# Approach to Equilibrium: Molecular Dynamics

The program implements a molecular dynamics simulation of a Lennard-Jones fluid in two dimensions. The particles are initialized in the middle third of the simulation cell. The number of particles in each of the three cells is plotted.

## Algorithm

The algorithm for simulating the evolution of the model can be summarized by the following steps:

1. The particles are placed at random in the center of the box with the constraint that no two particles can be closer than the length σ = 1 in the Lennard-Jones potential. This constraint prevents the initial force between any two particles from being too big, which would lead to the breakdown of the numerical method used to solve the differential equations. The velocity of each particle is assigned at random and then the velocity of the center of mass is set to zero.
2. The total force on each particle is computed and the positions and velocities are updated according to the Verlet algorithm.
3. The time is increased by the time step Δt.

## Reference:

Gould and Tobochnik Statistic and Thermal Physics to be published by Princeton University Press (2010). Draft chapters are available online at <http://stp.clarku.edu/>.

### Note:

This simulation was created by Wolfgang Christian using the Easy Java Simulations (Ejs) modeling tool. It is based on a Java program from the Statistical and Thermal Physics Project. You can modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu item. Information about Ejs is available at: <http://www.um.es/fem/Ejs/>.