arXiv subjects

Soumya Bhattacharya

Publications and source records attributed to Soumya Bhattacharya.

27 records · Page 2Linked to original sources

arXiv2018

Perturbations of spiky strings in AdS3

Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.

hep-th↗

arXiv2017

Finiteness of irreducible holomorphic eta quotients of a given level

We show that for any positive integer $N$, there are only finitely many holomorphic eta quotients of level $N$, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier's conjecture/ Mersmann's theorem which states that: Of any given weight, there are only finitely many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights.

math.NT↗

arXiv2017

Perturbations of spiky strings in flat spacetimes

Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal perturbations of the spiky string worldsheets embedded in a $2+1$ dimensional flat spacetime. Such perturbations lead to a rounding off of the spikes, which, in a way, demonstrates the stable nature of the unperturbed worldsheet. The same features appear for the dual spiky string solution and in the spiky as well as their dual solutions in $3+1$ dimensional flat spacetime. Our results are based on exact solutions of the corresponding Jacobi equations which we obtain and use while constructing the profiles of the perturbed configurations.

hep-th↗

arXiv2017

Infinite Families of Simple Holomorphic Eta Quotients

We address the problem of constructing a simple holomor- phic eta quotient of a given level N . Such constructions are known for all cubefree N . Here, we provide such constructions for arbitrarily large prime power levels. As a consequence, we obtain an irreducibility

math.NT↗

arXiv2016

Finiteness of simple holomorphic eta quotients of a given weight

We provide a simplified proof of Zagier's conjecture / Mersmann's theorem which states that of any particular weight, there are only finitely many holomorphic eta quotients, none of which is an integral rescaling of another eta quotient or a product of two holomorphic eta quotients other than 1 and itself.

math.NT↗

arXiv2016

Holomorphic eta quotients of weight 1/2

We give a short proof of Zagier's conjecture / Mersmann's theorem which states that each holomorphic eta quotient of weight 1/2 is an integral rescaling of some eta quotient from Zagier's list of fourteen primitive holomorphic eta quotients. In particular, given any holomorphic eta quotient $f$ of weight 1/2, this result enables us to provide a closed-form expression for the coefficient of qn in the $q$-series expansion of $f$, for all $n$. We also demonstrate another application of the above theorem in extending the levels of the simple (resp. irreducible) holomorphic eta quotients.

math.NT↗

arXiv2015

Colloidal graphite/graphene nanostructures using collagen showing enhanced thermal conductivity

Time kinetics of interaction of natural graphite (GR) to colloidal graphene (G) collagen (C) nanocomposites was studied at ambient conditions, and observed that just one day at ambient conditions is enough to form colloidal graphene directly from graphite using the protein collagen. Neither controlled temperature and pressure ambiance nor sonication was needed for the same; thereby rendering the process biomimetic. Detailed spectroscopy, X ray diffraction, electron microscopy as well as fluorescence and luminescence assisted characterization of the colloidal dispersions on day one and day seven reveals graphene and collagen interaction and subsequent rearrangement to form an open structure. Detailed confocal microscopy, in the liquid state, reveals the initial attack at the zigzag edges of GR, the enhancement of auto fluorescence and finally the opening up of graphitic stacks of GR to form near transparent G. Atomic Force Microscopy studies prove the existence of both collagen and graphene and the disruption of periodicity at the atomic level. Thermal conductivity of the colloid shows a 17% enhancement for a volume fraction of less than 0.00005 of G. Time variant increase in thermal conductivity provides qualitative evidence for the transient exfoliation of GR to G. The composite reveals interesting properties that could propel it as a future material for advanced bio applications including therapeutics.

q-bio.BM↗

arXiv2015

Anomalously augmented charge transport capabilities of biomimetically transformed collagen intercalated nano graphene based biocolloids

Collagen micro fibrils bio mimetically intercalate graphitic structures in aqueous media to form graphene nano platelets collagen complex (G Cl). Synthesized G Cl based stable, aqueous bio nanocolloids exhibit anomalously augmented charge transportation capabilities over simple collagen or graphene based colloids. The concentration tunable electrical transport properties of synthesized aqueous G Cl bio nanocolloids has been experimentally observed, theoretically analyzed and mathematically modeled. A comprehensive approach to mathematically predict the electrical transport properties of simple graphene and collagen based colloids has been presented. A theoretical formulation to explain the augmented transport characteristics of the G Cl bio nanocolloids based on the physico chemical interactions among the two entities, as revealed from extensive characterizations of the G Cl bio complex, has also been proposed. Physical interactions between the zwitterionic amino acid molecules within the collagen triple helix with the polar water molecules and the delocalized π electrons of graphene and subsequent formation of partially charged entities has been found to be the crux mechanism behind the augmented transport phenomena. The analysis has been observed to accurately predict the degree of enhancement in transport of the concentration tunable composite colloids over the base colloids. The electrically active G Cl bio nanocolloids with concentration tunability promises find dual utility in novel gel bio electrophoresis based protein separation techniques and advanced surface charge modulated drug delivery using biocolloids.

physics.bio-ph↗

arXiv2015

Spiky strings in $\varkappa$-deformed $AdS$

We study rigidly rotating strings in $\varkappa$-deformed $AdS$ background. We probe this classically integrable background with `spiky' strings and analyze the string profiles in the large charge limit systematically. We also discuss the dispersion relation among the conserved charges for these solutions in long string limit.

hep-th↗