Floppy Modes in Disordered Systems

9632182索普通过研究网络玻璃的软模，即低频本征模，可以分析网络玻璃的机械稳定性及其相关性质。使用最近设计的一种称为鹅卵石游戏的二维算法，PI已经成功地计算了大量站点的集群统计的几个度量。目前的拨款是探索将这项工作扩展到三维，探索相关热力学形式的发展，从而研究软性-刚性转变。这项研究应该会对硬度、隧道模式的结构行为以及脆弱和坚固的玻璃成型器的性质有更好的理解。%这笔赠款用于支持玻璃机械稳定性的研究。这项研究涉及强度测量和数学技术的发展，以便可靠地计算它们。这里的各种项目处于应用数学和材料科学之间的接口的前沿。这项研究应该会更好地理解硬度，它与弹性波的关系，以及脆弱和坚固的玻璃成型器的性质。***

9632182 Thorpe The mechanical stability and associated properties of network glasses can be analyzed by studying the floppy modes, the low frequency eigenmodes. Using a recently devised algorithm, called the pebble game, in two dimensions, the PI has been successful in calculating several measures of the cluster statistics for a large number of sites. The current grant is to explore extension of this work to 3 dimensions, to explore development of an associated thermodynamic formalism and thereby study floppy- rigid transitions. This research should produce an improved understanding of hardness, the structural behavior of tunneling modes and the nature of fragile and strong glass formers. %%% This grant supports research in the mechanical stability of glasses. The research involves developments of measures of strength and mathematical techniques for a reliable calculation of them. The various projects here are at the forefront of the interface between applied mathematics and materials science. This research should produce an improved understanding of hardness, of its relationship to elastic waves and the nature of fragile and strong glass formers. ***