ShantanuT01/DACTYL-Pretraining huggingface dataset:
In our previous work (Paper I) we applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central compact object in three Galactic microquasars assuming the possibility that the central compact body is a super-spinning object (or a naked singularity) with external spacetime described by Kerr geometry with a dimensionless spin parameter $a\equiv cJ/GM^2>1$. Here we extend our consideration, and in a consistent way investigate implications of a set of ten resonance models so far discussed only in the context of $a<1$. The same physical arguments as in Paper I are applied to these models, i.e. only a small deviation of the spin estimate from $a=1$, $a\gtrsim 1$, is assumed for a favoured model. For five of these models that involve Keplerian and radial epicyclic oscillations we find the existence of a unique specific QPO excitation radius. Consequently, there is a simple behaviour of dimensionless frequency $M\times\nu_{U}(a)$ represented by a single continuous function having solely one maximum close to $a\gtrsim1$. Only one of these models is compatible with the expectation of $a\gtrsim 1$. The other five models that involve the radial and vertical epicyclic oscillations imply the existence of multiple resonant radii. This signifies a more complicated behaviour of $M\times\nu_{U}(a)$ that cannot be represented by single functions. Each of these five models is compatible with the expectation of $a\gtrsim 1$.
We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the flux variation. This phenomenon is very similar to the well known Bloch's oscillation in crystals. The similitude is related to the charge discreteness in the charge-current representation, which plays the same role as the constant lattice in crystals.
Using a Hamiltonian formulation of Composite Fermions that I recently developed with R. Shankar, I compute the dependence of the spin polarization on the temperature for the translationally invariant fractional quantum Hall states at $\nu=1/3$ and $\nu=2/5$. I compare my results to experiments at $\nu=1/3$ and find reasonably good agreement.
We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a nonequilibrium (hot) steady state. We apply our results to a simple yet relevant Brownian model for carrier transport in GaAs. We obtain a negative differential conductivity regime (Gunn effect) and discuss and compare our results with experimental results.
While AGN are considered to be key drivers of the evolution of massive galaxies, their potentially significant role in the dwarf-galaxy regime (M*< 10^9 MSun) remains largely unexplored. We combine optical and infrared data, from the Hyper Suprime-Cam (HSC) and the Wide-field Infrared Explorer (WISE) respectively, to explore the properties of ~800 AGN in dwarfs at low redshift (z<0.3). Infrared-selected AGN fractions are ~10-30 per cent in dwarfs, which, for reasonable duty cycles, indicates a high BH-occupation fraction. Visual inspection of the deep HSC images indicates that the merger fraction in dwarf AGN (~6 per cent) shows no excess compared to a control sample of non-AGN, suggesting that the AGN-triggering processes are secular in nature. Energetic arguments indicate that, in both dwarfs and massive galaxies, bolometric AGN luminosities (L_AGN) are significantly greater than supernova luminosities (L_SN). L_AGN/L_SN is, in fact, higher in dwarfs, with predictions from simulations suggesting that this ratio only increases with redshift. Together with the potentially high BH-occupation fraction, this suggests that, if AGN feedback is an important driver of massive-galaxy evolution, the same is likely to be true in the dwarf regime, contrary to our classical thinking.
In the present paper, we report on a study of the anisotropic strange stars under Finsler geometry. Keeping in mind that Finsler spacetime is not merely a generalization of Riemannian geometry rather the main idea is the projectivized tangent bundle of the manifold $\mathpzc{M}$, we have developed the respective field equations. Thereafter, we consider the strange quark distribution inside the stellar system followed by the MIT bag model equation of state (EOS). To find out the stability and also the physical acceptability of the stellar configuration, we perform in detail some basic physical tests of the proposed model. The results of the testing show that the system is consistent with the Tolman-Oppenheimer-Volkoff (TOV) equation, Herrera cracking concept, different energy conditions and adiabatic index. One important result that we observe is that the anisotropic stress reaches to the maximum at the surface of the stellar configuration. We calculate (i) the maximum mass as well as corresponding radius, (ii) the central density of the strange stars for finite values of bag constant $B_g$ and (iii) the fractional binding energy of the system. This study shows that Finsler geometry is especially suitable to explain massive stellar systems.
