Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Fixed-node diffusion Monte Carlo computations for closed-shell jellium spheres

Fixed-node diffusion Monte Carlo computations are used to determine the ground state energy and electron density for jellium spheres with up to N = 106 electrons and background densities corresponding to the electron gas parameter 1 less than or equal to r(s)less than or equal to5.62. We analyze the density and size dependence of the surface energy, and we extrapolate our data to the thermodynamic limit. The results agree well with the predictions of density functional computations using the local density approximation. In the case of N = 20, we extend our computation to higher densities and identify a transition between atomic- and jelliumlike nodal structures occurring at the background density corresponding to r(s)=0.13. In this case the local density approximation is unable to reproduce the changes in the correlation energy due to the discontinuous transition in the ground state nodal structure. We discuss the relevance of our results for nonlocal approximations to density functional theory.

Thin Ta films: growth, stability, and diffusion studied by molecular-dynamics simulations

We report results of classical molecular-dynamics simulations of bcc and beta-Ta thin films. Thermal PVD film growth, surface roughness, argon ion bombardment, phase stability and transformation, vacancy and adatom diffusion, and thermal relaxation kinetics are discussed. Distinct differences between the two structures are observed, including a complex vacancy diffusion mechanism in beta-Ta. Embedded atom method potentials, which were fitted to bcc properties, have been used to model the Ta-Ta interactions. In order to verify the application of these potentials to the more complex beta-Ta structure, we have also performed density functional theory calculations. Results and implications of these calculations are discussed.