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Sunu Engineer

Publications and source records attributed to Sunu Engineer.

5 recordsLinked to original sources
arXiv2025

Transcendental Encoding conjecture

We propose the Transcendental Encoding Conjecture for decision problems, which asserts that every language in complexity class P encodes to an algebraic real (possibly rational or algebraic irrational) under its binary characteristic encoding or other relevant encodings, whereas every NP-complete language encodes to a transcendental real. In particular, we exhibit languages whose encodings are provably rational (hence algebraic), discuss the status of encodings for other "natural" languages such as PRIMES (its encoding is irrational but not known to be algebraic).

cs.CC↗
arXiv2021

The Life and Science of Thanu Padmanabhan

Thanu Padmanabhan was a renowned Indian theoretical physicist known for his research in general relativity, cosmology, and quantum gravity. In an extraordinary career spanning forty-two years, he published more than three hundred research articles, wrote ten highly successful technical and popular books, and mentored nearly thirty graduate students and post-doctoral fellows. He is best known for his deep work investigating gravitation as an emergent thermodynamic phenomenon. He was an outstanding teacher, and an indefatigable populariser of science, who travelled very widely to motivate and inspire young students. Paddy, as he was affectionately known, was also a close friend to his students and collaborators, treating them as part of his extended academic family. On September 17, 2021 Paddy passed away very unexpectedly, at the age of sixty-four and at the height of his research career, while serving as a Distinguished Professor at the Inter-University Centre for Astronomy and Astrophysics, Pune. His untimely demise has come as a shock to his family and friends and colleagues. In this article, several of them have come together to pay their tributes and share their fond memories of Paddy.

physics.hist-ph↗
arXiv1997

Nonlinear Gravitational Clustering: dreams of a paradigm

We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$ to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.

astro-ph↗