0000000000800691
AUTHOR
M. Malek Mansour
Hydrodynamic description of the adiabatic piston.
A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston's dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory's validity, in terms of the main system parameters, are established.
Molecular-dynamics studies of annihilation reactions
The validity of the reaction-diffusion formulation of annihilation kinetics, with randomly distributed initial conditions, is investigated by molecular-dynamics simulations of dense hard-disk fluids. For the reaction A + B → C + C quantitative agreement is found. Yet, this proves not to be the case for the reaction A + A → C + C, where major discrepancies are observed. For this latter reaction, more sophisticated theories predict a logarithmic decay law of the form ln (t)/t. The microscopic simulations essentially confirm this prediction.