ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let X be a hyperkaehler manifold of Kummer type. We study the 4 dimensional intermediate Jacobian J^3(X) constructed out of the 3rd cohomology of X, motivated by the desire to understand the Kuga-Satake torus associated to X. We prove that there is an embedding of Hodge structures of H^2(X) into H^2(J^3(X)). It follows that if X is projective with polarization L, the projective Kuga-Satake torus of (X,L) is isogenous to the fourth power of J^3(X). By studying the cohomology ring of X, we find that there is a natural smooth quadric Q(X) in the projectivization of H^3(X), with a natural choice of one of the two irreducible components of the variety parametrizing maximal linear subspaces of Q(X). Let Q^{+}(X) be the chosen irreducible component; then it is a smooth quadric in the projectivization of S^{+}(X), one of the two spinor representations of Spin H^3(X), where H^3(X) is equipped with the quadratic form whose zero locus is Q(X). Gauss-Manin parallel transport identifies the set of projectivizations of H^{2,1}(Y), for Y a deformation of X, with an open subset of a linear section of Q^{+}(X). This amounts to an effective description of the intermediate Jacobian J^3(X) in terms of the H.S. on H^2(X). A simple consequence is a new proof of a result of Mongardi giving (necessary) conditions for the action of monodromy on H^2(X). Lastly, we show that if X is projective, then J^3(X) is an abelian fourfold of Weil type.
The structural, dielectric, dynamical, elastic, piezoelectric and nonlinear optical (second-order susceptibility and Pockels tensors) properties of Bi2$WO6 in its P2_1ab ferroelectric ground state are determined using density functional theory. The calculation of infrared and Raman spectra on single crystal allowed us to clarify the assignment of experimental phonon modes, considering the good agreement between the calculated and the experimental Raman spectra obtained on polycrystal. The calculation of the elastic constants confirms the elastic stability of the crystal and allow us to estimate the Young and shear moduli of polycrystalline samples. The piezoelectric constants have significant intrinsic values comparable to those of prototypical ABO3 ferroelectrics. The electro-optic response is strongly dominated by the ionic contribution of transverse optic modes, yielding sizable Pockels coefficients around 9 pm/V along the polar direction.
We give a new local proof of Breuil-M\'ezard conjecture for two dimensional representations of the absolute Galois group of $\mathbb{Q}_p$, when $p\ge 5$ and the representation has scalar endomorphisms.
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_{n}^{(\mu,\nu)}(x), where \mu>-1, \nu>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_{2} and Ar_{2} molecules are also calculated and compared with the previous models and experiments.
We present preliminary results of seismic modeling of Beta Cephei-type stars in NGC 6910 based on simultaneous photometric and spectroscopic observations carried out in 2013 in Bialkow (photometry) and Apache Point (spectroscopy) observatories.
For every p >= 5, we determine all Z_p-invariant nonsingular quartic surfaces in the three dimensional projective space over an algebraically closed field of characteristic zero. In some cases, we also determine their full projective automorphism groups.
Heavy-traffic limit theory deals with queues that operate close to criticality and face severe queueing times. Let $W$ denote the steady-state waiting time in the ${\rm GI}/{\rm G}/1$ queue. Kingman (1961) showed that $W$, when appropriately scaled, converges in distribution to an exponential random variable as the system's load approaches 1. The original proof of this famous result uses the transform method. Starting from the Laplace transform of the pdf of $W$ (Pollaczek's contour integral representation), Kingman showed convergence of transforms and hence weak convergence of the involved random variables. We apply and extend this transform method to obtain convergence of moments with error assessment. We also demonstrate how the transform method can be applied to so-called nearly deterministic queues in a Kingman-type and a Gaussian heavy-traffic regime. We demonstrate numerically the accuracy of the various heavy-traffic approximations.
