ShantanuT01/DACTYL-Pretraining huggingface dataset:
There are two approaches to the homotopy theory of simplicial (pre-)sheaves. One developed by Joyal and Jardine works for all sites but produces a model structure which is not finitely generated even in the case of sheaves on a Noetherian topological space. The other one developed by Brown and Gersten gives a nice model structure for sheaves on a Noetherian space of finite dimension but does not extend to all sites. In this paper we define a class of sites for which a generalized version of the Brown-Gersten approach works.
The calculation of the tree-level QCD processes e+e- -> qqgggg, qqqqgg and qqqqqq has recently been accomplished. We highlight here the relevance of such reactions for some of the physics at future electron-positron linear accelerators.
In this paper, a comprehensive methodology for characterizing the high power resonance behavior of bulk piezoelectric ceramics using the burst method is described. In the burst method, the sample is electrically driven at its resonance frequency, and then either a short circuit or an open circuit condition is imposed, after which the vibration decays at the resonance or antiresonance frequency, respectively. This decay can be used to measure the quality factor in either of these conditions. The resulting current in the short circuit vibration condition is related to the vibration velocity through the "force factor." The generated voltage in the open circuit vibration condition corresponds to the displacement by the "voltage factor." The force factor and the voltage factor are related to material properties and physical dimensions of the sample. Using this method, the high power behavior of the permittivity, compliance, piezoelectric charge constant, electromechanical coupling factor, and material losses can be determined directly by measuring the resonance (short circuit) and antiresonance (open circuit) frequencies, their corresponding quality factors, the force factor $A$, and the voltage factor $B$. The experimental procedure to apply this method is described and demonstrated on commercially available hard and semi-hard PZT materials of $k_{31}$
We report magnetic, specific heat and ESR measurements on a series of $S=1/2$ spin ladder compounds Cu(Qnx)(Cl$_{(1-x)}$Br$_{x}$)$_{2}$. Down to $T=2$ K all the observables can be described by the spin ladder model with about 1% of $S=1/2$ impurities in the background, which are present even in a nominally pure Cu(Qnx)Cl$_{2}$ and Cu(Qnx)Br$_{2}$, for the whole range of $0\leq x\leq1$. We extract ladder exchange constants $J_{l}(x)$ and $J_{r}(x)$ as well as the gap value $\Delta(x)$ by comparing the experimental data to quantum Monte-Carlo simulations. As the ESR measurements show the $g$-factor of impurities to be precisely equal to $g$-factor of the ladder spins, we suppose the impurities to be the consequence of structural defects resulting in a broken ladder ends.
The recent discovery of extragalactic PeV neutrinos opens a new window to the exploration of cosmic-ray accelerators. The observed PeV neutrino flux is close to the Waxman-Bahcall upper bound implying that gamma-ray bursts (GRBs) may be the source of ultra-high energy cosmic rays (UHECRs). Starting with the assumption of the GRB-UHECR connection, we show using both analytical estimates and numerical simulations that the observed neutrinos can originate at the jet as a result of photopion interactions with the following implications: the neutrino spectra are predicted to have a cutoff at energy $\le 10$ PeV; the dissipation responsible for the GRB emission and cosmic-ray acceleration takes place at distances $r_{\rm diss} \approx 3 \times 10^{11}-3 \times 10^{13} \ {\rm cm}$ from the central engine; the Thomson optical depth at the dissipation region is $\tau_{\rm T} \sim 1$; the jet carries a substantial fraction of its energy in the form of Poynting flux at the dissipation region, and has a Lorentz factor $\Gamma \simeq 100-500$. The non-detection of $\sim$PeV neutrinos coincident with GRBs will indicate that GRBs are either poor cosmic accelerators or the dissipation takes place at small optical depths in the jet.
We present XMM-Newton observations of Mrk 359, the first Narrow Line Seyfert 1 galaxy discovered. Even among NLS1s, Mrk 359 is an extreme case with extraordinarily narrow optical emission lines. The XMM-Newton data show that Mrk 359 has a significant soft X-ray excess which displays only weak absorption and emission features. The (2-10) keV continuum, including reflection, is flatter than the typical NLS1, with Gamma approximately 1.84. A strong emission line of equivalent width approximately 200 eV is also observed, centred near 6.4 keV. We fit this emission with two line components of approximately equal strength: a broad iron-line from an accretion disc and a narrow, unresolved core. The unresolved line core has an equivalent width of approximately 120 eV and is consistent with fluorescence from neutral iron in distant reprocessing gas, possibly in the form of a `molecular torus'. Comparison of the narrow-line strengths in Mrk 359 and other low-moderate luminosity Seyfert 1 galaxies with those in QSOs suggests that the solid angle subtended by the distant reprocessing gas decreases with increasing AGN luminosity.
