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Research

Our research interests focus on the study of complex systems and soft matter physics. This involves the modelling of various physical & biological systems, using dynamical systems theory and methods. Problems we are interested in cover a large range of topics, solving which involves a multi-disciplinary approach, using concepts from various fields of physics. A typical system of interest would be a complex physical system, with an interplay of interactions at different scales, both spatial and temporal. Examples of systems that we are investigating are given below. These range from living systems at the nano and micro metre scale to physical systems like oceans at several hundred kilometres. Brief summaries of some of the topics of our research follow.

Instabilities in flows at small scales and in living systems

Some of our recent work investigates instabilities in flows in living systems. We are interested in learning about & predicting the behaviour of microfluidic flows under various conditions & control parameter values. The effects of geometry & external fields are being studied. The focus of research is on flows in both living systems as well as at nanometre and micrometre regimes in the context of practical applications.


Nonlinearities
in mechanical systems

Mechanical systems have long been a subject of study in nonlinear dynamics. We continue our work in that tradition nanogears
but with the motivation that mechanistic analogues of real-life living and physical systems can provide a deep, intuitive understanding of the working of very complex systems and the physical principles underlying them.

An earlier, related work involved modelling double-walled carbon nanotubes (DWCNTs) and considering their behaviour in the context of their uses as nanoscale nonlinear springs, nano-gears, ratchets and bearings. Good agreement was found between our mechanistic model and theresults obtained from quantum-mechanical density functional theory calculations for the system.

Bubble dynamics & cavitation

bubble
Another problem under study is that of bubble dynamics and cavitation in fluids.  This occurs in various situations & is associated with various phenomena, ranging from the cavitation damage to propellers of ships, single and multi-bubble sonoluminescence, forced bubble oscillations in living tissue, shock-wave generation and cavitation by living organisms such as shrimps, the sound associated with running water: the list goes on and on.  A forced oscillating bubble in a fluid is a very rich nonlinear system showing very surprising and interesting behaviour. We study the dynamics of  such a system, under acoustic forcing, using a modified Rayleigh-Plesset equation, investigating the effect of various physical parameters. Our recent work has focused on charged bubbles, investigating charge & pressure thresholds.



Dynamical instabilities, noise & sensory detection

Living things depend upon their various senses for their survival. Sensory cells detecting  different modalities have developed sophisticated mechanisms to convey the various features of the external environment to the living system in the shortest possible time. The essential nonlinearities inherent in the signal transduction mechanism can take advantage of the noise from the environment the system is subject to, to display a highly amplified response to stimuli in a frequency-selective manner.  We study the role of the Hopf  bifurcation in detection of stimuli in sensory processes.
Synchronization in nonlinear systems

We are also interested in the synchronization behaviour of nonlinear systems. Addition of weak noise may cause synchronization to occur in some systems.  We have studied noise-induced synchronization in a system of coupled nonlinear oscillators which exhibit self-sustained oscillations.

Dynamics of coupled neurons

neurontracefig
Studies of neuronal firing behaviour include investigations of neuron models as flows & maps, constructing models that replicate observed bursting behaviour, and understanding the dynamics of neuronal firing from a dynamical systems theory point of view.


Modelling climate phenomena

CSinkprecipThis includes some recent work on ocean carbon sinks & climate change,
which is expected to have a strong impact in understanding climate dynamics. Our work focuses on predicting the location & the spatio-temporal evolution of ocean carbon sinks and its influence on climate change. Our model's results & predictions seem to be in agreement with known data (present climate patterns as well as paleoclimate). We predict the evolution of the aqueous carbon dioxide absorbed by the world's oceans as a function of time and spatial location.

Other work includes construction of mathematical models that qualitatively capture the behaviour of complex climate phenomena such as tropical precipitation.

Modelling ecological systems

Another problem we have been working on involves modelling the effects of climate change on ecological systems & populations and some interesting results have been obtained.
 
Vesicular nanotubulation

An interesting problem, one motivated by nanotubulation  experiments concerns the dynamics of vesicle-pulling. This phenomenon of nanotube formation has practical applications – e.g., the formation of networks of nanotubes and containers that can be formed through mechanical excitation of vesicles, useful in making nanofluid devices & drug delivery systems. We have theoretically investigated the dynamical  behaviour of a vesicle attached to a substrate and pulled with a constant velocity. We have considered the effects of change in vesicular geometry and various dissipative  effects that come into play as the lipid layers are pulled out to form a nanotube. Our theoretical model is in substantial qualitative agreement with experimental observations.


Instabilities in combustion

Another problem of interest is the theoretical investigation of the behaviour of combustion growth fronts under various conditions. Phenomena like fingering instabilities & effect of geometry on the combustion dynamics are sought to be understood.

Other problems of interest:

  • Quantum computing with nonlinear oscillator networks (project funded by Mphasis under the auspices of the Mphasis Center for Cognitive Computing, IIIT Bangalore)
  • There are various other research problems that are of interest to us that we have worked on including:
    • Problems in complex fluids and constrained flows
    • Physics of polymeric & polyelectrolytic systems
    • Applications of concepts of statistical physics in search and optimization problems