Some variations on an extension of Caratheodory's normality criterion
In this note we give some variations on an extension of Caratheodory's normality criterion due to Grahl and Nevo.
math.CV↗
arXiv subjects
Rahul Kumar
Publications and source records attributed to Rahul Kumar.
Extensions of Watson's theorem and the Ramanujan-Guinand formula
Ramanujan provided several results involving the modified Bessel function $K_z(x)$ in his Lost Notebook. One of them is the famous Ramanujan-Guinand formula, equivalent to the functional equation of the non-holomorphic Eiesenstien series on $SL_2(z)$. Recently, this formula was generalized by Dixit, Kesarwani, and Moll. In this article, we first obtain a generalization of a theorem of Watson and, as an application of it, give a new proof of the result of Dixit, Kesarwani, and Moll. Watson's theorem is also generalized in a different direction using ${}_μK_z(x,λ)$ which is itself a generalization of $K_z(x)$. Analytic continuation of all these results are also given.
math.NT↗
Reducing Scattered Light in LIGO's Third Observing Run
Noise due to scattered light has been a frequent disturbance in the Advanced LIGO gravitational wave detectors, hindering the detection of gravitational waves. The non stationary scatter noise caused by low frequency motion can be recognized as arches in the time-frequency plane of the gravitational wave channel. In this paper, we characterize the scattering noise for LIGO's third observing run O3 from April, 2019 to March, 2020. We find at least two different populations of scattering noise and we investigate the multiple origins of one of them as well as its mitigation. We find that relative motion between two specific surfaces is strongly correlated with the presence of scattered light and we implement a technique to reduce this motion. We also present an algorithm using a witness channel to identify the times this noise can be present in the detector.
astro-ph.IM↗
Many Hands Make Light Work: Using Essay Traits to Automatically Score Essays
Most research in the area of automatic essay grading (AEG) is geared towards scoring the essay holistically while there has also been some work done on scoring individual essay traits. In this paper, we describe a way to score essays holistically using a multi-task learning (MTL) approach, where scoring the essay holistically is the primary task, and scoring the essay traits is the auxiliary task. We compare our results with a single-task learning (STL) approach, using both LSTMs and BiLSTMs. We also compare our results of the auxiliary task with such tasks done in other AEG systems. To find out which traits work best for different types of essays, we conduct ablation tests for each of the essay traits. We also report the runtime and number of training parameters for each system. We find that MTL-based BiLSTM system gives the best results for scoring the essay holistically, as well as performing well on scoring the essay traits.
cs.CL↗
Cryogenic suspension design for a kilometer-scale gravitational-wave detector
We report the mirror suspension design for Large-scale Cryogenic Gravitational wave Telescope, KAGRA, during bKAGRA Phase 1. Mirror thermal noise is one of the fundamental noises for room-temperature gravitational-wave detectors such as Advanced LIGO and Advanced Virgo. Thus, reduction of thermal noise is required for further improvement of their sensitivity. One effective approach for reducing thermal noise is to cool the mirrors. There are many technical challenges that must be overcome to cool the mirrors, such as cryocooler induced vibrations, thermal drift in suspensions, and reduction in duty cycling due to the increased number of potential failure mechanisms. Our mirror suspension has a black coating that makes radiative cooling more efficient. For conduction cooling, we developed ultra high purity aluminum heat links, which yield high thermal conductivity while keeping the spring constant sufficiently small. A unique inclination adjustment system, called moving mass, is used for aligning the mirror orientation in pitch. Photo-reflective displacement sensors, which have a large range, are installed for damping control on marionette recoil mass and intermediate recoil mass. Samarium cobalt magnets are used for coil-magnet actuators to prevent significant change of magnetism between room temperature and cryogenic temperature. In this paper, the design of our first cryogenic payload and its performance during bKAGRA Phase 1 are discussed.
