  In 2001, Knight constructed a stochastic process modeling the one dimensional
interaction of two particles, one being Newtonian in the sense that it obeys
Newton's laws of motion, and the other particle being Brownian. We construct a
multi-particle analog, using Skorohod map estimates in proving a propagation of
chaos and characterizing the hydrodynamic limit as the solution to a PDE with
free boundary condition. Stochastic methods are used to show existence and
uniqueness for the free boundary problem, and also present an algorithm of
approximating the solution.
