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 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} , to the right with 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} , 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.