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

DynSyst_Special_Topics：颗粒物质混合和分离的动力系统方法

• 批准号: 1000469
• 负责人: Julio Ottino
• 金额: $ 44万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1000469&HistoricalAwards=false
• 关键词: DynSyst_Special_Topics; Dynamical; Systems; Approach; Mixing

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.

颗粒混合及其与偏析的相互作用是复杂的，因为流动会引起颗粒大小或密度的偏析。研究颗粒流动的典型系统是部分填充的旋转滚筒。因为，在合理的近似下，翻斗中的动力学发生在一个薄的流动面层中，所以可以使用一个简单、紧凑和可扩展的连续体模型来研究流动。然而，一个合适的混合（和分离）的一般理论框架，以及适当的数学工具来实现理论是缺乏的。充分理解需要综合的努力，包括由抽象数学概念启发的新理论和支持计算和实验结果。本文提出的理论工作将集中在分段等距、链接扭曲映射和拉格朗日相干结构的应用上。该研究的最终目标是利用动力系统方法开发一个理论框架，该框架将导致新的数学工具，以预测具有稳定和时间周期强迫的二维和三维翻滚几何形状中的颗粒物质的流动，混合，分离和模式形成。该方法基于强迫（混合协议）产生的三维流的几何和对称性。补充实验和模拟将用于证实这些理论方法对实际颗粒混合和分离问题的适用性。粒状物质流动的物理学是科学中的重大问题之一。颗粒物质是一个复杂系统的原型，其集体行为远离平衡。然而，许多根本问题依然存在。同时，对颗粒流的理解在从滑坡到食品加工等各种情况下具有巨大的实际重要性。流动的颗粒系统具有强烈的无序性，但又表现出混沌（混合）和有序（分离）之间的竞争。但迄今为止进展不大。在这里，我们介绍了基于高等数学的颗粒物质研究的新动力系统方法。动力系统工具提供了可以用于颗粒流动研究的数学框架。这里的科学进步可以对技术和实践产生直接影响。此外，这里考虑的新的数学方法有可能对许多物理系统产生广泛的影响，也许会创造一个全新的范式，就像20世纪90年代混沌平流科学对流体混合所做的那样。