Microscopic dynamics underlying the anomalous diffusion

The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200

A Faceted Shape Model Approach to Altimetry and Velocimetry for Irregularly Shaped Bodies

Range and velocity sensors based on lidar or radar with multiple beams are often used to measure the altitude and velocity, respectively, of a spacecraft above a targetbody. A difficulty that arises when navigating about small bodies such as asteroids or comets, is that the notion of altitude is largely obscured by the irregular shape of the target surface. This paper develops a method to incorporate the multibeam altimeter and Doppler velocimeter measurements into the on-board spacecraft state estimator by using information from a faceted shape model representation of the target body surface

On the a and g families of symmetric periodic orbits in the photo-gravitational hill problem and their application to asteroids

This paper focuses on the exploration of families of planar symmetric periodic orbits around minor bodies under the effect of solar radiation pressure. For very small asteroids and comets, an extension of the Hill problem with Solar Radiation Pressure (SRP) perturbation is a particularly well-suited dynamical model. The evolution of the a and g families of symmetric periodic orbits has been studied in this model when SRP is increased from the classical problem with no SRP to levels corresponding to current and future planned missions to minor bodies, as well as one extreme case with very large SRP. In addition, the feasibility an applicability of these orbits for the case of asteroids was analysed, and the effect of SRP in their stability is presented