Dynamics of Growing Networks and Evolving Media

0227670Redner该奖项支持对增长网络结构的理论研究。要研究的网络通过基于流行度的规则递增地增长，其中已经具有相对大量的连接链路的节点具有更高的获得新链路的倾向。这一机制似乎构成了各种网络系统的基础，例如万维网、互联网和各种生物网络。本研究的主要目标是通过建立和分析用于原型网络模型演化的控制速率方程来发展对网络结构的全面的定量理解。网络结构的研究将有几个方向。本课程将研究衰变过程对网络完整性的作用，例如以有限速率移除节点或链路。另一个项目将专注于通过独立的节点和链路创建事件增长的网络的渗流特性。速率方程方法还将扩展到处理蛋白质相互作用网络，其中生长机制模拟小型生物有机体的基本过程，如酵母和细菌。除了研究本地网络的属性，如度分布，还将致力于揭示网络中的社区结构-社区之间联系较弱的紧密链接子网络。一项平行的工作将致力于研究由于流经介质的反应性流体的相互作用而演变的多孔网络。在过滤的情况下，由于悬浮颗粒的捕获，孔隙空间逐渐收缩。在溶解过程中，孔隙空间被逐渐消耗固体基质的流体扩大。这项研究的主要目标是了解孔隙空间几何和流动性质之间的耦合对长期动力学性质的作用，这将通过构建能够捕捉这些过程的本质并在其上进行分析计算的简化模型来实现。基本的学术目标是阐明流动的时间演变和多孔介质的物理性质之间的反馈的作用。在过滤问题中，重点将是制定一个标准，以确定过滤器的使用寿命，并了解由于捕获细小颗粒而导致的过滤动力学。在溶解中，一个基本的目标是了解纵向梯度对单管生长的基本动力学的作用。另一个主要目标将是将均匀溶解和虫洞增长之间的转变量化为相对流量和反应速率的函数。%该奖项支持对增长网络结构的理论研究。要研究的网络通过基于流行度的规则递增地增长，其中已经具有相对大量的连接链路的节点具有更高的获得新链路的倾向。这一机制似乎构成了各种网络系统的基础，例如万维网、互联网和各种生物网络。这项研究的主要目标是通过建立和分析原型网络模型演化的控制速率方程来发展对网络结构的全面定量理解。同时，将致力于研究由于流经介质的反应性流体的相互作用而演化的多孔网络。在过滤的情况下，由于悬浮颗粒的捕获，孔隙空间逐渐收缩。在溶解过程中，孔隙空间被逐渐消耗固体基质的流体扩大。这项研究的主要目的是了解孔隙空间几何和流动性质之间的耦合对长期动力学性质的作用。

0227670RednerThis award supports theoretical investigations into the structure of growing networks. The networks to be studied grow incrementally through popularity-based rules in which nodes that already have a relatively large number of attached links have a higher propensity for gaining new links. This mechanism appears to underlie a variety of networked systems, such as the world-wide web, the Internet, and various biological networks. The primary goal of this research is to develop a comprehensive quantitative understanding of network structure through the formulation and analysis of the governing rate equations for the evolution of prototypical network models.There are several directions in which research on network structure will be pursued. The role of decay processes, such as the removal of nodes or of links at a finite rate, on the integrity of networks will be studied. Another project will focus on the percolation properties of networks that grow by independent node and link creation events. The rate equation approach will also be extended to treat protein interaction networks in which the growth mechanisms model fundamental processes of small biological organisms, such as yeasts and bacteria. In addition to studying local network properties, such as the degree distribution, effort will be devoted to revealing community structures - tightly linked subnetworks with weaker linkages between communities - within networks. A parallel effort will be devoted to studying porous networks that evolve due to the interaction of a reactive fluid that flows through the medium. In the case of filtration, the pore space is gradually constricted, because of trapping of suspended particles. In dissolution, the pore space is enlarged by a fluid that gradually consumes the solid matrix. The principal goal of this research is to understand the role of the coupling between the pore space geometry and flow properties on long-time dynamical properties.This will be accomplished by constructing simplified models that capture the essence of these processes and upon which analytical calculations can be performed. The basic intellectual goal is to elucidate the role of feedback between the time evolution of the flow and the physical properties of the porous medium. In the problem of filtration, the focus will be to develop a criterion to determine the useful lifetime of a filter and to understand the kinetics of filtration due to the trapping of fine particles. In dissolution, one basic goal is to understand the role of longitudinal gradients on the basic dynamics of single tube growth. Another major goal will be to quantify the transition between homogeneous dissolution and wormhole growth as a function o the relative flow and reaction rates.%%%This award supports theoretical investigations into the structure of growing networks. The networks to be studied grow incrementally through popularity-based rules in which nodes that already have a relatively large number of attached links have a higher propensity for gaining new links. This mechanism appears to underlie a variety of networked systems, such as the world-wide web, the Internet, and various biological networks. The primary goal of this research is to develop a comprehensive quantitative understanding of network structure through the formulation and analysis of the governing rate equations for the evolution of prototypical network models.A parallel effort will be devoted to studying porous networks that evolve due to the interaction of a reactive fluid that flows through the medium. In the case of filtration, the pore space is gradually constricted, because of trapping of suspended particles. In dissolution, the pore space is enlarged by a fluid that gradually consumes the solid matrix. The principal goal of this research is to understand the role of the coupling between the pore space geometry and flow properties on long-time dynamical properties.***