Feedback and Dynamics of Evolving Media

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9978902RednerThis theoretical grant supports investigations of the non-equilibrium processes of depth filtration, coarsening in spatially modulated magnetic and alloy systems, and the cooling of inelastic gases. The primary goal of the research is to develop a comprehensive quantitative understanding of these processes. This will be accomplished by introducing simplifying models which both capture the essence of these processes and provide a convenient calculational approach to connect microscopic parameters with macroscopic observables. A related goal will be to elucidate the role of strong feedback between the time evolution and the material properties of these systems. In depth filtration, a fluid carrying suspended solid particles is cleaned as it traverses a porous medium by the deposition of the suspended particles in the pore space. This modification of the pore space geometry leads to gradual degradation and clogging at the filter. This research will build on earlier work which suggested that this clogging is a self-generated power-law gradient percolation phenomenon, and will investigate: (a) the time evolution of the overall clogging process; (b) the slow constriction of a medium by fine particle filtration; and (c) the behavior of the permeability near the clogging threshold.In another project the coarsening of magnetic systems with competing ferromagnetic and antiferromagnetic interactions will be studied. The existence of competing interactions leads to very different low-energy excitations compared to a purely ferromagnetic system, and this has profound consequences on dynamical behavior. Preliminary work on the one-dimensional Ising chain with competing interactions revealed rich coarsening behavior which can be viewed as the kinetics of a complex, but easily visualized, set of multispecies annihilation reactions. A geometrical approach in this spirit will be developed to treat the dynamical behavior of higher-dimensional systems with the goal of uncovering new types to coarsening kinetics.Finally, the cooling and spatial organization of monodisperse and polydisperse inelastic gases will be investigated. For a monodisperse gas, the average energy decays in time as one over time-squared in an intermediate time regime, after which large-scale spatial clumping sets in: this leads to a still slower decay of the energy. The hypothesis that this inelastic gas is in the same universality class as the completely inelastic, agglomerating gas will be tested by the development of bounds which are based on the relation between these two systems. The role of strong mass dispersity on the cooling rate will also be investigated, where the violent rebound of the lightest particles in the collision events with heavy particles is anticipated to give unusual dynamical behavior.%%%This theoretical grant supports investigations of the non-equilibrium processes of depth filtration, coarsening in spatially modulated magnetic and alloy systems, and the cooling of inelastic gases. The primary goal of the research is to develop a comprehensive quantitative understanding of these processes. This will be accomplished by introducing simplifying models which both capture the essence of these processes and provide a convenient calculational approach to connect microscopic parameters with macroscopic observables. A related goal will be to elucidate the role of strong feedback between the time evolution and the material properties of these systems. The research addresses fundamental issues which may have application to a number of non-equilibrium processes. ***