We consider the behavior of two particles on a one-dimensional ring interacting via the Lennard-Jones potential. A collision occurs when the distance between the particles falls within a range corresponding to the minimum potential energy of the system. Equilibrium is achieved when the kinetic energy, which is reduced to an amount proportional to the square of the velocity during particle-particle collision, is less than a fraction of the minimum potential energy. The model shows that as we increase the range in which the Lennard Jones potential is allowed to act on the system, the time needed to achieve equilibrium also increases.

},
author = {Karla V Belisario and Elise Agra and Kristine Eia S Antonio and Ronald S. Banzon}
}