research

Near Equilibrium Systems

In the pre-tenure phase, I worked on relaxation processes in two types of systems:

(1) quantum magnetic systems that are known to offer unique insights into dynamics and

(2) relaxation in disordered or glassy systems.

The focus of both of these efforts has been to understand relaxation processes that are so slow as to be inaccessible via state-of-the-art computer simulations (see below). The work led to the development of several exact solutions to describe relaxation processes in model systems in (1) and (2).

I use the Continued Fraction Formalism and Dynamical Simulations as tools for dynamical studies.

Non-Equilibrium Systems

I have focused on studies of four types of non-equilibrium systems:

(1) those that exhibit avalanches with a focus on predicting the time of onset of avalanches,

(2) shock propagation in granular media, and

(3) dust flow and filtration, and

(4) battle problems.

My work on (2) has encompassed three sub-areas within mechanical energy propagation in granular media.

First, my work predicted that solitary waves found in granular alignments would break to produce baby waves at boundaries. This prediction has been experimentally confirmed.

Second, I predicted that an alignment of grains where the grains progressively shrink in radius acts as a shock absorber. This system has now been experimentally validated and a project is under way to design a blast proof wall.

Third, my work suggests that granular alignments, tapered or otherwise, held within confined geometries and subjected to continuous forces can act as a noise filter that converts any time dependent signal into a well defined breathing frequency. These studies have led to independent work done by several research groups within the US and in other countries.

Since 2003, I have been working on dynamical problems of particulate flow through a fluid that belongs to (3). The work focuses on how skin flakes, dust mites, fiber, hair and like objects agglomerate as they flow through air, and how some of these objects can be removed from air.

Since 2006 I have been working on modeling battles - this work is done using simple lattice models. A part of this work explores how generic battle models can be used to effectively model disease spreading - in particular, I am working on how multiple sclerosis develops (in collaboration with Prof Murali Ramanathan in Pharmaceutical Sciences at SUNY-Buffalo).