physics.ins-det↗
On some $q$-series identities related to a generalized divisor function and their implications
In this article, a $q$-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one of the corollaries of our main theorem, we get results of Dilcher and Andrews, Crippa, and Simon. This main theorem involves a surprising new generalization of the divisor function $σ_s(n)$, which we denote by $σ_{s,z}(n)$. Analytic properties of $σ_{s,z}(n)$ are also studied. As a special case of one of our theorem we obtain result from a recent paper of Bringmann and Jennings-Shaffer.
math.NT↗
Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics
Einstein-Gauss-Bonnet (EGB) gravity is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in $ D > 4$ dimensions and EGB gravity is topologically invariant in $4D$. Recently several ways have been proposed for regularizing, a $ D \to 4 $ limit of EGB, for nontrivial gravitational dynamics in $ 4D $. Motivated by the importance of anti-de Sitter gravity/conformal field theory correspondence (AdS/CFT), we analyze black holes with AdS asymptotic to regularized $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED) field. For a static spherically symmetric \textit{ansatz} the field equations are solved exactly, using two different approaches, for a NED Lagrangian to obtain an identical solution$-$namely NED charged AdS black holes in $4D$ EGB gravity which retains several known solutions. Owing to the NED charge corrected EGB black holes, the thermodynamic quantities are also modified, and the entropy does not obey the usual area law. We calculate the heat capacity and Helmholtz free energy, in terms of horizon radii, to investigate both local and global thermodynamic stability of black holes. We observe a secondary Hawking-Page transition between the smaller thermally favoured black hole and thermal AdS space. Our results show that the behaviour of Hawking's evaporation abruptly halts at shorter radii regime such that the black holes do have a thermodynamically stable remnant with vanishing temperature.
gr-qc↗
Davydov Splitting, Resonance Effect and Phonon Dynamics in CVD grown Layered MoS2
We present a comprehensive temperature dependent Raman measurements for horizontally aligned CVD grown layered MoS2 in a temperature range of 4 to 330 K under resonance condition. Our analysis of temperature dependent phonon frequency shift and linewidth suggest a finite role of three and four phonon anharmonic effect. We observed Davydov splitting of the out-of-plane (A1g ) and in-plane (E12g ) modes, attributed to the weak interlayer interaction, and reflected in the appearance of additional modes with decreasing temperature for both 3 layers and few layers system. We also observed that the number of Davydov splitting components are more in few layers as compared to 3L MoS2, suggesting it increases with increasing number of layers. Temperature evaluation of the Raman spectra shows that the Davydov splitting, especially for A1g mode, is very strong and well resolved at low temperature. We note that A1g mode shows splitting at low temperature, while E12g mode is splitted even at room temperature, and that suggests to prominent role of A1g mode to the interlayer interaction. Further, the temperature dependence tuning of resonance effect is observed, via almost sixty fold increase in the intensity of the phonon modes at low temperature.
cond-mat.mtrl-sci↗
Gravitational lensing by charged black hole in regularized $4D$ Einstein-Gauss-Bonnet gravity
Among the higher curvature gravities, the most extensively studied theory is the so-called Einstein-Gauss-Bonnet (EGB) gravity, whose Lagrangian contains Einstein term with the GB combination of quadratic curvature terms, and the GB term yields nontrivial gravitational dynamics in $ D\geq5$. Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit of, the EGB gravity, and the resulting regularized $4D$ EGB gravity valid in $4D$. We consider gravitational lensing by Charged black holes in the $4D$ EGB gravity theory to calculate the light deflection coefficients in strong-field limits $\bar{a}$ and $\bar{b}$, while the former increases with increasing GB parameter $α$ and charge $q$, later decrease. We also find a decrease in the deflection angle $α_D$, angular position $θ_{\infty}$ decreases more slowly and impact parameter for photon orbits $u_{m}$ more quickly, but angular separation $s$ increases more rapidly with $α$ and charge $q$. We compare our results with those for analogous black holes in General Relativity (GR) and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes Sgr A* and M87*.
