Slow Dynamics and Extended Structures in Complex Fluids

凝聚态系统的复杂性和复杂性常常通过在大长度和时间尺度的限制下有效的理论来简洁地表达。这些理论，在平衡和非平衡统计力学中，产生于一个粗粒化过程，它依赖于微观和宏观长度和时间尺度的分离。这种尺度的分离在扩展空间结构导致大规模异质性的系统中变得可疑。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。这些系统的动力学行为与普通液体不同，这也表明动力学行为和响应的复杂性可以追溯到扩展空间结构的发生。解开这种复杂性的一种方法是确定导致异常动力学的扩展结构，然后为这些扩展自由度构建“有效”的运动方程。本理论研究项目的目标是在这些非均质性的介观尺度上制定有效的模型；介于分子动力学模拟的微观尺度和进入流体动力学描述的宏观尺度之间的一种尺度。这种公式应该提供理论和实验之间的直接接口，因为介观尺度上的信息通常可以直接从实验中获得。数值模拟将作为构建有效动力学理论的垫脚石。这些技术将在晶格模型的背景下发展，然后扩展到连续体模型。通过关注介观尺度上的几何结构，该项目旨在探索微观相互作用中宏观物理性质的出现。这个理论项目研究复杂和无序的凝聚态物质系统，如玻璃，并试图确定微观尺度上的行为如何影响大尺度上的行为。这是科学中的一个基本问题，其解决方案将产生广泛影响

The intricacy and complexity of condensed matter systems are often succinctly expressed through effective theories valid in the limit of large length and time scales. Such theories, both in equilibrium and non-equilibrium statistical mechanics, arise out of a coarse-graining process which relies on a separation of microscopic and macroscopic length and time scales. This separation of scales becomes suspect 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 and suggests that the complexity of dynamical behavior and response can be traced back to occurrence of extended spatial structures. One way of unraveling this complexity is to identify the extended structures responsible for the anomalous dynamics, and then construct 'effective' equations of motion for these extended degrees of freedom. The objective of this theoretical research project is to formulate effective models at the mesoscopic scale of these heterogeneities; a scale intermediate between the microscopic one characteristic of molecular dynamics simulations and the macroscopic one entering hydrodynamic descriptions. Such a formulation should provide a direct interface between theory and experiments since the information at the mesoscopic scale is often directly available from experiments. Numerical simulations will be used as a stepping stone in the construction of effective dynamical theories. The techniques will be developed in the context of lattice models and then extended to continuum models. By focusing on geometrical structures at the mesoscopic scale, the project aims to explore the emergence of macroscopic physical properties from microscopic interactions.%%%This theoretical project investigates complex and disordered condensed matter systems, such as glasses, and attempts to determine how behavior at the microscopic scale affects behavior at the large scale. This is a fundamental problem in science whose solution would have wide impact.***