Timestep

The fluctuations in the kinetic energy are about .1. So we want fluctuations in the total energy of less than .001. This happens at about a time step of .006.

Equilibration

There are only 16 particles, so the fluctuations in the kinetic energy are quite large, which make the equilbration hard to distinguish. To help distinguish, we did 16000 time steps. The data appears to be equilibrated after 200 data points. That's 2000 timesteps (the data is taken every 10 steps) and 2000 x.006 = 12 in simulation time units.

Trace of Energy

Trace of Energy

So throwing away the first 200 data points, we get an average kinetic energy of 1.493 +/- .025 and an average potential energy of -0.705 +/- .025.

The kinetic energy is higher than the desired temperature because the initial state (a lattice) had high potential energy, which converted to kinetic energy and raised the temperature during equilbration.

Nose Thermostat

Here are graphs of the total energy for inverse mass parameters of 0.01,0.1, and 1.0

h = 0.01 h = 0.1 h = 1.0
Using h=1.0, I get a value of 1.00 +/- .02 for the kinetic energy and -0.79 +/- .02 for the potential energy.

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