ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the Schur index of 4-dimensional $\mathcal{N}=2$ circular quiver theories. We show that the index can be expressed as a weighted sum over partition functions describing systems of free Fermions living on a circle. For circular $SU(N)$ quivers of arbitrary length we evaluate the large $N$ limit of the index, up to exponentially suppressed corrections. For the single node theory ($\mathcal{N}=4$ SYM) and the two node quiver we are able to go beyond the large $N$ limit, and obtain the complete, all orders large $N$ expansion of the index, as well as explicit finite $N$ results in terms of elliptic functions.
In [BN] the authors construct a special complex of degree 20 over M, which for an open three dimensional set parametrizes smooth complex surfaces of degree four invariant which are Heisenberg invariant and each member of the family contains 32 lines but only 16 skew lines. The coordinates of the lines however need not be real. For a point l in a Zariski open set of M an algorithm is presented which evaluates the real coefficients of l in terms of the K-coordinates of l. The author uses a code in Maple which allows him to construct very explicite examples of real smooth Heisenberg invariant Kummer surfaces containing the special configuration of 16 real skew lines. An example is constructed at the end of the paper.
We report the far-infrared spectra of the molecular nanomagnet Mn_12-acetate (Mn_12) as a function of temperature (5-300 K) and magnetic field (0-17 T). The large number of observed vibrational modes is related to the low symmetry of the molecule, and they are grouped together in clusters. Analysis of the mode character based on molecular dynamics simulations and model compound studies shows that all vibrations are complex; motion from a majority of atoms in the molecule contribute to most modes. Three features involving intramolecular vibrations of the Mn_12 molecule centered at 284, 306 and 409 cm-1 show changes with applied magnetic field. The structure near 284 cm$^{-1}$ displays the largest deviation with field and is mainly intensity related. A comparison between the temperature dependent absorption difference spectra, the gradual low-temperature cluster framework distortion as assessed by neutron diffraction data, and field dependent absorption difference spectra suggests that this mode may involve Mn motion in the crown.
Millimetre-VLBI is an important tool in AGN astrophysics, but it is limited by short atmospheric coherence times and poor receiver and antenna performance. We demonstrate a new kind of phase referencing for the VLBA, enabling us to increase the sensitivity in mm-VLBI by an order of magnitude. If a source is observed in short cycles between the target frequency, nu_t, and a reference frequency, nu_ref, the nu_t data can be calibrated using scaled-up phase solutions from self-calibration at nu_ref. We have demonstrated the phase transfer on 3C 279, where we were able to make an 86 GHz image with 90 % coherence compared to self-calibration at nu_t. We have detected M81, our science target in this project, at 86 GHz using the same technique. We describe scheduling strategy and data reduction. The main impacts of fast frequency switching are the ability to image some of the nearest, but relatively weak AGN cores with unprecedented high angular resolution and to phase-reference the nu_t data to the nu_ref core position, enabling the detection of possible core shifts in jets due to optical depth effects. This ability will yield important constraints on jet properties and might be able to discriminate between the two competing emission models of Blandford-Konigl jets and spherical advection-dominated accretion flows (ADAFs) in low-luminosity AGNs.
Let $A_\alpha(G)$ be the $A_\alpha$-matrix of a digraph $G$ and $\lambda_{\alpha 1}, \lambda_{\alpha 2}, \ldots, \lambda_{\alpha n}$ be the eigenvalues of $A_\alpha(G)$. Let $\rho_\alpha(G)$ be the $A_\alpha$ spectral radius of $G$ and $E_\alpha(G)=\sum_{i=1}^n \lambda_{\alpha i}^2$ be the $A_\alpha$ energy of $G$ by using second spectral moment. Let $\mathcal{G}_n^m$ be the set of non-strongly connected digraphs with order $n$, which contain a unique strong component with order $m$ and some directed trees which are hung on each vertex of the strong component. In this paper, we characterize the digraph which has the maximal $A_\alpha$ spectral radius and the maximal (minimal) $A_\alpha$ energy in $\mathcal{G}_n^m$.
