Teaching assistantships at IIT Mandi: Feb-Jun 2020 -CY514 Reaction dynamics, Kinetics and Catalysis Aug-Dec 2019-CY522 Computational Chemistry Feb- Jun 2019-IC 222P Physics Practicum Aug-Dec 2018-IC 121 Mechanics of Waves and Particles Feb-Jun 2018-CY 511 Group Theory and Spectroscopy Aug-Dec 2017-CY522 Computational Chemistry Research assistantships during MSc: 1) Title : Understanding Band Structures in Solids via solving Schrödinger equation for Dirac comb Duration : Dec 2015-Feb 2016 (winter) Supervisor : Dr. Pradeep Kumar Abstract : The free electron theory although was successful in explaining physical properties of solids (such as specific heat capacity, Magnetic susceptibility etc.,), the theory was inadequate to explain the existence of band gaps. The solid is assumed to have a periodic potential from the lattice sites and the Schrödinger equation for such a system was solved. The Schrödinger equation for one Dirac barrier was solved and is approximated to N-barriers using the Bloch function and the Dirac barrier was inverted to Dirac well to account for the attractive potential. Then the more realistic K-P potential was solved and on the barrier limits the results from the Dirac comb was verified with K-P model. The arisal of band gaps is shown graphically for various potential strengths and for number of lattice sites. It is seen that the band gaps are more for high strength nuclear potentials and for low internuclear distances. The band becomes a continuum under consideration of Avagadro (large) number of lattice sites.
2) Title : Phase transition in computationally complex systems Duration : Feb 2016-Jul 2016 Supervisor : Dr. Samar Agnihotri Description : There are longstanding problems such as satisfiability problem, traveling salesman, Euler cycles and other similar problems in computer science. Till now, a polynomial time taking algorithm for solving them is not known neither the existence of a one. If one could find an algorithm to one of the problem, it can be used to all other problems. Such class of problems are called NP-complete problems. We are interested in viewing that those problems exhibit a phase transition from solvable to non- solvable. The solubility can be predicted from the parametric dependence of the phase transition curves derived for a particular problem.
3) Title : Analytical solutions for Smoluchowski equation Duration : Jul 2016 (summer) Supervisor : Dr. Aniruddha chakraborty Abstract : Many stochastic (Physical, Chemical, Biological) processes are governed by a master equation, called Smoluchowski equation. Treating the equation (PDE) with Laplace transform meets with the problem that taking inverse Laplace transform is not known for many cases. So we are on the way of developing a mathematical technique to solve those equations analytically in time domain.
B.Sc., Thesis: Title : Developing Optical Power Testing Specification of Intraocular lens made out of 26% water content material Duration : Dec 2014 - Apr 2015 Supervisor : Mr. Sundara ganesh, Mr. Rajesh kanna Place : AuroLab, The Aravind Eye Hospital, Madurai, Tamil Nadu, India. Abstract : We fabricated intraocular lenses made of Polymethylmethacrylate material. The optical power changes during the course of fabrication and again when introduced into the eye environment since hydrophilic lenses absorb moisture and change their refractive index. These changes were estimated theoretically to adjust in the initial fabrication to provide the correct power inside the eye environment. The optical power is measured using interferometry. We fabricated lenses with 10, 15, 20, 25, and 30 D for the in-situ environment and then verified them.