Methods to recover the fossil record of galaxy evolution encoded in their optical spectra have been instrumental in processing the avalanche of data from mega-surveys along the last decade, effectively transforming observed spectra onto a long and rich list of physical properties: from stellar masses and mean ages to full star formation histories. This promoted progress in our understanding of galaxies as a whole. Yet, the lack of spatial resolution introduces undesirable aperture effects, and hampers advances on the internal physics of galaxies. This is now changing with 3D surveys. The mapping of stellar populations in data-cubes allows us to figure what comes from where, unscrambling information previously available only in integrated form. This contribution uses our starlight-based analysis of 300 CALIFA galaxies to illustrate the power of spectral synthesis applied to data-cubes. The selected results highlighted here include: (a) The evolution of the mass-metallicity and mass-density-metallicity relations, as traced by the mean stellar metallicity. (b) A comparison of star formation rates obtained from H{\alpha} to those derived from full spectral fits. (c) The relation between star formation rate and dust optical depth within galaxies, which turns out to mimic the Schmidt-Kennicutt law. (d) PCA tomography experiments.
We demonstrate that a quasi-uniform cosmological seed field is a much less suitable seed for a galactic dynamo than has often been believed. The age of the Universe is insufficient for a conventional galactic dynamo to generate a contemporary galactic magnetic field starting from such a seed, accepting conventional estimates for physical quantities. We discuss modifications to the scenario for the evolution of galactic magnetic fields implied by this result. We also consider briefly the implications of a dynamo number that is significantly larger than that given by conventional estimates.
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by no more than one other edge (and any pair of crossing edges cross only once). A non-1-planar graph $G$ is minimal if the graph $G-e$ is 1-planar for every edge $e$ of $G$. We construct two infinite families of minimal non-1-planar graphs and show that for every integer $n > 62$, there are at least $2^{(n-54)/4}$ nonisomorphic minimal non-1-planar graphs of order $n$. It is also proved that testing 1-planarity is NP-complete.
Let $(X,\mathcal H)$ be a $\mathcal P$-harmonic space and assume for simplicity that constants are harmonic. Given a numerical function $\varphi$ on $X$ which is locally lower bounded, let \begin{equation*}   J_\varphi(x):=\sup\{\int^\ast \varphi\,d\mu(x)\colon \mu\in \mathcal J_x(X)\}, \qquad x\in X, \end{equation*} where $\mathcal J_x(X)$ denotes the set of all Jensen measures $\mu$ for $x$, that is, $\mu$ is a compactly supported measure on $X$ satisfying $\int u\,d\mu\le u(x)$ for every hyperharmonic function on $X$. The main purpose of the paper is to show that, assuming quasi-universal measurability of $\varphi$, the function $J_\varphi$ is the smallest nearly hyperharmonic function majorizing $\varphi$ and that $J_\varphi=\varphi \vee \hat J_\varphi$, where $\hat J_\varphi$ is the lower semicontinuous regularization of $J_\varphi$. So, in particular, $J_\varphi $ turns out to be at least "as measurable as" $\varphi$.   This improves recent results, where the axiom of polarity was assumed. The preparations about nearly hyperharmonic functions on balayage spaces are closely related to the study of strongly supermedian functions triggered by J.-F. Mertens more than forty years ago.
Finding the best model to describe the {\alpha}-decay process is an old and ongoing challenge in nuclear physics. The present work systematically studied {\alpha}-decay half-lives for the favored ground-state-to-ground-state transitions of 344 isotopes of nuclei with 52 <= Z <= 107 using 28 versions of the proximity potential model in the framework of the WKB approximation. The present study introduces the best proximity versions with the fewest deviations with respect to experimental values. The models for Prox. 77-set 4, Prox. 77-set 5, and Dutt 2011 with the root-mean-square deviations (RMSDs) of <1 were found to predict {\alpha}-decay half-lives better than the other models. Comparison with fusion studies shows that Dutt 2011 is an appropriate model both for {\alpha}-decay studies and for prediction of the barrier characteristic in heavy-ion fusion reactions. The calculation of {\alpha}-decay half-lives were repeated for even-even, even-odd, odd-even, and odd-odd nuclei. This detailed comparative study reveals that for these versions the half-lives of the even-even nuclei with RMSDs of <0.6 show less deviation than the even-odd, odd-even, and odd-odd nuclei.
The supermassive black holes harboured in active galactic nuclei are at the origin of powerful jets which can emit copious amounts of gamma-rays. The exact interplay between the infalling matter, the black hole and the relativistic outflow is still poorly known, and this parallel session of the 12th Marcel Grossman meeting intended to offer the most up to date status of observational results with the latest generation of ground and space-based instruments, as well as the theoretical developments relevant for the field.
