Hi everyone I am into my third-year graduate school (being a student from India) pursuing my Ph.D. in physics at the University of Massachusetts Amherst (on an F1 Student Visa). I am a graduate from the Indian Institute of Technology, Bhubaneswar. All of my current and past research work, (along with Github and Google scholar profiles, current research and readings of interest) have been ascribed in my resume attached.
To be particular, I have been keenly working on perturbative low-Reynolds number flows and solutions to Navier-Stokes equations, and in my own individual pursuit, I have been quite interested in the notion of differential Galois theory and differential Groebner basis (links of related work mentioned below) in the pursuit of analysis of PDEs such as Navier-Stokes etc. 1. https://www3.risc.jku.at/publications/download/risc_4229/master.pdf 2. https://www.kent.ac.uk/ims/personal/elm2/liz/papers/thesis.pdf.gz 3. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.121.2187&rep=rep1&type=pdf In general as well, Mansfield's work shows examples with Korteweg de-Vries equations (in physics, it's used to model shallow water wave mechanics) and equations with symmetries from a Weyl algebra. I have tried using the algorithm in a dry run myself on some of the equations within my works in progress. Previously also, I have shown some keen interest in the applications of Groebner basis in related works in some specific problems in modern physics, one instance of this in my undergraduate thesis titled 'Novel applications of cellular automata in computing and computational astrophysics'. I have also explored the sympy function for the Groebner basis (sympy.polys.polytools.groebner(F, *gens, **args)) and similar forms in other CAS systems in the past. I was looking for an opportunity for someone to mentor and collaborate with me for contributing to the sympy for a module (or a set of modules) for computing the differential Groebner basis for a system of partial differential equations which may help simplify the solution for the same. I have been working it out from manual computation on Navier-Stokes very recently and have obtained results, proofreading of which is in progress right now. To begin with, even within the scope of 350 hour time span, I am quite optimistic that at least I can implement the Kolchin-Ritt algorithm for Sympy, the analogue of the Buchberger's algorithms used for the polynomial based systems to find the Groebner basis of a polynomial ideal. Only if time permits shall we be able to incorporate similar (even if not exactly the same) ideas from the Faugere's F4 or F5 algorithm to the differential ideals for Diff Groebner basis reduction. With this, I would like to express my interests in the participation in the Google Summer of Code this year and would like to work on the same with the Sympy organization. If interests match, we can discuss in my more elaborate proposal as to how the basic modules for the polynomial ideals (I believe which are already implemented in sympy in the aforementioned function) can be extended to differential systems. Thanking everyone and looking forward to work with you guys! Yours sincerely Shrohan Mohapatra HAS 306, Hasbrouck Laboratory University of Massachusetts, Amherst 666 N Pleasant St Amherst, MA, 01003 -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/be607a05-435b-4ac5-8bd0-91bf57dd8af2n%40googlegroups.com.
updatedCVShrohan.pdf
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