Slow Relaxations in Complex Fluids: Origin and Nature of Dynamical Heterogeneities

凝聚态物质系统的复杂性和复杂性通常是通过有效的理论最简洁地表达出来的。无论是在平衡统计力学中还是在非平衡统计力学中，这些理论都是从一个连续的粗粒化过程中产生的，这个过程依赖于微观和宏观尺度之间的物理分离。在扩展的空间结构导致大规模异质性的系统中，这种尺度的分离是困难的。来自实验和模拟的越来越多的证据表明，这种结构存在于颗粒系统、过冷液体和泡沫中。众所周知，这些体系的动力学行为使它们有别于普通液体。动力行为和响应的复杂性可以追溯到扩展空间结构的出现。解开这种复杂性的一种方法是了解导致异常动力学的几何结构的起源，然后为这些扩展的自由度构建有效的运动方程。这正是这项建议的目标。这项研究大致可分为两个部分：(A)研究过冷液体和颗粒系统中动力学异质性的来源；(B)在这些结构的尺度上建立有效的动力学模型，介于分子动力学模拟的微观特征和流体动力学描述的宏观特征之间的尺度。智力优势：(A)部分的研究将集中在液体和颗粒物质的微观模型中发展的相关性，目的是将代数性质与潜在的几何结构联系起来。通过有效动力学的表述，(B)部分的研究将旨在解释缓慢动力学，同时解决液体和颗粒材料中从流动相到堵塞相转变的普遍性问题。数值模拟将成为建立有效的动力学模型的垫脚石。液体和颗粒材料的技术应用关键依赖于它们的流动能力，因此预测干扰的能力。拟议研究的中心目标之一是通过更好地了解现象使干扰变得可预测，从而有助于颗粒和流体技术的合理设计。广泛影响：向本科生和研究生介绍统计场理论技术是拟议研究活动的组成部分。数值模拟提供了一种介绍复杂理论概念的方便方式，并将被用作主要的教育工具。计划与女子学院的教职员工合作，增加女本科生对学术研究的参与。

The intricacy and complexity of condensed matter systems are often most succinctly expressedthrough effective theories. Such theories, both in equilibrium and non-equilibrium statistical mechanics, arise out of a successive coarse-graining process which relies on a separation of the physics between the microscopic and the macroscopic scales. This separation of scales is difficult in systems where extended spatial structures lead to large-scale heterogeneities.There is mounting evidence from experiments and simulations that such structures exist in granular systems, supercooled liquids and foams. It is also well established that the dynamical behavior of these systems set them apart from ordinary liquids. The complexity of dynamical behavior and response can be traced back to the occurrence of extended spatial structures. One way of unraveling this complexity is to understand the origin of the geometrical structures responsible for the anomalous dynamics, and then construct effective equations of motion for these extended degrees of freedom. This is precisely the objective of this proposal. The proposed research can be broadly divided into two parts; (a) investigate the origin of dynamical heterogenities in supercooled liquids and granular systems and (b) formulate effective models of dynamics at the scale of these structures, a scale intermediate between the microscopic one characteristic of molecular dynamics simulations and the macroscopic one characteristic of hydrodynamic descriptions.Intellectual merit: The research in part (a) will focus on the correlations that develop in microscopic models of liquids and granular matter with the aim of relating the algebraic properties to underlying geometric structures. Through the formulation of effective dynamics, the research in part (b) will aim to provide an explanation of the slow dynamics and, at the same time, address questions regarding the universality of the transition from a flowing to jammed phase in liquids and granular materials. Numerical simulations will form the stepping stones for the construction of effective dynamical models.Technological applications of liquids and granular materials rely crucially on their ability to flow and, therefore, the ability to predict jamming. One of the central goals of the proposed research is to make jamming predictable through a better understanding of the phenomenon and, therefore, contribute to the rational design of granular and fluid technologies.Broader impacts: Introducing undergraduate and graduate students to the techniques of statistical field theory is an integral part of the proposed research activities. Numerical simulations offer a convenient mode of introduction to sophisticated theoretical concepts and will be adopted as a primary educational tool. Collaboration with faculty members from womens colleges is planned to increase the participation of women undergraduates in academic research.***