Slow Dynamics and Extended Structures in Complex Fluids

凝聚态系统的复杂性和复杂性通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。 这种理论，无论是在平衡和非平衡统计力学，产生了一个粗粒化的过程，依赖于微观和宏观的长度和时间尺度的分离。 在扩展的空间结构导致大尺度不均匀性的系统中，尺度的分离变得可疑。 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。 这也是公认的，这些系统的动力学行为设置它们除了普通的液体，并表明，动力学行为和响应的复杂性可以追溯到扩展的空间结构的发生。 解开这种复杂性的一种方法是确定负责异常动力学的扩展结构，然后为这些扩展的自由度构建“有效”的运动方程。 这个理论研究项目的目的是制定有效的模型在介观尺度的这些异质性;之间的微观分子动力学模拟的特征和宏观一个进入流体动力学描述的规模中间。 这样的公式应该提供理论和实验之间的直接接口，因为在介观尺度的信息往往是直接从实验中获得。 数值模拟将被用作有效的动力学理论建设的垫脚石。 这些技术将在晶格模型的背景下发展，然后扩展到连续模型。 通过关注介观尺度上的几何结构，该项目旨在探索宏观物理性质从微观相互作用中的出现。这个理论项目研究复杂和无序的凝聚态系统，如玻璃，并试图确定微观尺度的行为如何影响大尺度的行为。 这是科学中的一个基本问题，其解决将产生广泛的影响。

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.***