Langevin equation for the extended Rayleigh model with an asymmetric bath

In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The non-linear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the non-linear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the non-linear Langevin equation are derived. The transient solution of the non-linear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.Comment: 10 pages. To appear in Phys. Rev.

Langevin Equation for the Rayleigh model with finite-ranged interactions

Both linear and nonlinear Langevin equations are derived directly from the Liouville equation for an exactly solvable model consisting of a Brownian particle of mass $M$ interacting with ideal gas molecules of mass $m$ via a quadratic repulsive potential. Explicit microscopic expressions for all kinetic coefficients appearing in these equations are presented. It is shown that the range of applicability of the Langevin equation, as well as statistical properties of random force, may depend not only on the mass ratio $m/M$ but also by the parameter $Nm/M$, involving the average number $N$ of molecules in the interaction zone around the particle. For the case of a short-ranged potential, when $N\ll 1$, analysis of the Langevin equations yields previously obtained results for a hard-wall potential in which only binary collisions are considered. For the finite-ranged potential, when multiple collisions are important ($N\gg 1$), the model describes nontrivial dynamics on time scales that are on the order of the collision time, a regime that is usually beyond the scope of more phenomenological models.Comment: 21 pages, 1 figure. To appear in Phys. Rev.

Transient mobility mechanisms of deposited metal atoms on insulating surfaces: Pd on MgO (100)

The importance and mechanisms of transient mobility of atoms and molecules adsorbing at surfaces have been a subject of controversy for many years. We used classical molecular dynamics simulations to examine transient mobility of Pd atoms adsorbing on the MgO (100) surface with incident kinetic energies not exceeding 0.4 eV. The calculations show that deposited Pd atoms exhibit high mobility at temperatures below 80 K where the contribution from thermal diffusion processes should be negligible. For our selected deposition conditions, aimed at simulation of Pd cluster growth experiments, an estimated 76 of the impinging Pd atoms are expected to travel up to 20 à away from the collision site before capture on a 5 K surface. We find that mobility of metal atoms on oxide surfaces is expected to decrease with decreasing incident energy and increase with decreasing incident angle. Comparison with prior studies highlights similarities and differences with other surface diffusion processes, such as long jumps. At higher surface temperatures, the observed mobility will mainly be due to thermally activated processes rather than transient mobility mechanisms. Atoms that exhibit transient mobility upon deposition may quickly migrate to surface features and defects affecting kinetics of growth and structures of nanoclusters and surface layers. © 2012 American Chemical Society