NONCANONICAL POISSON BRACKETS AND HAMILTONIAN EVOLUTION EQUATIONS FOR NONEQUILIBRIUM MOLECULAR DYNAMICS SIMULATIONS

Abstract

Listen

Translate article

Nonequilibrium molecular dynamics (NEMD) simulations of fluids are generally based on either a DOLLS or SLLOD tensor algorithm. The former is always considered to be a Hamiltonian system, but not particularly useful in high strain rate flow simulations, while the latter is not considered to be a Hamiltonian system, but much more practical and accurate in flow simulations. We demonstrate herein using noncanonical transformations of the particle momenta of the system that the SLLOD equations, when written in terms of appropriate noncanonical variables, are completely Hamiltonian, whereas the DOLLS equations are not so. A modified set of DOLLS equations in terms of the noncanonical variables which again is completely Hamiltonian is also derived. Both algorithms then lead to a phase space distribution function which is canonical in both the coordinates and momenta.