Calculation of the Stability of Phase Space Trajectories using Molecular Dynamics Simulations


Principal Investigator

Denis Evans

Research School of Chemistry


Debra J. Searles

Department of Chemistry

University of Queensland

Owen Jepps

Research School of Chemistry


s02 - VPP, PC

The Lyapunov exponents of a liquid system are a
measure of the dynamical stability of a system and
can be related to transport properties of the liquid such as the viscosity and the thermal conductivity. If the spectrum of Lyapunov exponents is symmetric, calculation of these liquid state properties from the Lyapunov exponents is facilitated. Studies of the structure of the spectrum are therefore being carried out. To date, the behaviour of the Lyapunov spectrum as the thermodynamic limit is approached is unknown. Therefore studies into this behaviour are also important.

The construction of stable numerical integrators for non-Hamiltonian dynamics are considered in this project.

We have derived an expression that explains why it is so difficult to find initial microstates that will at long times, under the influence of an external dissipative field and a thermostat, lead to Second Law violating nonequilibrium steady states. This work has been extended to consider more general cases.



What are the results to date and the future of the work?

The Lyapunov spectrum for a non-Hamiltonian system (a fluid undergoing shear flow) has been determined and departures from the Conjugate Pairing Rule have been observed for this system for the first time. In some cases it has been shown that the departure from pairing is a system size effect and will be negligible in the thermodynamic limit.

New, stable integrators have been designed for application to the simulation of fluids undergoing non-Hamiltonian dynamics which ensure the kinetic energy of the system is maintained. The efficiency of these integrators for determining liquid properties has been analysed. The application of the new integrators to calculation of the Lyapunov exponents will now be carried out.

During the year it has become apparent that some important questions related to the microscopic origins of the (macroscopic) Second Law of Thermodynamics need to be addressed . These questions arose from previous work in this project on the 2nd Law violations in homogeneous, deterministic, reversible systems used to model liquids. This theory has now been extended to non-deterministic, non-homogeneous, irreversible systems. In addition the calculation of

Appendix A -




transport coefficients using Green-Kubo type relations has been shown to be true only in the linear regime.

Related work on the existence of nonlinear Burnett coefficients has been published.

What computational techniques are used?

Equilibrium and nonequilibrium molecular dynamics simulation methods are being used and are developed. Supercomputers are required to obtain statistically valid data for small systems and to study large systems in investigations of the influence of system size.


Debra J. Searles, Dennis J. Isbister and Denis J. Evans, Nonequilibrium molecular dynamics integrators using Maple, Mathematics and Computers in Simulation: Non-Standard Applications of Computer Science, 45, 1998, 147-162 .

Denis J. Evans, Debra J. Searles, Wm. G. Hoover, C. G. Hoover, B. L. Holian, H. A. Posch and G. P. Morris, Comment on: Modified nonequilibrium molecular dynamics for fluid flows with energy conservation, Journal of Chemical Physics, 108, 1998, 4351-4352.

Debra J. Searles, Denis J. Evans, Howard J. M. Hanley and Sohail Murad, Simulations of the thermal conductivity in the vicinity of the critical point, Molecular Simulation, 20, 1998, 385-395.

Karl P. Travis, Debra J. Searles and Denis J. Evans, Strain-rate dependent properties of a simple fluid, Molecular Physics, 95, 1998, 195-202.

Debra J. Searles, Denis J. Evans and Dennis J. Isbister, The conjugate pairing rule for non-Hamiltonian systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 8, 1998, 337-349.

Karl P. Travis, Debra J. Searles and Denis J. Evans, On the wavevector dependent shear viscosity of a simple fluid, Molecular Physics, accepted (1998).

- Appendix A