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

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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.***