Using first-principles density functional theory we predict a ferroelectric ground state -- driven by off-centering of the magnetic Mn$^{4+}$ ion -- in perovskite-structure BaMnO$_3$.   Our finding is surprising, since the competition between energy-lowering covalent bond formation, and energy-raising   Coulombic repulsions usually only favors off-centering on the perovskite $B$-site for non-magnetic $d^0$ ions.   We explain this tendency for ferroelectric off-centering by analyzing the changes in electronic structure between the centrosymmetric and polar states, and by calculating the Born effective charges; we find anomalously large values for Mn and O consistent with our calculated polarization of 12.8 $\mu$C/cm$^2$. Finally, we suggest possible routes by which the perovskite phase may be stabilized over the usual hexagonal phase, to enable a practical realization of a single-phase multiferroic.
The propagation of $\gamma$ rays over very large distances provides new insights on the intergalactic medium and on fundamental physics. On their path to the Earth, $\gamma$ rays can annihilate with diffuse infrared or optical photons of the intergalactic medium, producing $e^+ \, e^-$ pairs. The density of these photons is poorly determined by direct measurements due to significant galactic foregrounds. Studying the absorption of $\gamma$ rays from extragalactic sources at different distances allows the density of low-energy diffuse photons to be measured. Gamma-ray propagation may also be affected by new phenomena predicted by extensions of the Standard Model of particle physics. Lorentz Invariance is violated in some models of Quantum Gravity, leading to an energy-dependent speed of light in vacuum. From differential time-of-flight measurements of the most distant $\gamma$-ray bursts and of flaring active galactic nuclei, lower bounds have been set on the energy scale of Quantum Gravity. Another effect that may alter $\gamma$-ray propagation is predicted by some models of String Theory, namely the mixing of the $\gamma$ ray with a light fundamental boson called an "axion-like particle", which does not interact with low-energy photons. Such a mixing would make the Universe more transparent to $\gamma$ rays than what would otherwise be, in a sense it decreases the amount of modification to the spectrum that comes from the extragalactic background light. The present status of the search for all these phenomena in $\gamma$-ray astronomy is reviewed.
We estimate the incidence of multiply-imaged AGNs among the optical counterparts of X-ray selected point-like sources in the XXL field. We also derive the expected statistical properties of this sample, such as the redshift distribution of the lensed sources and of the deflectors that lead to the formation of multiple images, modelling the deflectors using both spherical (SIS) and ellipsoidal (SIE) singular isothermal mass distributions. We further assume that the XXL survey sample has the same overall properties as the smaller XMM-COSMOS sample restricted to the same flux limits and taking into account the detection probability of the XXL survey. Among the X-ray sources with a flux in the [0.5-2] keV band larger than 3.0x10$^{-15}$ erg cm$^{-2}$ s$^{-1}$ and with optical counterparts brighter than an r-band magnitude of 25, we expect ~20 multiply-imaged sources. Out of these, ~16 should be detected if the search is made among the seeing-limited images of the X-ray AGN optical counterparts and only one of them should be composed of more than two lensed images. Finally, we study the impact of the cosmological model on the expected fraction of lensed sources.