gr-qc↗
Generating black holes in $4D$ Einstein-Gauss-Bonnet gravity
In recent times there is a surge of interest in constructing Einstein-Gauss-Bonnet (EGB) gravity, in the limit $D \to 4 $, of the $D$-dimensional EGB gravity. Interestingly, the static spherically symmetric solutions in the various proposed $D \to 4 $ regularized EGB gravities coincide, and incidentally some other theories also admit the same solution. We prove a theorem that characterizes a large family of nonstatic or radiating spherically symmetric solutions to the $4D$ EGB gravity, representing, in general, spherically symmetric Type II fluid. An extension of the theorem, given without proof as being similar to the original theorem, generates static spherically symmetric black hole solutions of the theory. It not only enables us to identify available known black hole solutions as particular cases but also to generate several new solutions of the $4D$ EGB gravity.
gr-qc↗
Gravitational lensing by black holes in the $4D$ Einstein-Gauss-Bonnet gravity
Recently, a non-trivial $4D$ Einstein-Gauss-Bonnet (EGB) theory of gravity, by rescaling the GB coupling parameter as $α/(D-4)$, was formulated in \cite{Glavan:2019inb}, which bypasses Lovelock's theorem and avoids Ostrogradsky instability. The theory admits a static spherically symmetric black hole, unlike $5D$ EGB or general relativity counterpart, which can have both Cauchy and event horizons. We generalize previous work, on gravitational lensing by a Schwarzschild black hole, in the strong and weak deflection limits to the $4D$ EGB black holes to calculate the deflection coefficients $\bar{a}$ and $\bar{b}$, while former increases and later decrease with increasing $α$. We also find that the deflection angle $α_D$, angular position $θ_{\infty}$ and $u_{m}$ decreases, but angular separation $s$ increases with $α$. The effect of the GB coupling parameter $α$ on positions and magnification of the source relativistic images is discussed in the context of SgrA* and M87* black holes. A brief description of the weak gravitational lensing using the Gauss-Bonnet theorem is presented.
gr-qc↗
Maximal non valuative domains
The notion of maximal non valuative domain is introduced and characterized. An integral domain R is called a maximal non valuative domain if R is not a valuative domain but every proper overring of R is a valuative domain. Maximal non valuative domains have at most four maximal ideals. Various properties of maximal non valuative domains are discussed. Conditions are given under which pseudo-valuation domains and maximal non pseudo-valuation domains are maximal non valuative domains.
math.AC↗
Characterization of systematic error in Advanced LIGO calibration
The raw outputs of the detectors within the Advanced Laser Interferometer Gravitational-Wave Observatory need to be calibrated in order to produce the estimate of the dimensionless strain used for astrophysical analyses. The two detectors have been upgraded since the second observing run and finished the year-long third observing run. Understanding, accounting, and/or compensating for the complex-valued response of each part of the upgraded detectors improves the overall accuracy of the estimated detector response to gravitational waves. We describe improved understanding and methods used to quantify the response of each detector, with a dedicated effort to define all places where systematic error plays a role. We use the detectors as they stand in the first half (six months) of the third observing run to demonstrate how each identified systematic error impacts the estimated strain and constrain the statistical uncertainty therein. For this time period, we estimate the upper limit on systematic error and associated uncertainty to be $< 7\%$ in magnitude and $< 4$ deg in phase ($68\%$ confidence interval) in the most sensitive frequency band 20-2000 Hz. The systematic error alone is estimated at levels of $< 2\%$ in magnitude and $< 2$ deg in phase.
