Studies of random packings of non-spherical objects

技术总结该奖项支持理论研究和教育活动，旨在开发一种可用于估计任意形状物体在随机配置中的堆积密度的理论。PI将利用该理论在物体形状空间中搜索最优的随机布局。这项研究将结合自旋玻璃理论的数学公式，如腔方法和信念传播来计算力分布和配位数，以及体积涨落的统计力学公式。PI预计，这种协同方法将产生比以前更全面的非球形颗粒堆积问题的图景。该理论将估计一类形状的最佳堆积分数，作为球点的解析延续，从而为系统地研究随机堆积的Ulam猜想的推广铺平了道路。发展一种理论框架来解决物理和数学中的一个基本和古老的问题，将在使用颗粒物质的不同行业中得到应用，因此工程师、材料科学家、物理学家和数学家都非常感兴趣。国际学生联合会致力于让代表人数不足的群体的学生参与该项目。这项研究还将通过丰富颗粒物质的教学，为课程开发做出贡献。从模拟获得的数据将通过项目网站提供给更广泛的研究社区。非技术总结该奖项支持专注于研究非球形颗粒组的理论研究和教育活动。寻找最密集的物体堆积是一个突出的材料科学问题，起源于400多年前的开普勒猜想。自然界中存在的几乎所有形状都是非球形的，人们认为非球形颗粒或颗粒可以比球形颗粒堆积得更稠密。这为通过形状变化进行有效的布局优化打开了令人兴奋的可能性。从纳米颗粒的自组装到病毒组装，包装问题出现在广泛的科学学科中。该计划亦会对从混凝土到纳米复合材料的颗粒状材料加工行业产生潜在影响。该协会致力于让来自代表性不足群体的学生参与这项计划。这项研究还将通过丰富颗粒物质的教学，为课程开发做出贡献。从模拟中获得的数据将通过项目网站提供给更广泛的研究界。

TECHNICAL SUMMARY This award supports theoretical research and educational activities focused to develop a theory that can be used to estimate the packing density of objects of arbitrary shapes in random configurations. The PI will use the theory to search for the best random packing in the space of object shapes. This research will bring together mathematical formulations from spin-glass theory such as cavity methods and belief propagation to calculate the force distribution and the coordination number, and the statistical mechanics formulation of volume fluctuations. The PI expects that this synergistic approach will produce a more comprehensive picture of the packing problem of non-spherical particles than before. The theory will estimate the optimum packing fraction for a class of shapes as an analytical continuation from the spherical point, thus paving the way for a systematic investigation of an extension of Ulam's conjecture for random packings. The development of a theoretical framework to solve a fundamental and ancient problem in physics and mathematics will have applications in diverse industries that employ particulate matter, and is therefore of great interest to engineers, material scientists, physicists and mathematicians alike. The PI is committed to involve students from underrepresented groups in the project. The research will also contribute to curriculum development by enriching instruction in granular matter. Data obtained from simulations will be made available to the broader research community through the project website.NONTECHNICAL SUMMARY This award supports theoretical research and educational activities focused to study non-spherical particles pack. Finding the densest packing of objects is an outstanding materials science problem that originated with Kepler's conjecture more than 400 years ago. Almost all shapes existing in nature are non-spherical and it is believed that non-spherical particles or grains can pack more densely than spheres. This opens the exciting possibility for efficient packing optimization by shape variation. The packing problem appears in a broad range of scientific disciplines from self-assembly of nanoparticles to virus assemblies. It has also potential impact on industries involved in the processing of granular materials from concrete to nanocomposite materials.The PI is committed to involve students from underrepresented groups in the project. The research will also contribute to curriculum development by enriching instruction in granular matter. Data obtained from simulations will be made available to the broader research community through the project website.