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# demo3 - Demo#3 NVT Monte Carlo for the LJ 6-12...

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Demo #3: NVT Monte Carlo for the LJ 6-12 Potential (Author: G. H. Fredrickson (12/29/99). Program adapted from Allen and Tildesley program F.11. MC algorithm is standard Metropolis with no potential truncation.) In this demo, we are going to explore the Metropolis MC method for the NVT ensemble applied to the Lenard-Jones 6-12 potential. We will use the standard reduced units of epsilon for energy and sigma for lengths. Our goal will be to estimate the properties of the fluid at temperatures and densities near T*=1.0, rho*=0.85. Lets begin by defining some parameters for the simulation. Start with the number of particles, the box side length, and the temperature: n 27 ; boxl 3.167; tstar 1.0; We now calculate the half box dimension and density: boxl2 boxl s 2.; boxl3 boxl s n^ + 1. s 3. / ; rho n s boxl^3 0.850001 The density is thus equal to our target rho*=0.85 by design. Now, lets initialize the particle positions in the simulation box. We will start with a simple cubic lattice to ensure that no particles are too close initially. tempcoord Table # i, j, k , i, boxl3, boxl3, boxl3 , j, boxl3, boxl3, boxl3 , k, boxl3, boxl3, boxl3 ' ; + This next command, restructures the coordinates into an nx3 list / coord Partition # Flatten # tempcoord ' ,3 ' ;

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pltcoords : Show # Graphics3D # PointSize # 0.10 ' , Table # Point # coord ## i ''' , i, 1, n ' ' , PlotRange ! boxl2, boxl2 , boxl2, boxl2 , boxl2, boxl2 ' ; pltcoords D Graphics3D D Define a few other quantities that we will need. DRMAX is the maximum displacement of a trial move, NITER is the
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demo3 - Demo#3 NVT Monte Carlo for the LJ 6-12...

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