Feedback and Dynamics of Evolving Media

9978902 Redner这个理论资助支持深度过滤的非平衡过程的调查，在空间调制的磁性和合金系统的粗化，以及非弹性气体的冷却。 该研究的主要目标是对这些过程进行全面的定量了解。 这将通过引入简化模型来实现，这些模型既捕获了这些过程的本质，又提供了一种方便的计算方法来连接微观参数与宏观观测值。 一个相关的目标将是阐明这些系统的时间演化和材料性质之间的强反馈的作用。 在深层过滤中，携带悬浮固体颗粒的流体在穿过多孔介质时通过悬浮颗粒在孔隙空间中的沉积而被清洁。 孔隙空间几何形状的这种改变导致过滤器处的逐渐降解和堵塞。 本研究将建立在早期工作的基础上，认为这种堵塞是一种自发的幂律梯度渗流现象，并将研究：（a）整个堵塞过程的时间演变：（B）细颗粒过滤对介质的缓慢收缩;以及（c）在另一个项目中，研究了具有竞争铁磁和铁磁的磁性系统的粗化，将研究反铁磁相互作用。 与纯铁磁系统相比，竞争相互作用的存在导致非常不同的低能激发，这对动力学行为产生了深远的影响。 一维伊辛链与竞争相互作用的初步工作揭示了丰富的粗化行为，可以被视为一个复杂的，但很容易可视化，一套多物种湮灭反应的动力学。 在这种精神的几何方法将被开发来处理高维系统的动力学行为的目标是揭示新类型的粗化动力学。最后，冷却和单分散和多分散非弹性气体的空间组织将被调查。 对于单分散气体，平均能量在中间时间范围内随时间衰减为1/时间平方，之后出现大尺度空间聚集：这导致能量衰减更慢。 这种非弹性气体与完全非弹性的凝聚气体属于同一普适类的假设，将通过建立在这两个系统之间关系基础上的边界来检验。 还将研究强质量分散性对冷却速率的作用，其中最轻粒子在与重粒子碰撞事件中的剧烈反弹预计将产生不寻常的动力学行为。这个理论资助支持深度过滤的非平衡过程的调查，在空间调制的磁性和合金系统的粗化，以及非弹性气体的冷却。 该研究的主要目标是对这些过程进行全面的定量了解。 这将通过引入简化模型来实现，这些模型既捕获了这些过程的本质，又提供了一种方便的计算方法来连接微观参数与宏观观测值。 一个相关的目标将是阐明这些系统的时间演化和材料性质之间的强反馈的作用。 该研究解决了一些可能适用于非平衡过程的基本问题。***

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. ***