In this second article of the series, we apply our recently derived equation for the electric field propagation along light rays [arXiv:2004.03496], valid on the electromagnetic geometrical optics limit, to the special case of a toy interferometer used to detect gravitational waves in a flat background. Such an equation shows that, assuming the detector is in the transverse-traceless frame, which has a local shearing relative motion due to the gravitational wave perturbations, the electric field does not propagate as in an inertial reference frame in Minkowski spacetime. We present the electric field at the end of the interferometric process, for arbitrary arm configurations with respect to the plane gravitational wave packet propagation direction. Then, for normal incidence, we compute the interference pattern and, in addition to the usual term associated with the difference in path traveled by light in the arms, we deduce two new contributions to the final intensity, arising from: (i) the round-trip electromagnetic frequency shift and (ii) the divergence of the light beam. Their quantitative relevance is compared to the traditional contribution and shown to be typically negligible due to the geometrical optics regime of light. Moreover, a non-parallel transport of the polarization vector takes place, in general, because of the gravitational wave, a feature which could generate further contributions. However, we conclude that for the normal incidence case such vector is parallel transported, preventing this kind of correction.
Dirac fermions interacting with a cylindrically symmetric quantum dot potential created in single and bilayer graphene are not confined but form quasi-bound states. The broadening of these quasi-bound states (i. e. the inverse of their lifetimes) decreases (increases) with the orbital momentum of the electron in the case of graphene (bilayer). Quasi-bound states with energy below (above) the barrier height are dominantly electron(hole)-like. A remarkable decrease of the energy level broadening is predicted for electron energies close to the barrier height, which are a consequence of the total internal reflection of the electronic wave at the dot edge.
A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. This is a natural generalization of the surface singularities of types $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Since this idea was introduced, quotient singularities of this type have been classified in dimensions up to most $4$. This note extends that classification to dimension $5$.
We report high-energy spectral data of the prompt emission of GRB970228 and its X-ray afterglow. We establish that the nature of the X-ray afterglow emission is non-thermal and similar to the later portion of GRB970228. Our data can be used to discriminate different emission models of GRB afterglows. While cooling of excited compact objects can be ruled out, fireball models are constrained in the physics of the radiation emission processes and their evolution.
This paper deals with a study of the effects that spherically symmetric first-order metric perturbations and vacuum quantum fluctuations have on the stability of the multiply connected de Sitter spacetime recently proposed by Gott and Li. It is the main conclusion of this study that although such a spacetime is stable to the classical metric perturbations for any size of the nonchronal region, it is only stable against the quantum fluctuations of vacuum if the size of the multiply connected region is of the order the Planck scale. Therefore, boundary conditions for the state of the universe based on the notion that the universe created itself in a regime where closed timelike curves were operative and stable, still appear to be physically and philosophically so well supported as are those boundary conditions relying on the notion that the universe was created out of nothing.
In this work we investigate the extra packing of mass within the framework of gravitational decoupling by means of Minimal Geometric Deformation approach. It is shown that, after a suitable set of the free parameters involved, the like--Tolman IV solution extended by Minimal Geometric Deformation not only acquire extra packing of mass but it corresponds to a stable configuration according to the adiabatic index criteria. Additionally, it is shown that the extra packing condition induce a lower bound on the compactness parameter of the seed isotropic solution and a stringent restriction on the decoupling parameter.
We construct non-extremal fractional D-brane solutions of type-II string theory at the Z_2 orbifold point of K3. These solutions generalize known extremal fractional-brane solutions and provide further insights into N=2 supersymmetric gauge theories and dual descriptions thereof. In particular, we find that for these solutions the horizon radius cannot exceed the non-extremal enhancon radius. As a consequence, we conclude that a system of non-extremal fractional branes cannot develop into a black brane. This conclusion is in agreement with known dual descriptions of the system.
Instead of the Yukawa mechanism for intermediate- and short-range interaction some new approach based on formation of the symmetric six-quark bag in the state $|(0s)^6[6]_X,L=0>$ dressed due to strong coupling to $\pi$, $\sigma$ and $\rho$ fields are suggested. This new mechanism offers both a strong intermediate-range attraction which replaces the effective $\sigma$-exchange (or excitation of two isobars in the intermediate state) in traditional force models and also short-range repulsion. Simple illustrative model is developed which demonstrates clearly how well the suggested new mechanism can reproduce $NN$ data.
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.