Using the Echellete Spectrograph Imager (ESI) on the Keck II 10-m telescope we have measured the redshifts of the host galaxies of gamma-ray bursts GRB 990506 and GRB 000418, z=1.30658 +/- 0.00004 and 1.1181 +/- 0.0001, respectively. Thanks to the excellent spectral resolution of ESI we resolved the [O II] 3727 doublet in both cases. The measured redshift of GRB 990506 is the highest known for a dark burst GRB, though entirely consistent with the notion that dark and non-dark bursts have a common progenitor origin. The relative strengths of the [O II], He I, [Ne III], and H gamma emission lines suggest that the host of GRB 000418 is a starburst galaxy, rather than a LINER or Seyfert 2. Since the host of GRB 000418 has been detected at sub-millimeter wavelengths these spectroscopic observations suggest that the sub-millimeter emission is due to star-formation (as opposed to AGN) activity. The [O II]-derived unobscured star-formation rates are 13 and 55 M_solar/yr for the hosts of GRB 990506 and GRB 000418, respectively. In contrast, the star-formation rate of the host of GRB 000418 derived from sub-millimeter observations is twenty times larger.
We present multi-epoch near-infrared photo-spectroscopic observations of Nova Cephei 2014 and Nova Scorpii 2015, discovered in outburst on 2014 March 8.79 UT and 2015 February 11.84 UT respectively. Nova Cep 2014 shows the conventional NIR characteristics of a Fe II class nova characterized by strong CI, HI and O I lines, whereas Nova Sco 2015 is shown to belong to the He/N class with strong He I, HI and OI emission lines. The highlight of the results consists in demonstrating that Nova Sco 2015 is a symbiotic system containing a giant secondary. Leaving aside the T CrB class of recurrent novae, all of which have giant donors, Nova Sco 2015 is shown to be only the third classical nova to be found with a giant secondary. The evidence for the symbiotic nature is three-fold; first is the presence of a strong decelerative shock accompanying the passage of the nova's ejecta through the giant's wind, second is the H$\alpha$ excess seen from the system and third is the spectral energy distribution of the secondary in quiescence typical of a cool late type giant. The evolution of the strength and shape of the emission line profiles shows that the ejecta velocity follows a power law decay with time ($t^{-1.13 \pm 0.17}$). A Case B recombination analysis of the H I Brackett lines shows that these lines are affected by optical depth effects for both the novae. Using this analysis we make estimates for both the novae of the emission measure $n_e^2L$, the electron density $n_e$ and the mass of the ejecta.
Color screening and parton inelastic scattering modify the heavy-quark antiquark potential in the medium that consists of particles from quantum chromodynamics (QCD), leading to suppression of quarkonium production in relativistic heavy-ion collisions. Due to small charm/anti-charm ($c\bar{c}$) pair production number in proton-nucleus (pA) collisions, the correlation between different $c\bar{c}$ pairs is negligible, which makes the Schr\"odinger equation viable for tracking the evolution of only one $c\bar{c}$ pair. We employ the time-dependent Schr\"odinger equation with in-medium $c\bar{c}$ potential to study the evolution of charmonium wave functions in the hydrodynamic like QCD medium produced in pA collisions. We explore different parametrizations of real and imaginary parts of $c\bar{c}$ potential and calculate the nuclear modification factors ($R_{\rm pA}$) of $J/\psi$ and $\psi(2S)$ in $\sqrt{s_{NN}}=5.02$ TeV energy p-Pb collisions at Large Hadron Collider (LHC). Comparing a strong and a weak screening scenario with experimental data in this approach, we arrive at the conclusion that the color screening is weak at temperature close to deconfined phase transition. Moreover, the imaginary part of the potential is crucial to describe the experimental data which is consistent with widely studied semi-classical approaches where the dissociation rates are essential.
