### Academic Projects @ IISER Kolkata

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## + Revisiting the FitzHugh-Nagumo model

**Advisor(s):**Dr. Rumi De (IISER Kolkata, India)

**Duration:** Jan 2013 - May 2013

**Summary:**The project was carried as a part of the biological physics course at IISER Kolkata. The project involved a review of the FitzHugh-Nagumo model which although was motivated by the Hodgkin-Huxley model, yet is analytically simpler & effective in explaining neural firing.

## + Saturated Absorption Spectroscopy

**Advisor(s):**Dr. Ayan Banerjee (IISER Kolkata, India)

**Duration:** Jan 2013 - May 2013

**Summary:**The project was carried as a part of the lab rotation course at IISER Kolkata. The project involved Saturated Absorption Spectroscopy of Rubidium. The power broadening & cross over resonances of the

^{87}Rb F=2 to F'=2 transition was analyzed at different pump intensities. Natural line width for Rubidium was obtained.

## + Synchronization in coupled oscillators: A Kuramoto model perspective

**Advisor(s):**Dr. Anandamohan Ghosh (IISER Kolkata, India)

**Duration:** Jan 2013 - May 2013

**Summary:**The project was carried as a part of the seminar course at IISER Kolkata. The project involved a review of the phenomenon of spontaneous synchronization of a large population of coupled limit-cycle oscillators ('Kuramoto oscillators') whose natural frequencies are drawn from some prescribed distribution.

## + An inspection of the Landau-Zener effect & illustration with experimental applications

**Advisor(s):**Dr. Siddhartha Lal (IISER Kolkata, India)

**Duration:** Aug 2012 - Dec 2012

**Summary:**The project was carried as a term-paper for the Advanced Quantum Mechanics course at IISER Kolkata. The physical & mathematical concepts associated with the Landau-Zener effect along with experimental results to justify the theory were studied.

## + Synchronization in chaotic systems

**Advisor(s):**Dr. Anandamohan Ghosh (IISER Kolkata, India) & Dr. Rajesh Kubmle Nayak (IISER Kolkata, India)

**Duration:** Sep 2011 - Dec 2011

**Summary:**The project was carried out as a part of the MATLAB based Computational Physics course at IISER Kolkata. The project involved computationally studying the phenomenon of synchronization in chaotic systems such as Lorenz systems, Rossler systems etc. Further, the change in the bifurcation structure of the systems undergoing synchronization was studied. The simulations were carried out in MATLAB & Fortran.

## + Python's attack at LU-Decomposition

**Advisor(s):**Dr. Ananda Dasgupta (IISER Kolkata, India)

**Duration:** Jan 2010 - May 2010

**Summary:**The project was carried out as a part of the Python based computer laboratory course at IISER Kolkata. The project involved writing a Python program that takes a square matrix as an input & returns its LU form, given that it exists. The product of the lower triangular matrix L & the upper triangular matrix U gives the matrix which has been decomposed. But, there are conditions subject to which the LU form of the matrix exists. The LU factorization of a square matrix has wide usage in the field of mathematics.