Non-Linear Transport and Spatial Organization Processes

9632059将对非均匀介质中的非线性输运过程和相关集体性质进行雷德纳理论研究。将考虑两个一般主题，包括非弹性气体的动力学和过滤过程。主要目标将是开发新的模型和新的定性方法来解释基本现象。非弹性气体在小的温度和浓度梯度下的稳定响应将被用来帮助发展对瞬变冷却和潜在的聚集现象的基本见解。将对过滤的基本方面进行研究，在过滤中，通过使悬浮液通过多孔基质来去除流体中的小悬浮颗粒。这些去除的颗粒逐渐堵塞多孔介质，从而在传输和过滤效率之间产生反馈。将开发新的模型来解析地描述这种非稳定响应，并理解由堵塞网络引起的潜在渗流问题。还将进行调查，以了解竞争和适应行为的简单模型中的粗化过程和相关的动力学现象。“邪恶文明”模式似乎解释了真实文明的时间发展和相对优势的某些方面。确定了“公平”和“超级大国主导”世界之间的转变，并将对与这种转变相关的基本现象进行量化研究。同样，还将对“适应性”选民模型进行研究。在这些模型中，引入了新类型的转换率规则来模拟人类行为的几个基本元素。将调查这些系统的长期特性，特别强调意见变化的统计数据。这项研究涉及对统计模型的理论研究，这些模型描述了传输现象，如液体通过过滤器的流动和空间组织的演变，如流体中的图案形成。这一结果将引起数学、统计力学以及材料和加工界的广泛兴趣。***

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. ***