J. Grindlay

Reversible approach to statistical equilibrium in a nonlinear chain: an ensemble study

Abstract We describe the results of the numerical integration of the equations of motion of a 17-particle chain with fixed ends and linear and cubic nearest-neighbour forces. Detailed graphs of mode energies, mode trajectories, variation of the orbit periods and the squared modulus of the discrete Fourier transforms of mode displacements are shown for the case of the chain excited from rest in the 11th mode. The total system energy is always conserved to better than 0.02%. An additional 100 histories of this chain were calculated and stored for the same starting energy and a variety of starting velocities and displacements of the 11th mode. The data gathered constituted a constant energy ensemble. A coarse grained energy distribution function and corresponding Boltzmann H -functions were calculated for each mode. These H -functions proved to drop reversibly with time to a minimum value, indicating that each mode has reached a statistical equilibrium state. The mode energy distribution functions in this equilibrium state are shown to take a Maxwell-Boltzmann form. The associated mode temperatures range in value over two orders of magnitude.

Numerical ensemble study of the approach to equilibrium of an anharmonic chain

Abstract The equation of motion of a 17-particle chain with anharmonic nearest neighbour forces have been numerically integrated for 101 different initial conditions. The 101 stored histories constitute a constant energy ensemble. The time dependence of the coarse grained mode Boltzmann H functions indicates that the ensemble evolves reversibly from an initial non-equilibrium state to a final equilibrium state characterized by a minimum in each mode H function. There is no equipartition of energy among the modes.

Surface-traction boundary condition at a dielectric-conductor interface

Abstract A variational principle is used to obtain the boundary conditions for the applied surface tractions at a dielectric-conductor interface.