Stochastic p.d.e.'s arising from the long range contact and long range voter processes
A long range contact process and a long range voter process are scaled so that the distance between sites decreases and the number of neighbors of each site increases. The approximate densities of occupied sites, under suitable tine scaling, converge to continuous space time densities which solve stochastic p.d.e.'s. For the contact process the limiting equation is the Kolmogorov-Petrovskii-Piscuinov equation driven by branching white noise. For the voter process the limiting equation is the heat equation driven by Fisher-Wright white noise.
Abstract Many human operations have created a large population of small orbital debris in near Earth environment. The threat they represent for satellites is a major factor for the preparation of future space missions. Several experiments devoted to the study of this environment, as well as various materials exposed to space, have been retrieved in the past few years. The analysis of the results shows some differences with previous modeling. Comparison with data from LDEF and from EURECA give some insight in the long term evolution of particle size distribution. Chemical identification of particle remnants inside craters is difficult but provides valuable information on the origin of the impactors. Permanent monitoring of environment is obviously needed, especially for the type of orbits where data are presently scarce ie. heliosynchronous and geostationary orbits.