We used data from WISE, IRAS, and Herschel in conjuction with our previous observations with SABOCA and LABOCA, and constructed the far-IR to submillimetre spectral energy distributions (SEDs) of dense cores in the filamentary Seahorse infrared dark cloud (IRDC) G304.74+01.32. For the 12 analysed cores, which include two IR dark cores (no WISE counterpart), nine IR bright cores, and one HII region, the mean dust temperature of the cold (warm) component, the mass, luminosity, H$_2$ number density, and surface density were derived to be $13.3\pm1.4$ K ($47.0\pm5.0$ K), $113\pm29$ M$_{\odot}$, $192\pm94$ L$_{\odot}$, $(4.3\pm1.2)\times10^5$ cm$^{-3}$, and $0.77\pm0.19$ g cm$^{-3}$, respectively. The HII region IRAS 13039-6108a was found to be the most luminous source in our sample ($(1.1\pm0.4)\times10^3$ L$_{\odot}$). All the cores were found to be gravitationally bound (i.e. the virial parameter $\alpha_{\rm vir}<2$). Seven out of 12 of the analysed cores (58%) were found to lie above the mass-radius thresholds of high-mass star formation proposed in the literature. The surface densities of $\Sigma>0.4$ g cm$^{-3}$ derived for these seven cores also exceed the corresponding threshold for high-mass star formation. Five of the analysed cores (42%) show evidence of fragmentation into two components in the SABOCA 350 $\mu$m image. In addition to the HII region source IRAS 13039-6108a, some of the other cores in Seahorse also appear to be capable of giving birth to high-mass stars. The dense core population in the Seahorse IRDC has comparable average properties to the cores in the well-studied Snake IRDC G11.11-0.12. The Seahorse core fragmentation mechanisms appear to be heterogenous, including cases of both thermal and non-thermal Jeans instability. High-resolution follow-up studies are required to address the fragmented cores' genuine potential of forming high-mass stars.
We have been monitoring the supernova remnant (SNR) 1987A with {\it Chandra} observations since 1999. Here we report on the latest change in the soft X-ray light curve of SNR 1987A. For the last $\sim$1.5 yr (since day $\sim$8000), the soft X-ray flux has significantly flattened, staying (within uncertainties) at $f_{\rm X}$ $\sim$ 5.7 $\times$ 10$^{-12}$ erg cm$^{-2}$ s$^{-1}$ (corresponding to $L_{\rm X}$ $\sim$ 3.6 $\times$ 10$^{36}$ erg s$^{-1}$) in the 0.5--2 keV band. This remarkable change in the recent soft X-ray light curve suggests that the forward shock is now interacting with a decreasing density structure, after interacting with an increasing density gradient over $\sim$10 yr prior to day $\sim$8000. Possibilities may include the case that the shock is now propagating beyond a density peak of the inner ring. We briefly discuss some possible implications on the nature of the progenitor and the future prospects of our {\it Chandra} monitoring observations.
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration for some response function $f$. An equivalent view point is that each pair of points of the configuration establishes a random connection at an exponential time determined by $f$, which results in the death of one of the two points. We concentrate on space-motion invariant processes of this type. Under some natural conditions on $f$, we construct the unique time-stationary regime of this class of point processes by a coupling argument. We then use the birth and death structure to establish a hierarchy of balance integral relations between the factorial moment measures. Finally, we show that the time-stationary point process exhibits a certain kind of repulsion between its points that we call $f$-repulsion.
The analysis of long-term variations of several solar activity indices (AI) since in last 40 years has been performed. We studied the AI which characterize the fluxes from different areas in solar atmosphere. Our consideration of mutual correlations between the solar indices is based on the study of relationships between them in the period from 1950 to 1990. This period of time, covering activity cycles 19 -- 22, is characterized by relatively stable relations between the indices. We have studied the normalized variations of these indices in the recent time in relation to their values which have been calculated with help of the radiation of the sun in the radio range at a wavelength of 10.7 cm (F10.7) in 1950 -- 1990. The analysis of time series of variations of the normalized AI (AIFF) in solar cycles 23 -- 24 shows an existence of different trends for different indices in their long-term variations. We assume that variations of normalized SSN, F530.3 and Flare Index, which have shown a sharp decrease in last 40 years is possibly associated with a decrease in the intensity of large-scale magnetic fields in the photosphere (SSN) and in the corona (the coronal index and the Flare Index)
