Statistical Network Representations of Energy Landscapes in Soft-Sphere Models

就像球滚下山并在势能最低点静止一样，许多物理和生物系统在能量最小化状态下接近平衡。沙子就是这样一个系统的例子：被倒入容器中，它会以随机排列的状态静止，但可以通过敲击容器的形式增加能量，从而过渡到更低的能量状态。这个研究项目旨在预测这些颗粒状材料如何从其潜在能量景观的角度对施加的力做出反应，就像山脉一样，它是由广阔的山谷和山峰组成的。特别令人感兴趣的是微重力环境对颗粒系统的影响，比如由松散结合在一起的尘埃和破碎的岩石组成的碎石堆小行星。就像容器里的沙子一样，微弱的引力将小行星松散地固定在一起。小行星对探测或挖掘力量的反应对于开发此类近地小行星的采矿技术非常重要。该项目旨在开发量化高维复杂能量景观与系统动力学之间关系的新技术。这依赖于一种新的计算方法，通过形成低维二部图表示来提取能量景观的主要特征；一个网络有两种类型的节点，能量最小化节点和可达鞍点，由能量势垒高度加权的边连接。图形和发生在图形上的动力学然后被用来解释相互作用的球体的大型随机系统的行为，这是微重力下颗粒材料的模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Just as a ball rolls downhill and comes to rest at the lowest point of potential energy, many physical and biological systems approach equilibrium at an energy-minimizing state. Sand is an example of such a system: being poured in a container it comes to rest in a randomly arranged state, but can transition to an even lower energy state through the addition of energy in the form of tapping the container. This research project seeks to predict how such granular materials respond to applied forces from the viewpoint of their underlying energy landscape, which like a mountain range is a vast expanse of valleys and peaks. Of particular interest is the effect of microgravity environments on granular systems, such as rubble-pile asteroids composed of loosely held-together dust and fractured rock. Like the sand sitting in a container, the weak gravitational force loosely holds the asteroid together in its shape. How the asteroid responds to the forces of probing or digging is important for developing mining techniques for such near-earth asteroids. The project aims at developing new techniques for quantifying the relationship between high-dimensional complex energy-landscapes and the dynamics of the system. This relies on a new computational method for extracting the dominate features of the energy landscape by forming a low-dimensional bipartite graph representation; a network with two types of nodes, energy minimizers and accessible saddle points, connected by edges weighted by the energy barrier heights. The graph and dynamics taking place on the graph are then used to explain the behavior of large stochastic systems of interacting spheres, a model for granular materials in microgravity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.