Mean time to capture by diffusion in 1 dimension

• 1. A particle starts out at a position x=a between an adsorbing wall at x=0 and another at x=L.

You want to calculate the mean time that it takes before it is adsorbed. Look at Berg Links to an external site. Chapter 3 for an analytic solution to this problem.

Look at hw3/1d_diff/escape_time_hints.py. Fill in the lines that need to be completed. Then verify the formula given for this problem.

You should also try changing the length, L to make it larger, and change the number of steps used, to see how this changes the statistics.

• 2. Give an example of an in vitro biological experiment involving one dimensional diffusion. One possible experiment involves microtubules attached to dynein motors. Outline the techniques they used in their experiment and describe in more detail one technique related to measuring diffusion.