Non-Linear Transport and Spatial Organization Processes

非线性传输和空间组织过程

• 批准号: 9632059
• 负责人: Sidney Redner
• 金额: $ 18.2万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9632059&HistoricalAwards=false
• 关键词: Non; Linear; Transport; Spatial; Organization

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. ***

9632059 Redner理论研究将在非线性输运过程和相关的集体性质在异质介质。 两个一般性的主题将被考虑，包括非弹性气体和过滤过程的动力学。 一个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。 在小的温度和浓度梯度的非弹性气体的稳定响应将被用来帮助开发的瞬态冷却和潜在的集群现象的基本见解。 将对过滤的基本方面进行调查，其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，从而在输送和过滤效率之间产生反馈。 将开发新的模型来描述这种非稳态响应分析，并了解潜在的渗流问题引起的堵塞网络。 也将进行调查，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。 “恶性文明”模型似乎可以解释真实的文明的时间发展和相对优势的某些方面。 确定了“公平”世界与“超级大国主导”世界之间的过渡，并将进行研究，以量化与这一过渡有关的基本现象。 同样，将研究“自适应”选民模型。 在这些模型中，引入了新类型的转换率规则来模仿人类行为的几个基本要素。 这些系统的长期属性将调查，特别强调意见变化的统计。 这项研究涉及到描述传输现象的统计模型的理论研究，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。 结果将是广泛的兴趣，数学，统计力学和材料和处理社区。 ***