9632059 Redner Theoretical studies will be done on non-linear transport processes and related collective properties in heterogeneous media. Two general topics will be considered, including the dynamics of inelastic gases and filtration processes. A primary goal will be to develop new models and new qualitative methods to account for basic phenomena. The steady response of an inelastic gas in small temperature and concentration gradients will be used to help develop basic insights into the transient cooling and underlying clustering phenomenon. Investigations will be done on basic aspects of filtration in which small suspended particles in a fluid are removed by passing the suspension through a porous matrix. These removed particles gradually plug the porous medium giving rise to feedback between transport and filtration efficiency. New models will be developed to describe this non-steady response analytically and to understand the underlying percolation problem induced by the plugging network. Investigations will also be done to understand coarsening processes and related kinetic phenomena in simple models of competitive and adaptive behavior. The "vicious civilization" model appears to account for some aspects of the time development and relative strengths of real civilizations. A transition between a "fair" and a "superpower-dominated" world is identified and studies will be made to quantify the essential phenomena associated with this transition. Similarly, studies of "adaptive" voter models will be done. In these models new types of transition rate rules are introduced to mimic several basic elements of human behavior. The long-time properties of these systems will be investigated with particular emphasis on the statistics of opinion changes. %%% This research involves theoretical studies of statistical models which describe transport phenomena, such as the flow of liquids, through filters and th eevolution of spatial organization, such as p attern formation in fluids. The results will be of wide interest to the mathematics, statistical mechanics and materials and processing communities. ***
