Projects done in M.Sc: 1) Title : Understanding Band Structures in Solids via solving Schrödinger equation for Dirac comb Duration : Dec 2015-Feb 2016 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 : Analytical solutions for Smoluchowski equation Duration : Jul 2016-Dec 2016 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.
3)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 some of the optimization problems in field of computation. Till now, a polynomial time taking algorithm 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 of a problem is studied from the phase transition curves obtained in the problem.
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 : The project is concerned with the fabrication of Polymethylmethacrylate intraocular lens and to overcome the problems faced during fabrication and to attain the desired optical power. It also includes testing the optical power using interferometry and to deal with the lens characteristics (For example, hydrophilic lenses absorb moisture, swells and its refractive index changes) that has influence on the optical power of the Inocular lens. The lens with optical powers 10, 15, 20, 25, 30 D for in situ (eye environment) were fabricated and tested.