I have worked with the chemical engineering division at BITS(Goa) for
formulating research plans. I mention this work as it involved parabolic
diffusion equations, Navier Stokes equations (especially along with rheological issues) and nonlinear population balance scenarios.
I have also collaborated with people who study complex systems. The work involved parabolic differential equations in the guise of coupled map lattices. Results we obtained formed essentially a small part of comparison of coupled map lattices to stochastic processes using dynamic order parameters.
A collaborative work was commenced with an experimental group in microfluidics in the Dept. of Physics, University of Pune. We have succeeded in applying partial differential equations to important design considerations in fabricating microfluidic channels for mixing fluids passively. This work involved maximum principles for elliptic PDES.
As a part of industrial process modeling work at the Dept. of Electronics, University of Pune, certain thin film deposition techniques were required to be addressed from the point of view of process control. I have been a part of a team which came up with an empirical mathematical model which was validated for low process parameters. The analysis of the model required certain mathematical techniques which we developed at our centre.
In collaboration with departments in defence institutions like ARDE in India certain studies were conducted at our centre. In particular, a programme concerning ballistics of munitions has been initiated which addresses computational modeling of trajectories and stability of missiles in flight. I have been involved in the same along with the CAE subgroup at our centre.