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 the hints file. Download hints file.

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?