We have found that a beryllium (Be) atom on nanostructured materials with H2 molecules generates a Kubas-like dihydrogen complex [H. Lee et al. arXiv:1002.2247v1 (2010)]. Here, we investigate the feasibility of Be-decorated fullerenes for hydrogen storage using ab initio calculations. We find that the aggregation of Be atoms on pristine fullerenes is energetically preferred, resulting in the dissociation of the dihydrogen. In contrast, for boron (B)-doped fullerenes, Be atoms prefer to be individually attached to B sites of the fullerenes, and a maximum of one H2 molecule binds to each Be atom in a form of dihydrogen with a binding energy of ~0.3 eV. Our results show that individual dispersed Be-decorated B-doped fullerenes can serve as a room-temperature hydrogen storage medium.
Gravitational waves from precessing black-hole binaries exhibit features that are absent in nonprecessing systems. The most prominent of these is a parity-violating asymmetry that beams energy and linear momentum preferentially along or opposite to the orbital angular momentum, leading to recoil of the binary. The asymmetry will appear as amplitude and phase modulations at the orbital frequency. For strongly precessing systems, it accounts for at least 3% amplitude modulation for binaries in the sensitivity band of ground-based gravitational-wave detectors, and can exceed 50% for massive systems. Such asymmetric features are also clearly visible when the waves are decomposed into modes of spin-weighted spherical harmonics, and are inherent in the waves themselves---rather than resulting from residual eccentricity in numerical simulations, or from mode-mixing due to precession. In particular, there is generically no instantaneous frame for which the mode decomposition will have any symmetry. We introduce a method to simplify the expressions for waveforms given in analytical relativity, which can be used to combine existing high-order waveforms for nonprecessing systems with expressions for the precessing contributions, leading to improved accuracy and a unified treatment of precessing and nonprecessing binaries. Using this method, it is possible to clarify the nature and the origins of the asymmetries and show the effects of asymmetry on recoils more clearly. We present post-Newtonian (PN) expressions for the waveform modes that include these terms, complete to the relative 2PN level in spin (proportional to $v^4/c^4$ times a certain combination of the spins). Comparing the results of those expressions to numerical results, we find good qualitative agreement. We also demonstrate how these expressions can be used to efficiently calculate waveforms for gravitational-wave astronomy.
The so called $k$-normal elements appear in the literature as a generalization of normal elements over finite fields. Recently, questions concerning the construction of $k$-normal elements and the existence of $k$-normal elements that are also primitive have attracted attention from many authors. In this paper we give alternative constructions of $k$-normal elements and, in particular, we obtain a sieve inequality for the existence of primitive, $k$-normal elements. As an application, we show the existence of primitive $k$-normal elements for a significant proportion of $k$'s in many field extensions. In particular, we prove that there exist primitive $k$-normals in $\mathbb F_{q^n}$ over $\mathbb F_q$ in the case when $k$ lies in the interval $[1, n/4]$, $n$ has a special property and $q, n\ge 420$.
