Probability of capture by a spherical adsorber by diffusion

1.

• Read Berg Links to an external site. Ch 3 page 38-39. A numerical implementation using random walkers is hw3/3d_diff/sphere.py. Add comments to the code to explain how it works in detail.

• Use this to verify the analytic solution.

Note that you can turn off or on the graphics by setting the variable "graphics" to 0 or 1. With the graphics on, the calculations are much slower because the program is spending most of its time displaying images.

2 Give at least two biological examples of this kind of process:

1. What would the absorbing sphere correspond to? What does absorption of the walker mean in you example?
2. Give some examples of molecules or particles that get absorbed, again, in the same biological context.
3. Are there some systems where walkers that will get absorbed on most locations on the sphere as opposed to just at certain specific locations?
4. If the walkers are only being absorbed at specific locations, under what conditions is the absorbing boundary condition a good approximation?