The pairing corrections, the single particle occupation numbers, are investigated within density-dependent delta interaction formalism for pairing residual interactions. The potential barrier is computed in the framework of the macroscopic-microscopic model. The microscopic part is based on the Woods-Saxon two center shell model. The alpha-decay of a superheavy element is treated, by paying a special attention to the region of the scission configurations. The sequence of nuclear shapes follows the superasymmetric fission path for alpha decay. It was found that the pairing gaps of the states that reach asymptotically the potential well of the alpha particle have large values at scission but become zero after scission. The 1s1/2 single particle levels of the nascent alpha particle are fully occupied while the superior levels are empties in the scission region and remains in the same states during the penetration of the Coulomb barrier. The projection of the numbers of particle on the two fragments are obtained naturally. At scission, the nascent alpha particle forms a very bound cluster.
A detailed description of the tunneling processes within Aharonov-Bohm (AB) rings containing two-dimensional quantum dots is presented. We show that the electronic propagation through the interferometer is controlled by the spectral properties of the embedded dots and by their coupling with the ring. The transmittance of the interferometer is computed by the Landauer-B\"uttiker formula. Numerical results are presented for an AB interferometer containing two coupled dots. The charging diagrams for a double-dot interferometer and the Aharonov Bohm oscillations are obtained, in agreement with the recent experimental results of Holleitner {\it et al}. [Phys. Rev. Lett. {\bf 87}, 256802 (2001)] We identify conditions in which the system shows Fano line shapes. The direction of the asymetric tail depends on the capacitive coupling and on the magnetic field. We discuss our results in connection with the experiments of Kobayashi {\it et al} [Phys. Rev. Lett. {\bf 88}, 256806 (2002)] in the case of a single dot.
We describe hadronization events, using the AdS/CFT Correspondence, which display many of the qualitative features expected in QCD. In particular we study the motion of strings with separating end points in a back-reacted hard wall geometry. The solutions show the development of a linear QCD-like string. The end points oscillate in the absence of string breaking. We introduce string breaking by hand and evolve the new state forward in time to observe the separation of two string segments. A kink associated with this breaking evolves to the end points of the string inducing rho meson production. We explicitly compute the rho meson production at the end point.
Seymour's Splitter Theorem is a basic inductive tool for dealing with $3$-connected matroids. This paper proves a generalization of that theorem for the class of $2$-polymatroids. Such structures include matroids, and they model both sets of points and lines in a projective space and sets of edges in a graph. A series compression in such a structure is an analogue of contracting an edge of a graph that is in a series pair. A $2$-polymatroid $N$ is an s-minor of a $2$-polymatroid $M$ if $N$ can be obtained from $M$ by a sequence of contractions, series compressions, and dual-contractions, where the last are modified deletions. The main result proves that if $M$ and $N$ are $3$-connected $2$-polymatroids such that $N$ is an s-minor of $M$, then $M$ has a $3$-connected s-minor $M'$ that has an s-minor isomorphic to $N$ and has $|E(M)| - 1$ elements unless $M$ is a whirl or the cycle matroid of a wheel. In the exceptional case, such an $M'$ can be found with $|E(M)| - 2$ elements.
We analyze the full $\mathit{Kepler}$ phase curve of KOI-964, a binary system consisting of a hot white dwarf on an eclipsing orbit around an A-type host star. Using all 18 quarters of long-cadence photometry, we carry out a joint light curve fit and obtain improved phase curve amplitudes, occultation depths, orbital parameters, and transit ephemeris over the previous results of Carter et al. 2011. A periodogram of the residuals from the phase curve fit reveals an additional stellar variability signal from the host star with a characteristic period of $0.620276\pm0.000011$ days and a full amplitude of $24\pm2$ ppm. We also present new Keck/HIRES radial velocity observations which we use to measure the orbit and obtain a mass ratio of $q=0.106\pm0.012$. Combining this measurement with the results of a stellar isochrone analysis, we find that the masses of the host star and white dwarf companion are $2.23\pm0.12\,M_{\odot}$ and $0.236^{+0.028}_{-0.027}\,M_{\odot}$, respectively. The effective temperatures of the two components are $9940^{+260}_{-230}$ K and $15080\pm400$ K, respectively, and we determine the age of the system to be $0.21^{+0.11}_{-0.08}$ Gyr. We use the measured system properties to compute predicted phase curve amplitudes and find that while the measured Doppler boosting and mutual illumination components agree well with theory, the ellipsoidal distortion amplitude is significantly underestimated. We detail possible explanations for this discrepancy, including interactions between the dynamical tide of the host star and the tidal bulge and possible non-synchronous rotation of the host star.