We use three-dimensional hydrodynamic simulations to investigate the nonlinear gravitational responses of gas to, and the resulting drag forces on, very massive perturbers moving on circular orbits. This work extends our previous studies that explored the cases of low-mass perturbers on circular orbits and massive perturbers on straight-line trajectories. The background medium is assumed to be non-rotating, adiabatic with index 5/3, and uniform with density rho0 and sound speed a0. We model the gravitating perturber using a Plummer sphere with mass Mp and softening radius rs in a uniform circular motion at speed Vp and orbital radius Rp, and run various models with differing R=rs/Rp, Mach=Vp/a0, and B=G*Mp/(a0^2*Rp). A quasi-steady density wake of a supersonic model consists of a hydrostatic envelope surrounding the perturber, an upstream bow shock, and a trailing low-density region. The continuous change in the direction of the perturber motion makes the detached shock distance reduced compared to the linear-trajectory cases, while the orbit-averaged gravity of the perturber gathers the gas toward the center of the orbit, modifying the background preshock density to rho1=(1 + 0.46B)*rho0 depending weakly on Mach. For sufficiently massive perturbers, the presence of a hydrostatic envelope makes the drag force smaller than the prediction of the linear perturbation theory, resulting in F = 4*pi*rho1*(G*Mp/Vp)^2 * (0.7/etaB) for etaB = B/(Mach^2 -1) > 0.1; the drag force for low-mass perturbers with etaB < 0.1 agrees well with the linear prediction. The nonlinear drag force becomes independent of R as long as R < etaB/2, which places an upper limit on the perturber size for accurate evaluation of the drag force in numerical simulations.
Let F be a polarized irreducible holomorphic symplectic fourfold, deformation equivalent to the Hilbert scheme parametrizing length-two zero-dimensional subschemes of a K3 surface. The homology group H^2(F,Z) is equipped with an integral symmetric nondegenerate form, the Beauville form. We give precise conjectures for the structure of the cone of effective curves - and by duality - the cone of ample divisors. Formally they are completely analogous to the results known for K3 surfaces, and they are expressed entirely in terms of the integers represented by the Beauville form restricted to Pic(F). We prove that these conjectures are true in an open subset of the moduli space using deformation theory.   The Fano variety of lines contained in a cubic fourfold is an example of a holomorphic symplectic fourfold. Our conjectures imply many concrete geometric statements about cubic fourfolds which may be verified using projective geometry.
Let $K$ be a number field and $r$ an integer. Given an elliptic curve $E$, defined over $K$, we consider the problem of counting the number of degree two prime ideals of $K$ with trace of Frobenius equal to $r$. Under certain restrictions on $K$, we show that "on average" the number of such prime ideals with norm less than or equal to $x$ satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors.
We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimen- sional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a triangulation. The variation of this function under local rescalings of the edge lengths sharing a vertex is the Euler density, and we use it to illustrate how continuous concepts can have natural discrete analogs.
In our recent work [8], we have studied the homogenization of the Poisson equation in a class of non periodically perforated domains. In this paper, we examine the case of the Stokes system. We consider a porous medium in which the characteristic distance between two holes, denoted by $\epsilon$, is proportional to the characteristic size of the holes. It is well known (see [1],[17] and [19]) that, when the holes are periodically distributed in space, the velocity converges to a limit given by the Darcy's law when the size of the holes tends to zero. We generalize these results to the setting of [8]. The non-periodic domains are defined as a local perturbation of a periodic distribution of holes. We obtain classical results of the homogenization theory in perforated domains (existence of correctors and regularity estimates uniform in $\epsilon$) and we prove $H^2$--convergence estimates for particular force fields.
We construct a large class of vacuum solutions of the Einstein equations without any symmetries and with controlled asymptotics near a timelike singularity. The solutions are obtained by a Fuchs analysis of the equations which evolve the metric in a spacelike direction.   We further observe that the changes of signs of some of the terms (walls) in the associated Hamiltonian invalidate the "cosmological billards" heuristic arguments for existence of singularities of mixmaster type in the current context.
The abundance of chlorine is determined from X-ray spectra obtained with the RESIK instrument on {\em CORONAS-F} during solar flares between 2002 and 2003. Using weak lines of He-like Cl, \ion{Cl}{16}, between 4.44 and 4.50 \AA, and with temperatures and emission measures from {\em GOES} on an isothermal assumption, we obtained $A({\rm Cl}) = 5.75 \pm 0.26$ on a scale $A({\rm H}) = 12$. The uncertainty reflects an approximately factor 2 scatter in measured line fluxes. Nevertheless our value represents what is probably the best solar determination yet obtained. It is higher by factors of 1.8 and 2.7 than Cl abundance estimates from an infrared sunspot spectrum and nearby \ion{H}{2} regions. The constancy of the RESIK abundance values over a large range of flares ({\em GOES} class from below C1 to X1) argues for any fractionation that may be present in the low solar atmosphere to be independent of the degree of solar activity.