The mechanisms which could lead to chemo-thermal instabilities and fragmentation during the formation of primordial protostars are investigated analytically. We introduce approximations for H2 cooling rates bridging the optically thin and thick regimes. These allow us to discuss instabilities up to densities when protostars become optically thick to continuum radiation (n~10^16 cm^-3). During the collapse, instability arises at two different stages: at low density (n~10^8-10^11 cm^-3), it is due to fast 3-body reactions converting H into H2; at high density (n>10^13 cm^-3), it is due to Collisional Induced Emission (CIE). In agreement with the 3D simulations, we find that the instability at low densities cannot lead to fragmentation, because fluctuations do not survive turbulent mixing, and because their growth is slow. The situation at high density is similar. The CIE-induced instability is as weak as the low density one, with similar ratios of growth and dynamical time scales. Fluctuation growth time is longer than free fall time, and fragmentation seems unlikely. One then expects the first stars to be massive, not to form binaries nor harbour planets. Nevertheless, full 3D simulations are required. They could become possible using simplified estimates of radiative transfer effects, which we show to work very well in the 1D case. This indicates that the effects of radiative transfer during the initial stages of formation of primordial protostars can be treated as local corrections to cooling. (Abridged)
The purpose of this paper is to collect and make explicit the results of Gel'fand, Graev and Piatetski-Shapiro and Miyazaki for the $GL(3)$ cusp forms which are non-trivial on $SO(3,\mathbb{R})$. We give new descriptions of the spaces of cusp forms of minimal $K$-type and from the Fourier-Whittaker expansions of such forms give a complete and completely explicit spectral expansion for $L^2(SL(3,\mathbb{Z})\backslash PSL(3,\mathbb{R}))$, accounting for multiplicities, in the style of Duke, Friedlander and Iwaniec's paper on Artin $L$-functions. We directly compute the Jacquet integral for the Whittaker functions at the minimal $K$-type, improving Miyazaki's computation. The primary tool will be the study of the differential operators coming from the Lie algebra on vector-valued cusp forms.
We present the previously unanalysed high quality XMM-Newton spectrum of an ultraluminous X-ray source candidate in NGC 4517. As with other high quality ULX spectra, a downturn in the spectrum is observed at ~6 keV. Both of the recent disc reflection and Comptonisation interpretations of this feature are applied, in order to present a direct comparison, and are found to provide statistically equivalent representations of the current data. We find that the reflection model requires the accretion disc to have a highly super-solar iron abundance, while the Comptonisation model requires low temperature Comptonising electrons, and for the corona to be optically thick. These physical requirements are discussed in detail, and physically motivated scenarios are highlighted in which each model can be considered a viable explanation for the observed emission. By extending our consideration of these two interpretations to high energies, we demonstrate that observations of ULXs at energies above ~10 keV should be extremely useful when attempting to distinguish between them. With current instrumentation, it is only viable to perform these observations for M82 X-1, but future high angular resolution hard X-ray imaging spectrometers, such as the Hard X-ray Imaging System due to fly on Astro-H, should go a long way to resolving this issue.
The driving mechanism of protostellar outflows and jets and their effects on the star formation process obtained from recent theoretical and numerical studies are described. Low-velocity outflows are driven by an outer region of the circumstellar disk, while high-velocity jets are driven near an inner edge of the disk. The disk angular momentum is effectively transferred by magnetic effects in the outflow and jet driving regions where the magnetic field is well coupled with neutral gas. On the other hand, in a high density gas region of the disk (or intermediate region), the magnetic field dissipates and is decoupled from neutral gas. Thus, in such a magnetically inactive region, no outward flow appears and the disk angular momentum is not effectively transferred by magnetic effects. Therefore, in the disk intermediate region, the disk surface density continues to increase and gravitational instability occurs and produce a non-axisymmetric (or spiral) structure. After spiral arms sufficiently develop, the disk angular momentum is transferred by gravitational torque and a large amount of the disk mass accretes onto the central protostar from the circumstellar disk. The episodic accretion induces time-variable high-velocity jets. The jets do not significantly contribute to a dynamical evolution of the protostar and circumstellar disk, while the low-velocity outflows can eject a large fraction of the infalling gas and determine the final stellar mass.
