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Rahul Kumar

Publications and source records attributed to Rahul Kumar.

122 records · Page 7Linked to original sources
arXiv2018

Rotating black hole in Rastall theory

Rotating black hole solutions in theories of modified gravity are important as they offer an arena to test these theories through astrophysical observation. The non-rotating black hole can be hardly tested since the black hole spin is very important in any astrophysical process. We present rotating counterpart of a recently obtained spherically symmetric exact black hole solution surrounded by perfect fluid in the context of Rastall theory, viz, rotating Rastall black hole that generalize the Kerr-Newman black hole solution. In turn, we analyze the specific cases of the Kerr-Newman black holes surrounded by matter like dust and quintessence fields. Interestingly, for a set of parameters and a chosen surrounding field, there exists a critical rotation parameter ($a=a_{E}$), which corresponds to an extremal black hole with degenerate horizons, while for $a a_{E}$ with value $a_E$ is also influenced by these parameters. We also discuss the thermodynamical quantities associated with rotating Rastall black hole, and analyze the particle motion with the behavior of effective potential.

gr-qc↗
arXiv2018

Generalized Lambert series, Raabe's integral and a two-parameter generalization of Ramanujan's formula for $ζ(2m+1)$

A comprehensive study of the generalized Lambert series $\displaystyle\sum_{n=1}^{\infty}\frac{n^{N-2h}\exp{(-an^{N}x)}}{1-\exp{(-n^{N}x)}}, 0 0$, $N\in\mathbb{N}$ and $h\in\mathbb{Z}$, is undertaken. Two of the general transformations of this series that we obtain here lead to two-parameter generalizations of Ramanujan's famous formula for $ζ(2m+1)$, $m>0$ and the transformation formula for $\logη(z)$. Numerous important special cases of our transformations are derived. An identity relating $ζ(2N+1), ζ(4N+1),\cdots, ζ(2Nm+1)$ is obtained for $N$ odd and $m\in\mathbb{N}$. Certain transcendence results of Zudilin- and Rivoal-type are obtained for odd zeta values and generalized Lambert series. A criterion for transcendence of $ζ(2m+1)$ and a Zudilin-type result on irrationality of Euler's constant $γ$ are also given. New results analogous to those of Ramanujan and Klusch for $N$ even, and a transcendence result involving $ζ\left(2m+1-\frac{1}{N}\right)$, are obtained.

math.NT↗
arXiv2017

Zeros of combinations of the Riemann $Ξ$-function and the confluent hypergeometric function on bounded vertical shifts

In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Recently the first author obtained an integral representation involving the Riemann $Ξ$-function and the confluent hypergeometric function linked to the general theta transformation. Using this result, we show that a series consisting of bounded vertical shifts of a product of the Riemann $Ξ$-function and the real part of a confluent hypergeometric function has infinitely many zeros on the critical line, thereby generalizing a previous result due to the first and the last authors along with Roy and Robles. The latter itself is a generalization of Hardy's theorem.

math.NT↗
arXiv2017

Malware Detection Approach for Android systems Using System Call Logs

Static detection technologies based on signature-based approaches that are widely used in Android platform to detect malicious applications. It can accurately detect malware by extracting signatures from test data and then comparing the test data with the signature samples of virus and benign samples. However, this method is generally unable to detect unknown malware applications. This is because, sometimes, the machine code can be converted into assembly code, which can be easily read and understood by humans. Furthuremore, the attacker can then make sense of the assembly instructions and understand the functioning of the program from the same. Therefore we focus on observing the behaviour of the malicious software while it is actually running on a host system. The dynamic behaviours of an application are conducted by the system call sequences at the end. Hence, we observe the system call log of each application, use the same for the construction of our dataset, and finally use this dataset to classify an unknown application as malicious or benign.

cs.CR↗
arXiv2017

Accretion onto a noncommutative geometry inspired black hole

The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate $\dot{M}$, sonic speed $a_s$ and other flow parameters are generalised for the NC inspired black hole and compared with the results obtained for the standard Schwarzschild black holes. We also derive explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon. This analysis is a generalisation of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters have also been modified. It turns out that $ \dot{M} \approx {M^2}$ is still achievable but $r_s$ seems to be substantially decreased due to NC effects, that in turn does affect the accretion process.

gr-qc↗
arXiv2016

Low Cost Autonomous Navigation and Control of a Mechanically Balanced Bicycle with Dual Locomotion Mode

On the lines of the huge and varied efforts in the field of automation with respect to technology development and innovation of vehicles to make them run autonomously, this paper presents an innovation to a bicycle. A normal daily use bicycle was modified at low cost such that it runs autonomously, while maintaining its original form i.e. the manual drive. Hence, a bicycle which could be normally driven by any human and with a press of switch could run autonomously according to the needs of the user has been developed.

cs.RO↗
arXiv2016

Static Analysis Using the Cloud

In this paper we describe our experience of using Microsoft Azure cloud computing platform for static analysis. We start by extending Static Driver Verifier to operate in the Microsoft Azure cloud with significant improvements in performance and scalability. We present our results of using SDV on single drivers and driver suites using various configurations of the cloud relative to a local machine. Finally, we describe the Static Module Verifier platform, a highly extensible and configurable platform for static analysis of generic modules, where we have integrated support for verification using a cloud services provider (Microsoft Azure in this case).

cs.DC↗
arXiv2016

Ultrahigh Energy Cosmic Rays: A Galactic Origin?

