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

凝聚态系统的复杂性和复杂性通常通过有效的理论得到最简洁的表达。这种理论，无论是平衡态还是非平衡态统计力学，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。这种尺度的分离在扩展的空间结构导致大尺度非均匀性的系统中是困难的。越来越多的实验和模拟证据表明，这种结构存在于颗粒系统、过冷液体和泡沫中。人们也已经确定，这些系统的动力学行为使它们有别于普通液体。动力学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理解导致反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的。拟议的研究可以大致分为两个部分;（a）调查过冷液体和颗粒系统中动力学不均匀性的起源和（B）在这些结构的尺度上制定有效的动力学模型，这是一个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。（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。通过有效动力学的公式化，部分（B）的研究将旨在提供对缓慢动力学的解释，同时，解决关于液体和颗粒材料中从流动相到堵塞相转变的普遍性的问题。数值模拟将成为构建有效动力学模型的基础。液体和颗粒材料的技术应用关键取决于它们的流动能力，因此也取决于预测堵塞的能力。拟议的研究的中心目标之一是通过更好地理解的现象，使堵塞可预测的，因此，有助于合理设计的颗粒和流体technologies.Broader影响：介绍本科生和研究生的统计场理论的技术是拟议的研究活动的一个组成部分。数值模拟提供了一个方便的模式，介绍了复杂的理论概念，并将通过作为一个主要的教育工具。计划与女子学院的教员合作，以增加女大学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.***