Molecular mechanics
Partial differential equations

Having emphasized the equations of fluid mechanics on the macroscopic scale and how they can be completed in less precise scales (turbulence models) it is appropriate to return to the beginning of this hierarchy of equations. Thus we consider a gas of N molecules of position x _k (t) and velocity v _k (t) (1 ≤ k ≤ N) subject to binary interactions described by an interaction potential Φ. The evolution is described by the Hamiltonian :