DynSyst_Special_Topics: A Dynamical Systems Approach to Mixing and Segregation of Granular Matter

点击翻译按钮获取中文摘要

Granular mixing and its interplay with segregation are complicated, since flow induces segregation by particle size or density. A canonical system for the study of granular flow is a partially filled rotating tumbler. Because, to a reasonable approximation, the dynamics in a tumbler take place in a thin flowing surface layer, a simple, compact, and extensible continuum model can be used to study the flow. However, a suitable general theoretical framework for mixing (and segregation) as well as appropriate mathematical tools to implement the theory are lacking. Full understanding requires an integrated effort consisting of new theory inspired by abstract mathematical concepts and supporting computational and experimental results. The theoretical work proposed here will focus on the application of Piecewise Isometries, Linked Twist Maps, and Lagrangian Coherent Structures. The ultimate objective of the research is to develop a theoretical framework using a dynamical systems approach that will lead to new mathematical tools to predict flow, mixing, segregation, and pattern formation for granular matter in 2d and 3d tumbler geometries with steady and time-periodic forcing. The approach is based on the geometry and symmetries of the 3d flow generated by the forcing (mixing protocols). Complementary experiments and simulations will be used to confirm the applicability of these theoretical approaches to real granular mixing and segregation problems. The physics of the flow of granular matter is one of the big questions in science. Granular matter is a prototype of a complex system with collective behavior far from equilibrium. Yet many fundamental questions remain. At the same time, an understanding of granular flow has tremendous practical importance in situations ranging from landslides to food processing. Flowing granular systems are strongly disordered and yet display competition between chaos (mixing) and order (segregation). But inroads to date have been modest. Here, we introduce new dynamical systems approaches for the study of granular matter that are grounded in higher mathematics. Dynamical systems tools offer mathematical frameworks that can be exploited in the study of granular flow. Scientific progress here can have an immediate impact on technology and practice. Furthermore, the new mathematical approaches considered here have potential for broad-ranging impact on many physical systems, perhaps creating an entirely new paradigm much like the science of chaotic advection did for mixing of fluids in the 1990s.