astro-ph.IM↗
Sensitivity and Performance of the Advanced LIGO Detectors in the Third Observing Run
On April 1st, 2019, the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO), joined by the Advanced Virgo detector, began the third observing run, a year-long dedicated search for gravitational radiation. The LIGO detectors have achieved a higher duty cycle and greater sensitivity to gravitational waves than ever before, with LIGO Hanford achieving angle-averaged sensitivity to binary neutron star coalescences to a distance of 111 Mpc, and LIGO Livingston to 134 Mpc with duty factors of 74.6% and 77.0% respectively. The improvement in sensitivity and stability is a result of several upgrades to the detectors, including doubled intracavity power, the addition of an in-vacuum optical parametric oscillator for squeezed-light injection, replacement of core optics and end reaction masses, and installation of acoustic mode dampers. This paper explores the purposes behind these upgrades, and explains to the best of our knowledge the noise currently limiting the sensitivity of each detector.
astro-ph.IM↗
Improving the Robustness of the Advanced LIGO Detectors to Earthquakes
Teleseismic, or distant, earthquakes regularly disrupt the operation of ground--based gravitational wave detectors such as Advanced LIGO. Here, we present \emph{EQ mode}, a new global control scheme, consisting of an automated sequence of optimized control filters that reduces and coordinates the motion of the seismic isolation platforms during earthquakes. This, in turn, suppresses the differential motion of the interferometer arms with respect to one another, resulting in a reduction of DARM signal at frequencies below 100\,mHz. Our method greatly improved the interferometers' capability to remain operational during earthquakes, with ground velocities up to 3.9\,$μ\mbox{m/s}$ rms in the beam direction, setting a new record for both detectors. This sets a milestone in seismic controls of the Advanced LIGO detectors' ability to manage high ground motion induced by earthquakes, opening a path for further robust operation in other extreme environmental conditions.
physics.ins-det↗
Rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity and its shadow
Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit of, the Einstein-Gauss-Bonnet (EGB) gravity, and the resulting regularized $4D$ EGB gravity has nontrivial dynamics. The theory admits spherically symmetric black holes generalizing the Schwarzschild black holes. We consider the rotating black hole in regularized $4D$ EGB gravity and discuss their horizon properties and shadow cast. The effects of the GB coupling parameter on the shape and size of shadows are investigated in the context of recent M87* observations from the EHT. Interestingly, for a given spin parameter, the apparent size of the shadow decreases and gets more distorted due to the GB coupling parameter. We find that within the finite parameter space, e.g. for $a=0.1M$, $α\leq 0.00394M^2$, and within the current observational uncertainties, the rotating black holes of the $4D$ EGB gravity are consistent with the inferred features of M87* black hole shadow.
gr-qc↗
Shadow and deflection angle of rotating black hole in asymptotically safe gravity
We analytically investigate the shadows cast by rotating black holes in the asymptotically safe gravity (ASG) by deriving complete null geodesics and observables using the Hamilton-Jacobi equation and Carter separable method. It turns out that the apparent shape and size of the shadow depend on the ASG parameters ($ζ, γ$) in addition to other black hole parameters ($M, a$). The size of black hole shadows monotonically decreases and shadows get more distorted with increasing values of ASG parameters when compared with the Kerr black hole shadows. In turn, we use shadow observables to estimate black hole spin and ASG parameters. Noteworthy, we find that the deflection angle of the light has been modified by ASG parameters to generalize the Kerr deflection angle, and the corrections in the deflection angle are of $\mathcal{O}(μ$as). In the vanishing limits of ASG parameters, our results smoothly reduced to the Kerr black holes. The inferred circularity deviation $ΔC\leq 0.10$ for the M87* black hole shadow merely constrains the ASG parameter $ζ$, however, shadow angular diameter $θ_d=42\pm 3\, μ$as, within the $1σ$ region, places bounds $ζ\leq 0.1324$ for $γ=0.10$.
gr-qc↗
Some Normality Criteria for Families of Holomorphic Functions of Several Complex Variables
We prove a Zalcman-Pang lemma in several complex variables and apply it to obtain several complex variables analogues of the known normality criteria like Lappan's five-point theorem and Schwick's theorem.
math.CV↗