Granular Matter: How Structure Determines Response Far From Equilibrium

颗粒流，无论是自然雪崩还是工业溜槽流，都是在组成颗粒的数量密度相当大时发生的。从统计物理学的角度来看，颗粒物质，很自然地假设多粒子系统的结构及其对外部扰动的响应是密切相关的。在平衡流体中，波动耗散定理普遍提供了这种联系。由于耗散的碰撞作用，颗粒流本质上远离平衡。因此，平衡定理不适用。本计画的目的是推导并发展颗粒物质在玻璃化转变密度与随机密堆积密度之间密度反应的动力学理论。有了这些理论在手，它将有可能确定颗粒流的结构，从他们的响应行为，反之亦然，预测响应的结构信息。理论预测应根据实验进行验证，并应在本构方程形式的流体动力学数值模型中实施。

Granular flows, be it natural avalanches or industrial chute flows, occur at considerable number densities of the constituting particles. Regarding granular matter from a statistical physics point of view, it is natural to assume that the structure of the many-particle system and its response to external perturbations is closely linked. In equilibrium fluids, this link is universally provided by fluctuation dissipation theorems. Granular flows are essentially far from equilibrium due to the dissipative collisional interactions. Consequentially, the equilibrium theorems due not apply. The aim of this project is to derive and develop kinetic theories for the Response of granular matter at densities between the glass transition density and the random close packing density. With these theories at hand it will be possible to determine the structure of granular flows from their response behaviour and, vice versa, predict the response from structural information. The predictions of the theories shall be validated against experiments and shall be implemented in numerical models of fluid dynamics in the form of constitutive equations.