Numerical Comparison of Dynamics

The test model we shall use to study this problem will be a Lennard-Jones liquid. We place N = 125 atoms with unit mass in a 3D periodic box with total potential 

The particles positions are initialized on a 5 x 5 x 5 grid, with equidistant grid spacing 2 / the minimum of the Lennard-Jones potential cpu(r). We will sample canonically at reciprocal temperature P = 10, with a force cutoff chosen equal to the side length of the periodic box. The size of the box defines the particle density of the simulation and hence the phase of matter that we shall study. After some experimentation, a cubic box with side length 7 was found to give conditions for a liquid state. 

For the Nose-Hoover-Langevin method, we observe that, while small values of IX increase the high frequency oscillations observed in the kinetic energy, the rate of convergence is essentially determined by y and die average kinetic energy indeed converges in the timescale of these simulations. The presence of the stochastic 

Results for the convergence of potential energy are shown in Fig. 8.3 are entirely consistent with the results for kinetic energy. One subtle observation to note is that 

Nosi-Hoover Nosi-Hoover-Langevin Nose-Hoover-Langevin Langevin 

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