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

复杂流体中的慢弛豫：动力学异质性的起源和本质

• 批准号: 0549762
• 负责人: Bulbul Chakraborty
• 金额: $ 29.1万
• 依托单位: Brandeis University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-03-01 至 2010-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0549762&HistoricalAwards=false
• 关键词: Slow; Relaxations; Complex; Fluids; Origin

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.***

凝聚态物质系统的复杂性往往可以通过有效的理论来最简洁地表达。平衡和非平衡统计力学中的此类理论都源于连续的粗粒度过程，该过程依赖于微观和宏观尺度之间的物理分离。在扩展空间结构导致大规模异质性的系统中，这种尺度分离是困难的。实验和模拟中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，这些系统的动力学行为使它们有别于普通液体。动态行为和响应的复杂性可以追溯到扩展空间结构的出现。解决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。这正是本提案的目的。拟议的研究可大致分为两部分； （a）研究过冷液体和颗粒系统中动力学不均匀性的起源，（b）在这些结构的尺度上制定有效的动力学模型，这是一种介于分子动力学模拟的微观特征和流体动力学的宏观特征之间的尺度智力价值：（a）部分的研究将重点关注液体和颗粒物质微观模型中发展的相关性，目的是将代数性质与基础几何结构联系起来。通过有效动力学的公式化，(b)部分的研究旨在提供对慢动力学的解释，同时解决有关液体和颗粒材料从流动相到堵塞相转变的普遍性问题。数值模拟将成为构建有效动力学模型的垫脚石。液体和颗粒材料的技术应用在很大程度上依赖于它们的流动能力，因此也依赖于预测干扰的能力。拟议研究的中心目标之一是通过更好地理解干扰现象来预测干扰，从而有助于颗粒和流体技术的合理设计。更广泛的影响：向本科生和研究生介绍统计领域的技术理论是拟议研究活动的一个组成部分。数值模拟提供了一种介绍复杂理论概念的便捷方式，并将被采用作为主要的教育工具。计划与女子学院的教职人员合作，以增加女本科生对学术研究的参与。***