Edouard Kestemont

Order and fluctuations in nonequilibrium molecular dynamics simulations of two-dimensional fluids

Finite systems of hard disks placed in a temperature gradient and in an external constant field have been studied, simulating a fluid heated from below. We used the methods of nonequilibrium molecular dynamics. The goal was to observe the onset of convection in the fluid. Systems of more than 5000 particles have been considered and the choice of parameters has been made in order to have a Rayleigh number larger than the critical one calculated from the hydrodynamic equations. The appearance of rolls and the large fluctuations in the velocity field are the main features of these simulations.

Molecular dynamic study of density fluctuation in a non-Equilibrium system

The introduction of high-speed computers has undoubtedly added a new dimension to the physics of fluids. Most computational work in hydrodynamics may be classified as either strictly microscopic or strictly macroscopic. The microscopic simulations trace the trajectories of interacting particles, while macroscopic algorithms integrate transport equations for selected initial and boundary conditions. The problem at hand dictates the choice of the simulation method.

The Approach to Equilibrium and Molecular Dynamics

Some of the first studies in Molecular Dynamics were already concerned with the problem of approach to equilibrium. Alder and Wainwright1 and later Bellemans and Orban2 have calculated the time evolution of the Boltzmann H-function for a dilute gas of hard disks and hard spheres put initially in a non-equilibrium state. This was realized by choosing initial velocities of particles having all the same magnitude but pointing in random directions. These simulations have shown that the irreversible behavior predicted by Boltzmann already appears for systems made of a few hundred particles; these experiments have also illustrated the fact that MD trajectories in phase space are accurate over a few collision times only, as can be seen by reversing the particle velocities.

Velocity Correlations and Irreversibility: A Molecular Dynamics Approach

It is a great privilege to contribute to this volume dedicated to Benno Hess. The impact of his work goes far beyond biochemistry. It has stressed the importance of the role of time and irreversibility in the description of biological and chemical systems. This is now well accepted on the phenomenological level. However the relation of irreversibility with the underlying microscopic dynamics remains a subject of some controversy. Let us remember the classical point of view expressed concisely by Smoluchowski /1/: “If we continued our observation for an immeasurably long time, all processes would appear to be reversible”. With Smoluchowski, Chandrasekhar /2/ concludes that “a process appears irreversible (or reversible) according to whether the initial state is characterized by a long (short) average time of recurrence compared to the time during which the system is under observation”. Irreversibility would then appear as an artifact due to the time scale of observation!