Slow Dynamics and Extended Structures in Complex Fluids

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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.***