3 research outputs found
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 interacting with ideal gas molecules of mass 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 but
also by the parameter , involving the average number of molecules in
the interaction zone around the particle. For the case of a short-ranged
potential, when , 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 (), 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