Please review my statement of purpose, PhD in Physics

[aravindhv10]

Ever since my childhood, I was interested to know how nature and the things around me worked. A science fest I attended while in my 6th grade brought about my first tryst with the elegance of physical sciences. At this science fest, I came across the gas laws and ideal gas, which kept me puzzled for days. With this, I went to my brother to ask for help in understanding th. The next couple of hours were marked by heated discussions about thermodynamics. The discussions ended up stirring more questions than it answered so I was lead to study the Newton's laws, calculus and subsequently the reformulation of gas laws and thermodynamics using Newton's laws which lead to statistical mechanics and kinetic theory of gasses. I further came across the laws of planetary motion, this was quite impressive as a simple set of four laws could explain such a diverse phenomenon of the world. This lead me to realize that Physics lies at the heart of all natural sciences. My next great inspiration came in the way of the Electromagnetism, how simple ideas like Guass's divergence theorem could be used to make marvellous devices like the Van der Graaf Generator. Subsequently, I learnt how apparently different branches of physics like electricity, magnetism and optics were again united with a simple set of four equations and lead to special relativity. I now believe that the next great breakthrough is the unification of general relativity with quantum mechanics. Thus began my academic journey in theoretical physics.

    I was able to obtain a good score (top 1%) in the undergraduation entrance exams (IITJEE) and had the chance to join the popular IITs (Indian Institute of Technology) or the newly formed  IISERs (Indian Institute of Science Education and Research). I chose to join IISER, Pune over IIT even though the former was new and had not attained enough fame as it was an institution established mainly for science education unlike the IITs. I was also awarded the prestigious INSPIRE scholarship from DST.

    During the first 2 years of my undergraduation, I had to study all three branches of natural sciences along with mathematics which gave me a broad overview of present state of natural sciences. For the next two years, we were allowed to choose the courses which we had to study as long as they satisfied certain minimum requirements, I choose various advanced topics in physics and mathematics. In addition to my course work, I also tookup semester projects the first of which was a workshop on gravitational waves organised by IUCAA and INDIGO, In  this workshop, I was introduced to the basics of gauge theory for Einstein's field equation and the quadrupole formula, approximating and calculating the radiation due to a massive binary system using asymptotic expansions. I also studied Gel'fand functions and their applications for predicting the motion of detectors in the transverse traceless gauge with Prof Sanjeev Dhurandhar. This further strengthened my foundations in general relativity and some of its applications. I ended up taking 4 major courses more than what we were expected to, this impacted a bit of my CGPA but significantly helped me later on. Due to my strong foundations, I was able to secure 11th rank in the entrance exam, NET organised by CSIR. My course work helped me again when I worked with Prof Aninda Sinha on obtaining a numerical solution to the non-trivial cases of black hole accretion and solving for the sonic point. Normal methods of solution (Euler and Runge-Kutta) fail because of singularity at the sonic point, so we had to develop a method which involved discretisation of derivatives to obtain an algebraic system of equations which had to be solved simultaneously. For this purpose, I learnt various algorithms like bi-conjugate gradient method and multi-frontal solver. Next I worked on alternative formalisms of relativity like Palatini formulation with higher corrections to the Hilbert-Einstein action and the Gauss-Bonnet theorem. My previous knowledge of differential topology and Riemannian geometry greatly helped me to work with spaces where geodesic curve does not correspond to the shortest curve between two points.

  My M.S thesis was on experimental verification (or falsification) of Born's rule of probability in quantum mechanics, I worked with Prof. Aninda Sinha and Prof. Urbasi Sinha. Our aim was to obtain a bound on a parameter using calculations and compare it with the experimental value. For the theoretical calculations, we decided to try two methods, one of the was using by the Feynman path integral methods applied to the Helmholtz equation. The other method, which I was responsible for implementing was by exploiting the similarities of the Schrodinger equation to the classical diffusion equation and develop a random walk which would accurately model the Schrodinger equation. My previous experience with non-equilibrium statistical mechanics under Prof. Anil. D. Gangal was extremely helpful in providing me with the insights and possible ways in which this could be done. Once the theory was developed, I also had to implement the method numerically on a computer. Since our course work hardly had enough numerical methods, I had to learn a lot of additional portions like multi-threaded C programming on my own. I was successful in this regard, the results between the two methods agreed better than what we had hoped for and The results of this work will be published shortly. During the second part of my thesis, I studied the correspondence between fluid mechanics and quantum mechanics. The results were quite surprising since it showed that the Schrodinger's equation can be thought of as just classical fluid system with the potential corrected by the quantum potential. This lead me to a vast and exciting topic of Bohmian mechanics on which I am presently working.

[Cookie]

It would be better if you use spellcheck in your word processor first. 

[aravindhv10]

thanks for pointing that out, hope this is better...

