hw3 - 3. Using demo2 as a guide, perform a NVE MD...

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Department of Chemical Engineering University of California, Santa Barbara ChE 210B Winter 2010 Instructor: Glenn Fredrickson Homework #3 Homework Due: Friday, February 12, 2010 1. Starting from the “virial equation” connecting g ( r ) to the pressure, show that βp ρ = 1 - β 3 N h X i X <j w ( r ij ) i where w ( r ) = r du ( r ) /dr is the pair virial function. 2. Using a MC method, evaluate the following triple integral: I = Z 2 0 dx Z 2 0 dy Z 2 0 dz sin( xyz ) Compare with the “exact” numerical result obtained from Mathematica’s NIn- tegrate function (which uses a direct quadrature method) and show how the error in the MC method scales with the number of points used.
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Unformatted text preview: 3. Using demo2 as a guide, perform a NVE MD simulation of a model uid with a LJ 6-8 potential: u ( r ) = 10 [( /r ) 8-( /r ) 6 ] Estimate the compressibility factor and internal energy at T * = 1 . 5 and * = . 8, where standard LJ units are employed ( T * = k B T/ , * = 3 ). Perform an error analysis. 4. Using demo3 as a guide, perform an NVT MC simulation of the same LJ 6-8 uid as in problem 3 at the same temperature and density. Perform an error analysis and compare with your MD results....
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