At wide separations, planetary-mass and brown dwarf companions to solar type stars occupy a curious region of parameters space not obviously linked to binary star formation or solar-system scale planet formation. These companions provide insight into the extreme case of companion formation (either binary or planetary), and due to their relative ease of observation when compared to close companions, they offer a useful template for our expectations of more typical planets. We present the results from an adaptive optics imaging survey for wide (50-500 AU) companions to solar type stars in Upper Scorpius. We report one new discovery of a ~14 M_J companion around GSC 06214-00210, and confirm that the candidate planetary mass companion 1RXS J160929.1-210524 detected by Lafreniere et al (2008) is in fact co-moving with its primary star. In our survey, these two detections correspond to ~4% of solar type stars having companions in the 6-20 M_J mass and 200-500 AU separation range. This figure is higher than would be expected if brown dwarfs and planetary mass companions were drawn from an extrapolation of the binary mass function. Finally, we discuss implications for the formation of these objects.
Previous studies of the X-ray flux and spectral properties of 1RXS J170849-400910 showed hints of a possible correlation with the spin glitches that occurred in 1999 and 2001. However, due to the sparseness of spectral measurements and the paucity of detected glitches no firm conclusion could be drawn. We retrieved and analysed archival XTE pointings of 1RXS J170849-400910 covering the time interval between January 2003 and June 2006 and carried out a detailed timing analysis by means of phase fitting techniques. We detected two relatively large glitches Delta nu / nu of 1.2 and 2.1 10^-6 occurred in January and June 2005. Interestingly, the occurrence times of these glitches are in agreement with the predictions made in our previous studies. This finding strongly suggests a connection between the flux, spectral and timing properties of 1RXS J170849-400910.
Both observational and theoretical research over the past decade has demonstrated that the probability distribution function (PDF) of the gas density in turbulent molecular clouds is a key ingredient for understanding star formation. It has recently been argued that the PDF of molecular clouds is a pure power-law distribution. It has been claimed that the log-normal part is ruled out when using only the part of the PDF up/down to which it is complete, that is where the column density contours are still closed. By using the results from high-resolution magnetohydrodynamical simulations of molecular cloud formation and evolution, we find that the column density PDF is indeed composed of a log-normal and, if including self-gravity, a power-law part. We show that insufficient sampling of a molecular cloud results in closed contours that cut off the log-normal part. In contrast, systematically increasing the field of view and sampling the entire cloud yields a completeness limit at the lower column densities, which also recovers the log-normal part. This demonstrates that the field of view must be sufficiently large for the PDF to be complete down to its log-normal part, which has important implications for predictions of star-formation activity based on the PDF.
An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define a complex orthogonal structure on the bundle of 2-forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3-frames on the bundle of 2-forms in a manner that essentially parallels their construction in terms of self-dual complex 2-forms. It is shown that one can still discuss the Debever-Penrose classification of the Riemannian curvature tensor in terms of the representation presented here.
Third-order bound-charge electronic nonlinearities of Si nanocrystals (NCs) embedded in a wide band-gap matrix representing silica are theoretically studied using an atomistic pseudopotential approach. Nonlinear refractive index, two-photon absorption and optical switching parameter are examined from small clusters to NCs up to a size of 3 nm. Compared to bulk values, Si NCs show higher third-order optical nonlinearities and much wider two-photon absorption threshold which gives rise to enhancement in the optical switching parameter.
We previously showed that we can use di quark pairs as a model of how nucleation of a new universe occurs. We now can construct a model showing evolution from a dark matter dark energy mix to a pure cosmological constant cosmology due to changes in the slope of the resulting scalar field,using much of Scherrer's k-essence model.This same construction permits a use of the speed of sound,in k-essence models evolving from zero to one. Having the sound speed eventually reach unity permits matching conventional cosmological observations in the aftermath of change of slope of a di quark pair generated scalar field during the nucleation process of a new universe. These results are consistent with applying Bunyi and Hu's semi classical criteria for cosmological potentials to indicate a phase transition alluded to by Dr. Edward Kolbs model of how the initial degrees of freedom declined from over 100 to something approaching what we see today in flat space cosmology.
We consider four approaches to relative Gromov-Witten theory and Gromov-Witten theory of degenerations: Jun Li's original approach, Bumsig Kim's logarithmic expansions, Abramovich-Fantechi's orbifold expansions, and a logarithmic theory without expansions due to Gross-Siebert and Abramovich-Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov-Witten invariants associated to all four of these theories are identical.
We investigate the spin-dependent transport properties of a two-dimensional electron gas formed at oxides' interface in the presence of a magnetic field. We consider several scenarios for the oxides' properties, including oxides with co-linear or spiral magnetic and ferroelectric order. For spiral multiferroic oxides, the magnetoelectric coupling and the topology of the localized magnetic moments introduce additional, electric field controlled spin-orbit coupling that affects the magneto-oscillation of the current. An interplay of this spin-orbit coupling, the exchange field, and of the applied magnetic field results in a quantum, gate-controlled spin and charge Hall conductance.