 

    Ever since my childhood, I was interested in knowing how nature and the things around me worked. A science fest I attended while in my 6th grade brought about my first tryst with the elegance of physical sciences. At this science fest, I came across the gas laws and the ideal gas, which had me puzzled for days. With this, I asked my brother to help me understand the underlying theory. The next couple of hours were marked by heated discussions about thermodynamics. The discussions ended up stirring more questions in me than it actually answered. My subsequent quest for answers led me to study Newton's laws and calculus. Next, I learnt about how Newton’s laws can be used to reformulate gas laws and thermodynamics, which in turn introduced me to statistical mechanics and kinetic theory of gasses. Over the coming months, I came across the laws of planetary motion. For me, this was quite impressive, as a simple set of four laws could explain such diverse phenomena in this world. This lead me to realize that Physics lies at the heart of all natural sciences. My next great inspiration came in the way of the Electromagnetism. I was fascinated with how simple ideas like Gauss's divergence theorem could be used to make marvellous devices like the Van der Graaf Generator. Hungry for more knowledge, I learnt how apparently different branches of physics like electricity, magnetism and optics could be united with a simple set of four equations, which in turn led to special relativity. I believed the next great breakthrough is in the unification of general relativity with quantum mechanics. Thus began my academic journey in theoretical physics.
    After deciding to pursue undergraduate studies in Physics, I ended up scoring 99th percentile in the entrance exams (IIT-JEE). This presented me with a difficult choice, since I was offered admissions to study Physics at two of the best engineering and sciences schools in India: IIT, Kanpur (Indian Institute of Technology) and IISER, Pune (Indian Institute of Science, Education and Research). IIT Kanpur was among the best schools, but I ended up selecting IISER Pune due to it’s strong focus on research in basic sciences, even though it was a newly established school and not as popular as the IITs. I was also awarded the prestigious INSPIRE scholarship from DST at this time.
    During the first 2 years of my undergraduation, I had to study all three branches of natural sciences (Physics, Chemistry and Biology) along with mathematics, which gave me a broad overview of present state of natural sciences. In the subsequent years, we were allowed to choose the courses which interests us as long as they satisfied certain minimum requirements and I ended up choosing a bunch of advanced topics in physics and mathematics. In addition to my course work, I also undertook semester projects. One of them was a workshop on gravitational waves organised by IUCAA and INDIGO. In  this workshop, I was introduced to the basics of gauge theory for Einstein's field equation and the quadrupole formula, approximating and calculating the radiation due to a massive binary system using asymptotic expansions. I also studied Gel'fand functions and their applications for predicting the motion of detectors in the transverse traceless gauge with Prof Sanjeev Dhurandhar. This further strengthened my foundations in general relativity and some of its applications. At this time, I ended up taking four more courses than what we were expected to. This had a slight negative impact on my CGPA, but far greatly helped me prepare for the research work that was to come up. Due to my strong foundations, I was able to secure 11th rank in the entrance exam, NET organised by CSIR. My course work helped me again when I worked with Prof Aninda Sinha on obtaining a numerical solution to the non-trivial cases of black hole accretion and solving for the sonic point. Normal methods of solution (Euler and Runge-Kutta) fail because of singularity at the sonic point, so we had to develop a method which involved discretisation of derivatives to obtain an algebraic system of equations which had to be solved simultaneously. For this purpose, I learnt various algorithms like bi-conjugate gradient method and multi-frontal solver. Next I worked on alternative formalisms of relativity like Palatini formulation with higher order corrections to the Hilbert-Einstein action and the Gauss-Bonnet theorem. My previous knowledge of differential topology and Riemannian geometry greatly helped me to work with spaces where geodesic curve does not correspond to the shortest curve between two points.
    My M.S thesis was on experimental verification (or falsification) of Born's rule of probability in quantum mechanics, I worked with Prof. Aninda Sinha and Prof. Urbasi Sinha. Our aim was to obtain a bound on a parameter using calculations and compare it with the experimental value. For the theoretical calculations, we decided to try two methods, one of the was using by the Feynman path integral methods applied to the Helmholtz equation. The other method, which I was responsible for implementing was by exploiting the similarities of the Schrodinger equation to the classical diffusion equation and develop a random walk which would accurately model the Schrodinger equation. My previous experience with non-equilibrium statistical mechanics under Prof. Anil. D. Gangal was extremely helpful in providing me with the insights and possible ways in which this could be done. Once the theory was developed, I also had to implement the method numerically on a computer. Since our course work hardly had enough numerical methods, I had to learn a lot of additional portions like multi-threaded C programming on my own. I was successful in this regard, the results between the two methods agreed better than what we had hoped for and The results of this work will be published shortly. During the second part of my thesis, I studied the correspondence between fluid mechanics and quantum mechanics. The results were quite surprising since it showed that the Schrodinger's equation can be thought of as just classical fluid system with the potential corrected by the quantum potential. This lead me to a vast and exciting topic of Bohmian mechanics on which I am presently working.
 

[Flandre Scarlet]

I PMed you.