Physics 434, 2014: Homework 3

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Back to Physics 434, 2014: Information Processing in Biology.

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

1. Undergraduate students: Problem 5.1 in the Nelson's book.
2. Undergraduate students: Problem 5.2 in the Nelson's book.
3. Problem 5.3 in the Nelson's book.
4. Problem 5.6 in the Nelson's book
5. Calculate the drift and the diffusion constants for a random walk on a lattice with a lattice spacing of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} , where particles hop between the sites every Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta t} units of time, and they have a probability of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} going left, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q=1-p} going right. What are these quantities if the particle goes to the left with the probability $p$, to the right with Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle q} , and stays in place with the probability Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=1-p-q} ?
6. Graduate students: Problem 5.11 in Nelson's book.
7. Graduate students: Problem 5.13 in Nelson's book.
8. Graduate students: Problem 5.14 in Nelson's book.