Physics 380, 2011: Homework 4

From Ilya Nemenman: Theoretical Biophysics @ Emory
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Back to Physics 380, 2011: Information Processing in Biology.

Please turn on the assignment either as a PDF file to me by email, or as a printout/writeup to my mailbox in physics. Detailed derivations (with explanations) and calculations must be present for the problems for full credit.

  1. Let's suppose a particle starts at Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=0} and diffuses with a diffusion coefficient D and no drift. Calculate the distribution of particle locations at time .
  2. How does the above distribution change if there is drift v?