Determinations of vuds with super-allowed Fermi beta-decay in nuclei and of the weak charge of the cesium in atomic parity-violation deviate from the Standard Model predicitions by 2 sigma or more. In both cases, the Standard Model over-predicts the magnitudes of the relevant observables. I discuss the implications of these results for R-parity violating (RPV) extensions of the minimal supersymmetric Standard Model. I also explore the possible consequences for RPV supersymmetry of prospective future low-energy electroweak measurements.
Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary, we find that any entire solution of the fourth order Hamiltonian stationary equation with Lagrangian phase angle uniformly larger than the critical angle must be a quadratic.
We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution. The advantage of qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin. The qutrits are encoded into the orbital angular momentum of photons, namely Laguerre-Gaussian modes with azimuthal index l +1, 0 and -1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated keys. A key is obtained with a qutrit error rate of approximately 10 %.
We present deep GALEX images of NGC 5128, the parent galaxy of Centaurus A. We detect a striking "weather ribbon" of Far-UV and H$\alpha$ emission, which extends more than 35 kpc northeast of the galaxy. The ribbon is associated with a knotty ridge of radio/X-ray emission, and is an extension of the previously known string of optical emission-line filaments. Many phenomena in the region are too short-lived to have survived transit out from the inner galaxy; something must be driving them locally. We also detect Far-UV emission from the galaxy's central dust lane. Combining this with previous radio and Far-IR measurements, we infer an active starburst in the central galaxy, which is currently forming stars at $\sim 2 M_{sun}$yr$^{-1}$, and has been doing so for 50-100Myr. If the wind from this starburst is enhanced by energy and mass driven out from the AGN, the powerful augmented wind can be the driver needed for the northern weather system. We argue that both the diverse weather system, and the enhanced radio emission in the same region, result from the wind's encounter with cool gas left by one of the recent merger/encounter events in the history of NGC 5128.
We study moduli of holomorphic vector bundles on non-compact varieties. We discuss filtrability and algebraicity of bundles and calculate dimensions of local moduli. As particularly interesting examples, we describe numerical invariants of bundles on some local Calabi-Yau threefolds.
We present a benchmark in the parameter space of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) that provides for a dramatic multi-lepton signal and no jets containing 5 or more leptons resulting from the cascade decays of the third lightest neutralino, $\chi^{0}_{3}$, and the lightest chargino, $\chi^{\pm}_{1}$, via light charged sleptons. This is a very clean signal with almost no Standard Model (SM) background. In some cases, a total signal of $\ge 3 $leptons + 0 jets can be detected at the $5 \sigma$ level at the LHC running at $\sqrt{s}=7$ TeV with approximately 3 fb$^{-1}$ of data and with less than 1 fb$^{-1}$ when running at $\sqrt{s}=14$ TeV. In addition, kinematic edges in the invariant mass distributions of 2, 3, and 4 leptons are easily detectable with large integrated luminosities ($\sim 600$ fb$^{-1}$) which can lead to simple measurements of the mass differences of heavy particles in the decay chains, including all combinations of the three lightest neutralinos.
