Stress Networks in Weakly Connected Matter

9975533证人该奖项支持关于材料皱缩的理论研究。PI试图扩展之前的工作，这些工作找到了组成皱巴巴的薄片的单个脊线的简单数学描述。进一步的工作旨在找到确定山脊何时以及如何弯曲的数学关系。将研究将材料压皱成越来越小的体积，目的是找到该过程的普遍特征。专责小组亦会调查散粒物料(例如沙堆)的堆积情况。利用对完全坚硬、无摩擦的小球体的数值模拟，PI将研究颗粒在微小扰动下的微观运动。将寻求导致微观运动的最小扰动，以努力了解颗粒如何运动，以及在导致沉降的扰动下力如何重新分配。该奖项支持关于纸张等材料如何崩塌以及颗粒如何作为颗粒状材料(例如沙堆中的沙粒)沉降或对某些扰动做出反应的理论研究。PI将使用复杂的数学技术和计算机模拟来洞察褶皱和颗粒状运动。这些过程对理解材料很重要，在我们的日常经验中无处不在。随着研究的进展，学生和下一代研究人员将获得高质量的教育体验。

9975533WittenThis award supports theoretical research on the crumpling of materials. The PI seeks to extend previous work that found a simple mathematical description of the individual ridges that make up a crumpled sheet. Further work is aimed at finding mathematical relations that determine when and how the ridges will buckle. The crumpling of materials down to smaller and smaller volumes will be investigated with the aim of finding characteristic features of the process that are universal. The PI will also investigate the packing of granular materials (e.g. sandpiles). Using numerical simulations of perfectly hard, small frictionless spheres, the PI will study the microscopic motion of the grains that occurs in response to small disturbances. The smallest disturbances that lead to microscopic motion will be sought in an effort to understand how grains move and how forces redistribute under disturbances that lead to settling. This award supports theoretical research on how materials, like paper, crumble and how grains move as granular materials (for example, grains of sand in sandpiles) settle or respond to some disturbance. The PI will use sophisticated mathematical techniques and computer simulations to gain insight into crumpling and granular motion. These processes are important to the understanding of materials and are ubiquitous in our everyday experience. Students and the next generation of researchers will receive high quality educational experiences as the research progresses.