Unformatted text preview: σ = 1 and μ = 0. Then, make a histogram of their distribution with a bin width of 0.01 and the area normalized to unity. Plot the result. Additionally, create the same Gaussian distribution f ( x ) = [2 π ]1 / 2 ex 2 / 2 (1) analytically and plot it in the same ±gure as the distribution created with random numbers. ³or exercises 1 and 2, return the ±gures in any rational format as well as the source code. Remember, codes that don’t compile give 0 p. 3. (7 p) The equipartition theorem states the following: Every degree of freedom of a body that contributes a square term of a coordinate or momentum to the total energy has a mean energy of k B T/ 2 in that degree of freedom. Based on this, explain why the temperature drops by a factor of 2 in the beginning of an unthermalized MD simulation (see lectures). Would you expect the factor to be 2 even at very high temperatures?...
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 Winter '12
 Kotakoski
 Randomness, random numbers, Monte Carlo method, Monte Carlo simulations, Molecular dynamics

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