Parameters of the nuclear density functional theory (DFT) models are usually adjusted to experimental data. As a result they carry certain theoretical error, which, as a consequence, carries out to the predicted quantities. In this work we address the propagation of theoretical error, within the nuclear DFT models, from the model parameters to the predicted observables. In particularly, the focus is set on the Skyrme energy density functional models.
Ultrathin epitaxial films of EuNiO3 were grown on a series of substrates traversing highly compressive (- 2.4%) to highly tensile (2.5%) lattice mismatch. X-ray diffraction measurements showed the expected c-lattice parameter shift for compressive strain, but no detectable shift for tensilely strained substrates, while reciprocal space mapping confirmed the tensile strained film maintained epitaxial coherence. Transport measurements showed a successively (from tensile to compressive) lower resistance and a complete suppression of the metalinsulator transition at highly compressive lattice mismatch. Corroborating these findings, X-ray absorption spectroscopy measurements revealed a strong multiplet splitting in the tensile samples that progressively weakens with increasing compressive strain that, combined with cluster calculations, showed enhanced covalence between Ni-d and O-p orbitals leads to the metallic state.
We present a statistical study on parsec scale properties of a sample of Brigthest Cluster Galaxies (BCGs) in Abell Clusters. These data show a possible difference between BCGs in cool core clusters (two-sided parsec scale jets) and in non cool core clusters (one-sided parsec scale jet). We suggest that the two-sided morphology in cool core clusters could be due to the presence of mildly relativistic jets slowed down already at mas scale as consequence of the jet interaction with a dense surrounding medium.
We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers-Geroch transform are discussed. Example spacetimes that support the appropriate anisotropic stress-energy are found and the transformation applied. The 3+1 black string solution is one of the spacetimes with the appropriate matter distribution. Use of the transform with a black string seed is discussed.
At age two, humans are just learning to speak, and they see the world in an unbiased way. At age two, the COMPLETE (COordinated Molecular Probe Line Extinction Thermal Emission) Survey of Star-Forming Regions is just beginning to hint at what it will do for our world view, and it is unbiased as well. The coordinated observations that comprise COMPLETE have already shown us: 1) that large (~10pc) scale bubbles created by winds from evolved stars dominate maps of extended dust emission even in relatively low-mass star-forming regions (e.g. Perseus and Ophiuchus); 2) that "giant" (>1 pc-scale) outflows from young stars can be easily detected by applying statistical tools to an unbiased CO survey (e.g. we have doubled the number of known outflows in Perseus using the Spectral Correlation Function); and 3) that many apparent high column-density "clouds" seen in projection are actually the superposition of many velocity features (likely at different distances) along the line of sight. The upcoming detailed analysis of these new observations will quantify the degree to which the apparently ubiquitous spherical and collimated outflows can sculpt and stir molecular clouds. Taken together with recent numerical simulations' results and measurements of high velocities for some young stars, the COMPLETE Survey also raises, and should soon answer, questions about how, when, and how far stars move away from their birthplaces as functions of time.
Classical and nonclassical states of quantum complex oscillators with real spectrum are presented. Such states are bi-orthonormal superpositions of $n+1$ energy eigenvectors of the system with binomial-like coefficients. For large values of $n$ these optimized binomial states behave as photon added coherent states when the imaginary part of the potential is cancelled.
