and time step is $\Delta{t}$. Thus $l=\sqrt{2D\Delta{t}}$.
The problem is defined as $a\ll V^{1/3}$, which makes sense due to its name.
This is a 2D illustration of what I am trying to do in 3D.
Here $l=1$, which is much larger than I use in simulations as this is just for illustration purposes. 189 is the number of iterations it takes for the particle to leave $V$.
My questions are:
- Is it important to have $l\ll a$?
- If the problem was a simple Brownian Motion simulation, i.e., no such surface as $A$, is it important to have $l\ll V^{1/3}$?
Thanks in advance.