A
special type of reaction-diffusion systems are those where the reacting
mass is conserved. These systems have some characteristics that
might shed some light on the
general processes of chemotaxis and find applications in the biological
context. These are the systems I am also looking at.

One dimensional systems of interacting particles transported by diffusion and driven is an area of my interest. These systems are very strongly correlated due to volume exclusion constraint and hydrodynamic models have been shown to fail at this regime. Strong correlation makes application of kinetic theory a difficult job as well. The problem is challenging and is a subject of active research these days.

One dimensional systems of interacting particles transported by diffusion and driven is an area of my interest. These systems are very strongly correlated due to volume exclusion constraint and hydrodynamic models have been shown to fail at this regime. Strong correlation makes application of kinetic theory a difficult job as well. The problem is challenging and is a subject of active research these days.

We
developed an efficient method of measuring the solvent accessible
surface are of amino acids and have designed an effective
hydrophobic interaction potential based on this. Hydrophobicity is the
dominant long range force that makes the protein collapse onto a
conformation close to its native fold and then other interactions are
believed to take up the fine tuning process to lead to the final native fold. In minimization of the
free energy corresponding to the native fold of the protein, the
hydrophobic interaction is expected to have a lot of contributions. This fact is
strongly supported through the potential function we have designed.
Depending on hydrophobic interaction alone we could discriminate
between the native fold and several thousands of decoys for about 20
small proteins. I intend to carry on this research to understand the
statistical mechanics of the folding process.

In
the quantitative genetics part of our work we focused on understanding
sympatric speciation ( competition driven speciation) under the action
of a Lotka-Volterra dynamics. The competition drives species apart on a
trait space in time so that they eventually become reproductively
isolated leading to speciation. Considering a coupled set of species,
strong competition in the population of one of them can even induce
sympatric speciation onto the other species which themselves do not
have much of competition within their populations. This is an
interesting
statistical problem under non equilibrium conditions.

We
have put forward an efficient Monte Carlo cluster algorithm to capture
the equilibrium statistics of a self assembling molecular system. Self
assembly of molecules of various microscopic symmetries give rise to
exotic
macroscopic structures. This is a fascinating statistical problem
involving multiple scales. Processes are generally hierarchical and to
capture the statistics of
such self-assembling transitions one has to simulate the system at
multiple space and time scales. Applying a cluster move Monte Carlo
keeping the
detailed balance intact is always tricky. We have proposed a general
scheme in continuum modifying the famous Swendsen-Wang-Woolf method for
spins on a lattice which applies to a wide class of self assembling
systems. Our method enables one have a lot of control over the
simulation and is extremely powerful. Carrying on this research further
is a priority to me.

#### Networks and synchronization:

Collective
dynamics of interacting nodes on a network, emergent properties,
synchronization etc. are the issues that I am presently having
interest on. At present we would like to look at systems where the
time scales of the nodal dynamics matches that of the spreading of the
connections between nodes or the time scale of the network growth. Such
processes are commonplace in biological contexts, like spreading of a
viral disease where the lifetime of the virus is comparable to the time
scale of its spreading in a community. Emergent properties in such web
of interconnected dynamic units have so far been mostly observed at a
scale where the local and global time scales are much different. Its an
active field of research with a lot of scope for applications and
understanding.