CDI-Type II: Collaborative Research: Computational Homology, Jamming, and Force Chains in Dense Granular Flows

该项目将采用高度跨学科的方法，将新的几何技术，建模和实验相结合，以解决有关颗粒介质和其他堵塞材料（如玻璃，泡沫和胶体）的物理特性的基本问题。堵塞材料的特点是它们像固体一样抵抗外力，但像液体一样无序。此外，当施加外力时，许多堵塞的材料具有称为力链网络的异质、分支结构。尽管人们知道力链的存在已经有几十年了，但对它们在物理过程中的作用的定量理解已经被证明是难以捉摸的，部分原因是以前的研究无法为它们设计一个公正和普遍的定义。力链的精确识别和表征以及堵塞材料对外力的响应可能会在许多领域产生变革性的影响。例如，仅在美国，处理和加工颗粒状材料的财务和能源成本（通常具有高效率）估计至少为1万亿美元。此外，雪崩和地震是颗粒介质不可预测的行为对人类产生负面影响的例子。在这项工作中，我们将运用新颖的数学技术，结合计算机模拟和实验，以获得一个定量的，预测性的描述堵塞的材料。该项目的推广工作强调提供教育机会，以学生从代表性不足的群体。我们将组织教育和招聘旅行到东北部以女性为主的文理学院和北卡罗来纳州历史上的黑人学校，如北卡罗来纳州中央大学和东南部的其他学校。这些旅行将包括技术和流行的讲座，包括演示，以表明对堵塞材料的研究是有趣的和重要的。在与学生的非正式会议上，我们将强调，科学和技术的职业生涯是有益的，并向那些代表性不足的群体开放。为了进一步激发学生对这项研究的兴趣，我们将举行一年两次为期两天的实验室开放日，以便有前途的本科生可以接触到我们研究的实验和理论方面。为了鼓励研究人员在堵塞材料领域的密切合作，我们将组织一年两次的跨学科研讨会。首届研讨会，“计算同源工具应用于堵塞和流动颗粒材料”定于2009年冬季。

This project will employ a highly interdisciplinary approach that integrates newgeometrical techniques, modeling, and experiments to address fundamental, openquestions concerning the physical properties of granular media and other jammedmaterials such as glasses, foams, and colloids. The hallmark of jammed materials isthat they resist applied forces like solids, but are disordered like liquids. In addition,many jammed materials possess heterogeneous, ramified structures known as forcechain networks when external forces are applied. Although the existence of forcechains has been known for decades, a quantitative understanding of their role inphysical processes has proved elusive in part because previous studies have beenunable to devise an unbiased and general definition for them. Precise identification andcharacterization of force chains and the response of jammed materials to applied forceswill likely have a transformative impact in many arenas. For example, financial andenergy costs of handling and processing of granular materials, typically with highinefficiency, is estimated to be at least one trillion dollars in the US alone. Also,avalanches and earthquakes are examples where the unpredictable behavior ofgranular media detrimentally impacts mankind. In this work, we will apply novelmathematical techniques coupled with computer simulations and experiments to obtaina quantitative, predictive description of jammed materials.The outreach efforts of this project emphasize providing educational opportunities tostudents from underrepresented groups. We will organize education and recruiting tripsto predominantly female liberal arts colleges in the Northeast and historically blackschools in North Carolina, such as North Carolina Central University, and others in theSoutheast. These trips will include giving technical and popular lectures, includingdemonstrations to show that research on jammed materials is intriguing and important.During informal meetings with students we will emphasize that careers in science andtechnology are rewarding and open to those in underrepresented groups. To stimulatefurther student interest in this research, we will hold biannual 2-day lab open houses sothat promising undergraduates can be exposed to both experimental and theoreticalaspects of our research. To encourage close collaboration among researchers in thefield of jammed materials, we will organize biannual interdisciplinary workshops. Theinaugural workshop, ``Computational Homology Tools Applied to Jamming and Flow inGranular Materials'' is scheduled for the winter of 2009.