Steady state solution of the diffusion eq in 1 dimension

1 A particle start at point x=L and performs a random walk. If a particle hits the origin it's adsorbed. If it steps to the right it's restarted at x=L. Calculate the density of particles as a function of x in steady state. Normalize it so that the density is unity at x=L. Look at Berg Links to an external site. Ch 2 and Boas for useful information.

Now look at hw3/1d_diff/SteadyState_hints.py. Fill in the lines that are needed to get the program to work. Compare this with your analytic solution.

2 The density of particles you find should vary with position giving rise to a gradient in density. Give an example of a biological technique that makes use of gradients in the density of small molecules. Explain how such a technique is used. Are such gradients maintained in steady state as in the above problem, or do you expect them to change with time? Why?