We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus $g$, the partition function $Z$ is defined for a triangulation consisting of $n$ triangles of area $\epsilon$. The reason these models are called quasi-topological is that $Z$ depends on $g$, $n$ and $\epsilon$ but not on the details of the triangulation. They are also soluble in the sense that the computation of their partition functions can be reduced to a soluble one dimensional problem. We show that the continuum limit is well defined if the model approaches a topological field theory in the zero area limit, i.e., $\epsilon \to 0$ with finite $n$. We also show that the universality classes of such quasi-topological lattice field theories can be easily classified. Yang-Mills and generalized Yang-Mills theories appear as particular examples of such continuum limits.
The strength of perpendicular anisotropy is known to drive the spin reorientation in thin magnetic films. Here we consider the effect different order anisotropies have on two phase transitions; the spin reorientation transition and the orientational order transition. We find that the relative magnitude of different order anisotropies can significantly enhance or suppress the degree to which the system reorients. Specifically Monte Carlo simulations reveal significant changes in the cone angle and planar magnetization. In order to facilitate rapid computation we have developed a stream processing technique, suitable for use on GPU systems, for computing the transition probabilities in two dimensional systems with dipole interactions.
The purpose of this paper is to construct non-trivial elements in the Abel-Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical invariants at points with different transcendence degrees over a subfield in $\CC$.
Lithium detectors have a high sensitivity to CNO neutrinos from the Sun. The present experimental data and prospects for future experiments on the detection of CNO neutrinos are discussed. A nonstationary case is considered when the flux of 13N neutrinos is higher than the standard solar model predicts due to the influx of fresh material from the peripheral layers to the solar core.
Extremely high velocity emission likely related to jets is known to occur in some proto-Planetary Nebulae. However, the molecular complexity of this kinematic component is largely unknown. We observed the known extreme outflow from the proto-Planetary Nebula IRAS 16342-3814, a prototype water fountain, in the full frequency range from 73 to 111 GHz with the RSR receiver on the Large Millimetre Telescope. We detected the molecules SiO, HCN, SO, and $^{13}$CO. All molecular transitions, with the exception of the latter are detected for the first time in this source, and all present emission with velocities up to a few hundred km s$^{-1}$. IRAS 16342-3814 is therefore the only source of this kind presenting extreme outflow activity simultaneously in all these molecules, with SO and SiO emission showing the highest velocities found of these species in proto-Planetary Nebulae. To be confirmed is a tentative weak SO component with a FWHM $\sim$ 700 km s$^{-1}$. The extreme outflow gas consists of dense gas (n$_{\rm H_2} >$ 10$^{4.8}$--10$^{5.7}$ cm$^{-3}$), with a mass larger than $\sim$ 0.02--0.15 M$_{\odot}$. The relatively high abundances of SiO and SO may be an indication of an oxygen-rich extreme high velocity gas.
Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant~1 in terms of lattice paths. Here we generalize this result by refining the matrix entries to be multivariate polynomials, and by determining not only the determinant but also the Smith normal form of these matrices. A priori the Smith form need not exist but its existence follows from the explicit computation. It will be more convenient for us to state our results in terms of partitions rather than lattice paths.
The weakness of electron-electron correlations in the itinerant antiferromagnet Cr doped with V has long been considered the reason that neither new collective electronic states or even non Fermi liquid behaviour are observed when antiferromagnetism in Cr$_{1-x}$V$_{x}$ is suppressed to zero temperature. We present the results of neutron and electron diffraction measurements of several lightly doped single crystals of Cr$_{1-x}$V$_{x}$ in which the archtypal spin density wave instability is progressively suppressed as the V content increases, freeing the nesting-prone Fermi surface for a new striped charge instability that occurs at x$_{c}$=0.037. This novel nesting driven instability relieves the entropy accumulation associated with the suppression of the spin density wave and avoids the formation of a quantum critical point by stabilising a new type of charge order at temperatures in excess of 400 K. Restructuring of the Fermi surface near quantum critical points is a feature found in materials as diverse as heavy fermions, high temperature copper oxide superconductors and now even elemental metals such as Cr.