It is suggested that essentially all of the UHECRs we detect, including those at the highest energy, originate in our Galaxy. It is shown that even if the density of sources decreases with Galactic radius, then the anisotropy and composition can be understood. Inward anisotropy, as recently reported by the Auger collaboration can be understood as drift along the current sheet of UHECRs originating outside the solar circle, as predicted in Kumar and Eichler (2014), while those originating within the solar circle exit the Galaxy at high latitudes.

astro-ph.HE↗
arXiv2015

Entanglement like properties in Spin-Orbit Coupled Ultra Cold Atom and violation of Bell like Inequality

We show that the general quantum state of synthetically spin-orbit coupled ultra cold bosonic atom whose condensate was experimentally created recently ( Y. J. Lin {\it et al.}, Nature, {\bf 471}, 83, (2011)), shows entanglement between motional degrees of freedom ( momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provides a unique opportunity to verify fundamental principle like quantum non-contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such atom-laser system and how that influneces quantities like entanglement entropy, violation of Bell like Inequality etc. We also discuss the implication of our result in testing the quantum non-contextuality and Bell's Inequality vioaltion by macroscopic quantum object like Bose-Einstein Condensate of ultra cold atoms.

cond-mat.quant-gas↗
arXiv2015

Electron Heating in a Relativistic, Weibel-Unstable Plasma

The dynamics of two initially unmagnetized relativistic counter-streaming homogeneous ion-electron plasma beams are simulated in two dimensions using the particle-in-cell (PIC) method. It is shown that current filaments, which form due to the Weibel instability, develop a large scale longitudinal electric field in the direction opposite to the current carried by the filaments as predicted by theory. Fast moving ions in the current filaments decelerate due to this longitudinal electric field. The same longitudinal electric field, which is partially inductive and partially electrostatic, is identified as the main source of acceleration of electrons in the current filaments. The transverse electric field, though larger than the longitudinal one, is shown to play a smaller role in heating electrons, contrary to previous claims. It is found that, in 1D, the electrons become strongly magnetized and are \textit{not} accelerated beyond their initial kinetic energy. Rather, the heating of the electrons is enhanced by the bending and break-up of the filaments, which releases electrons that would otherwise be trapped within a single filament and hence slow the development of the Weibel instability (i.e. the magnetic field growth) via induction as per Lenz's law. In 2D simulations electrons are heated to about one quarter of the initial kinetic energy of ions. The magnetic energy at maximum is about 4 percent, decaying to less than 1 percent by the end of the simulation. Most of the heating of electrons takes place while the longitudinal electric field is still growing while only a small portion of the heating is a result of subsequent magnetic field decay. The ions are found to gradually decelerate until the end of the simulation by which time they retain a residual anisotropy less than 10 percent.

astro-ph.HE↗
arXiv2014

Metamorphosis of Fuzzy Regular Expressions to Fuzzy Automata using the Follow Automata

To deal with system uncertainty, finite automata have been generalized into fuzzy automata. Stamenkovic and Ciric proposed an approach using the position automata for the construction of fuzzy automata from fuzzy regular expressions. There exist multifarious methodologies for the construction of finite automata from regular expressions known as Thompson construction, Antimirov partial derivatives, Glushkov automata and follow automata etc. In this paper, we propose an approach for the conversion of fuzzy regular expressions into fuzzy automata using the concept of follow automata. The number of states of the obtained Fuzzy automata using the proposed approach is lesser than the extant approaches in the literature.

cs.FL↗
arXiv2013

The isotropy problem of Sub-ankle Ultra-high energy cosmic rays

We study the time dependent propagation of sub-ankle ultra-high energy cosmic rays (UHECRs) originating from point-like Galactic sources. We show that drift in the Galactic magnetic field (GMF) may play an important role in the propagation of UHECRs and their measured anisotropy, particularly when the transport is anisotropic. To fully account for the discreteness of UHECR sources in space and time, a Monte Carlo method is used to randomly place sources in the Galaxy. The low anisotropy measured by Auger is not generally characteristic of the theoretical models, given that the sources are distributed in proportion to the star formation rate, but it can possibly be understood as a) intermittency effects due to the discrete nature of the sources or, with extreme parameters, b) a cancellation of drift current along a current sheet with the outward radial diffusive flux. We conclude that it is possible to interpret the Galactic sub-ankle CR flux as being due entirely to intermittent discrete Galactic sources distributed in proportion to star formation, but only with probability of roughly 35 percent, of which the spectrum is in accord with observations about 30 percent of the time. An alternative explanation for the low anisotropy may be that they are mostly extragalactic and/or heavy.

astro-ph.HE↗
arXiv2013

Is the Galactic Cosmic Ray Spectrum Constant in Time?

The hypothesis is considered that the present Galactic cosmic ray spectrum is at present softer than its time average due to source intermittency. Measurements of muogenic nuclides underground could provide an independent measurement of the time averaged spectrum. Source intermittency could also account for the surprising low anisotropy reported by the IceCube collaboration. Predictions for Galactic emission of ultrahigh-energy quanta, such as UHE gamma rays and neutrinos, might be higher or lower than previously estimated.

astro-ph.HE↗