53 research outputs found
Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation
Based on the generalized Langevin equation for the momentum of a Brownian
particle a generalized asymptotic Einstein relation is derived. It agrees with
the well-known Einstein relation in the case of normal diffusion but continues
to hold for sub- and super-diffusive spreading of the Brownian particle's mean
square displacement. The generalized asymptotic Einstein relation is used to
analyze data obtained from molecular dynamics simulations of a two-dimensional
soft disk fluid. We mainly concentrated on medium densities for which we found
super-diffusive behavior of a tagged fluid particle. At higher densities a
range of normal diffusion can be identified. The motion presumably changes to
sub-diffusion for even higher densities
Wall-mediated self-diffusion in slit and cylindrical pores
Analytical and numerical simulation studies are performed on the diffusion of simple fluids in both thin slits and long cylindrical pores. In the region of large Knudsen numbers, where the wall-particle collisions outnumber the intermolecular collisions, we obtain analytical results for the self-diffusion coefficients for both slit and cylindrical pore shapes. The results show anomalous behavior of the mean square displacement and the velocity autocorrelation for the case of slits, unlike the case of cylindrical pores which shows standard Fick's law. Molecular dynamics simulations confirm the analytical results. We further study the wall-mediated diffusion behavior conducted by a Smoluchowski thermal wall and compare with our analytical results obtained from the stochastic thermal wall model proposed by Mon and Percus
Stochastic Processes and the Dirac Equation with External Fields
The equation describing the stochastic motion of a classical particle in
1+1-dimensional space-time is connected to the Dirac equation with external
gauge fields. The effects of assigning different turning probabilities to the
forward and the backward moving particles in time are discussed.Comment: 9 pages, 1 figure, scalar parts eliminate
Effect of Potential Energy Distribution on the Melting of Clusters
We find that the potential energy distribution of atoms in clusters can consistently explain many important phenomena related to the phase changes of clusters, such as the nonmonotonic variation of melting temperature with size, the dependence of melting, boiling, and sublimation temperatures on the interatomic potentials, the existence of a surface-melted phase, and the absence of a premelting peak in heat capacity curves. We also find a new type of premelting mechanism in double icosahedral Pd19 clusters, where one of the two internal atoms escapes to the surface at the premelting temperature.Peer reviewe
Nature of self-diffusion in two-dimensional fluids
Self-diffusion in a two-dimensional simple fluid is investigated by both
analytical and numerical means. We investigate the anomalous aspects of
self-diffusion in two-dimensional fluids with regards to the mean square
displacement, the time-dependent diffusion coefficient, and the velocity
autocorrelation function using a consistency equation relating these
quantities. We numerically confirm the consistency equation by extensive
molecular dynamics simulations for finite systems, corroborate earlier results
indicating that the kinematic viscosity approaches a finite, non-vanishing
value in the thermodynamic limit, and establish the finite size behavior of the
diffusion coefficient. We obtain the exact solution of the consistency equation
in the thermodynamic limit and use this solution to determine the large time
asymptotics of the mean square displacement, the diffusion coefficient, and the
velocity autocorrelation function. An asymptotic decay law of the velocity
autocorrelation function resembles the previously known self-consistent form,
, however with a rescaled time.Comment: 10 pages, to appear in New Journal of Physic
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