Broad Research Goal :

To use the tools of equilibrium and non-equilibrium statistical mechanics to understand emergent phenomena in complex fluids, novel soft materials and biological systems.

Current Projects

1. Self Propelled Particles :

Generically, these can be defined as particles that draw energy from internal or external sources and dissipate this energy by moving through the medium they inhabit. Such a definition encompasses a wide class of systems such as fish schools, bacterial colonies and monolayers of vibrated granular rods. In all of these the energy input that maintains the system out of equilibrium is on each unit, rather than at the boundaries as in more conventional non-equilibrium situations. These systems exhibit spectacularly different behavior such as long range order in 2D, anomalous fluctuations about steady states and exotic instabilities and pattern formations.

Collaborator : M. Cristina Marchetti, Syracuse University

Progress : We have shown that a traditional model for a nematic, namely hard rods that interact with Onsager excluded volume interaction, together with a minimal implementation of activity namely a non-equilibrium self replenishing velocity along the long axis is sufficient to capture many anomalous fluctuations exhibited by these systems (paper). Further, we have shown that modifications from this self propulsion velocity to the momentum transfer that occurs when these rods collide accounts for enhanced orientational ordering and enhanced longitudinal diffusion that have been observed in numerical simulations (to be published).

Currently on the drawing board : All of the above considerations have been in the context of a passive medium (i.e., no hydrodynamic interactions) and in the case of formally infinite systems. We are now looking at minimal models of swimmers with momentum conserving interactions with a fluid to capture the dominant fluid mediated effects in terms of our "bottoms up" approach. Also, we are considering effects of confinement on the behavior of our model systems.

Outreach : A popular introduction to this topic available here.

systems of interest

2. Liquid Crystalline Elastomers :

These are materials formed by crosslinking liquid crystalline polymer melts. They are soft incompressible rubbers in that they can undergo large reversible shear deformations. The interplay between liquid crystalline degrees of freedom of the polymer melt and the elastic degrees of freedom of the crosslink mass points gives rise to novel physical properties in these materials, such as soft modes that involve simultaneous shear and director rotations and nontrivial optical response.

Collaborator : Xiangjun Xing, Syracuse University

Progress : We have considered an elastomer formed by crosslinking a chiral nematic polymer melt in its isotropic state and used free energy considerations to address two questions : 1) What is the effect of the incipient chirality of the melt on the elasticity of the solid in the disordered state? (to be published) 2) When such a solid is cooled below the order disorder transition of the melt, what is the kind of director pattern and spontaneous elastic deformation that emerge? (preprint).

Outreach : A popular introduction to the physics of rubbery materials available here.

3. Granular Fluids :

Granular systems span a broad spectrum that encompasses sand dunes, planetary rings to gas fluidized beds in pharmaceutical and petrochemical industries. When activated, through vibration or shear, these systems exhibit many fluid like properties. This class of systems have been termed granular fluids. A useful approach has been to take the grains as the smallest entities in the system that interact with each other through collisions that conserve momentum but dissipate energy. Further, the interstetial fluid is effectively a continuous medium on these scales and can be modeled at the level of hydrodynamics. In a subset of these systems, the interstitial fluid does not play a critical role and hence can be dropped in theoretical modeling. Such systems have been termed dry granular fluids.

Collaborators : James W. Dufty, University of Florida and J. Javier Brey, Universidad de Sevilla

Progress : Systematic application of the tools of non-equilibrium statistical mechanics to simple model systems of dry granular fluids was the focus of my research and some of the results were reported in my dissertation and in these papers.

Currently on the drawing board : We are working towards flushing out the formal results reported in earlier work through systematic approximations with the explicit aim of understanding the role of velocity correlations in this inherently non-equilibrium system in hydrodynamic transport.