The Supernova Remnant (SNR) HESS J1731-347 displays strong non-thermal TeV gamma-ray and X-ray emission, thus the object is at present time accelerating particles to very high energies. A distinctive feature of this young SNR is the nearby (~30 pc in projection) extended source HESS J1729-345, which is currently unidentified but is in spatial projection coinciding with known molecular clouds (MC). We model the SNR evolution to explore if the TeV emission from HESS J1729-345 can be explained as emission from runaway hadronic cosmic rays (CRs) that are illuminating these MCs. The observational data of HESS J1729-345 and HESS J1731-347 can be reproduced using core-collapse SN models for HESS J1731-347. Starting with different progenitor stars and their pre-supernova environment, we model potential SNR evolution histories along with the CR acceleration in the SNR and the diffusion of the CRs. A simplified 3-dimensional structure of the MCs is introduced based on 12CO data, adopting a distance of 3.2 kpc to the source. A Monte Carlo-based diffusion model for the escaping CRs is developed to deal with the inhomogeneous environment. The fast SNR forward shock speed as implied from the X-ray data can easily be explained when employing scenarios with progenitor star masses between 20 and 25 solar masses, where the SNR shock is still expanding inside the main sequence (MS)-bubble at present time. The TeV spectrum of HESS J1729-345 is satisfactorily fitted by the emission from the highest-energy CRs that have escaped the SNR, using a standard galactic CR diffusion coefficient in the inter-clump medium. The TeV image of HESS J1729-345 can be explained with a reasonable 3-dimensional structure of MCs. The TeV emission from the SNR itself is dominated by leptonic emission in this model. We also explore scenarios where the shock is starting to encounter the dense MS progenitor wind bubble shell.
The Planck and Herschel missions are currently measuring the farIR-mm emission of dust, which combined with existing IR data, will for the first time provide the full SED of the galactic ISM dust emission with an unprecedented sensitivity and angular resolution. It will allow a systematic study of the dust evolution processes that affect the SED. Here we present a versatile numerical tool, DustEM, that predicts the emission and extinction of dust given their size distribution and their optical and thermal properties. In order to model dust evolution, DustEM has been designed to deal with a variety of grain types, structures and size distributions and to be able to easily include new dust physics. We use DustEM to model the dust SED and extinction in the diffuse interstellar medium at high-galactic latitude (DHGL), a natural reference SED. We present a coherent set of observations for the DHGL SED. The dust components in our DHGL model are (i) PAHs, (ii) amorphous carbon and (iii) amorphous silicates. We use amorphous carbon dust, rather than graphite, because it better explains the observed high abundances of gas-phase carbon in shocked regions of the interstellar medium. Using the DustEM model, we illustrate how, in the optically thin limit, the IRAS/Planck HFI (and likewise Spitzer/Herschel for smaller spatial scales) photometric band ratios of the dust SED can disentangle the influence of the exciting radiation field intensity and constrain the abundance of small grains relative to the larger grains. We also discuss the contributions of the different grain populations to the IRAS, Planck and Herschel channels. Such information is required to enable a study of the evolution of dust as well as to systematically extract the dust thermal emission from CMB data and to analyze the emission in the Planck polarized channels. The DustEM code described in this paper is publically available.
We report on the discovery of an extended stellar halo surrounding the distant Galactic globular cluster NGC 5694, based on new deep (V ~ 24.5) wide-field (24' * 20') photometry acquired with VIMOS at VLT. Stars with colour and magnitude consistent with the Main Sequence of the cluster are clearly identified out to r ~ 9'(~ 93 pc) from the cluster center, much beyond the tidal radius of the King model that best fits the inner profile (r_t=3.15'). We do not find a clear end of the structure within our field. The overall observed profile cannot be properly fitted with either a King (1966) model, an Elson et al. (1987) model, or a Wilson (1975) model; however it is very smooth and does not show any sign of the break near the tidal radius that is typically observed in stellar systems with tidal tails. The density map we derived does not show evidence of tidal tails, within the considered field. The extra-tidal component contains ~ 3.5% of the cluster light (mass) and has a surface density profile falling as ~ r^{-3.2}. The possible origin of the detected structure is discussed, as a clear-cut conclusion cannot be reached with the available data.
I conjecture a certain explicit determinant evaluation, whose proof would imply the solution of certain enumeration problem that I have been working on, and that I find interesting. I am pledging \$500 to the OEIS Foundation (in honor of the prover!) for a proof, and \$50 (in honor of the disprover)