In this short note we investigate the natur of the phase transitions in a spin market model as a function of the interaction strength between local and global effects. We find that the stochastic dynamics of this stylized market model exhibit a periodicity whose dependence on the coupling constant in the Ising-like Hamiltonian is robust to changes in the temperature and the size of the market.
We apply the absorptive boundary prescription to include saturation effects in CCFM evolution equation. We are in particular interested in saturation effects in exclusive processes which can be studied using Monte Carlo event generator CASCADE. We calculate cross section for three-jet production and distribution of charged hadrons.
Aiming to statistically study the variability in the mid-IR of young stellar objects, we have compared the 3.6, 4.5, and 24 um Spitzer fluxes of 1478 sources belonging to the C2D (Cores to Disks) legacy program with the WISE fluxes at 3.4, 4.6, and 22 um. From this comparison we have selected a robust sample of 34 variable sources. Their variations were classified per spectral Class (according to the widely accepted scheme of Class I/flat/II/III protostars), and per star forming region. On average, the number of variable sources decreases with increasing Class and is definitely higher in Perseus and Ophiuchus than in Chamaeleon and Lupus. According to the paradigm Class <=> Evolution, the photometric variability can be considered to be a feature more pronounced in less evolved protostars, and, as such, related to accretion processes. Moreover, our statistical findings agree with the current knowledge of the star formation activity in different regions. The 34 selected variables were further investigated for similarities with known young eruptive variables, namely the EXors. In particular we analyzed : (1) the shape of the spectral energy distribution (SED); (2) the IR excess over the stellar photosphere; (3) magnitude versus color variations; and (4) output parameters of model fitting. This first systematic search for EXors ends up with 11 bona fide candidates that can be considered as suitable targets for monitoring or future investigations.
This work deals with a mathematical analysis of sodium's transport in a tubular architecture of a kidney nephron. The nephron is modelled by two counter-current tubules. Ionic exchange occurs at the interface between the tubules and the epithelium and between the epithelium and the surrounding environment (interstitium). From a mathematical point of view, this model consists of a 5x5 semi-linear hyperbolic system. In the literature similar models neglect the epithelial layers. In this paper, we show rigorously that such models may be obtained by assuming that the permeabilities between lumen and epithelium are large. Indeed we show that when these grow, solutions of the 5x5 system converge in a certain way to solutions of a reduced 3x3 system where no epithelial layer is present. The problem is dened on a bounded spacial domain with initial and boundary data. Establishing BV compactness forces to introduce initial layers and to handle carefully the presence of lateral boundaries.
Motivated by the numerous examples of 1/3 magnetization plateaux in the triangular lattice Heisenberg an- tiferromagnet with spins ranging from 1/2 to 5/2, we revisit the semiclassical calculation of the magnetization curve of that model, with the aim of coming up with a simple method that allows one to calculate the full mag- netization curve, and not just the critical fields of the 1/3 plateau. We show that it is actually possible to calculate the magnetization curve including the first quantum corrections and the appearance of the 1/3 plateau entirely within linear spin-wave theory, with predictions for the critical fields that agree to order 1/S with those derived a long-time ago on the basis of arguments that required to go beyond linear spin-wave theory. This calculation relies on the central observation that there is a kink in the semiclassical energy at the field where the classical ground state is the collinear up-up-down structure, and that this kink gives rise to a locally linear behavior of the energy with the field when all semiclassical ground states are compared to each other for all fields. The magnetization curves calculated in this way for spin 1/2, 1 and 5/2 are shown to be in good agreement with available experimental data.
An detailed study of the thermodynamical state of nuclear matter in transport calculations of heavy--ion reactions is presented. In particular we determine temperatures from an analysis of the local momentum space distribution on one hand, and from a fit to fragment energy spectra in terms of a blast model with radial flow and temperature on the other. We apply this to spectator and participant matter. In spectator we find regions of spinodal instability with temperatures and densities which are consistent with experiments. In the participant we find different temperatures for different fragment masses, indicating that the fragments are not emitted from a source in thermal and chemical equilibrium.