ShantanuT01/DACTYL-Pretraining huggingface dataset:
An ADM-like Hamiltonian approach is proposed for static spherically symmetric relativistic star configurations. For a given equation of state the entire information about the model can be encoded in a certain 2-dimensional minisuperspace geometry. We derive exact solutions which arise from symmetries corresponding to linear and quadratic geodesic invariants in minisuperspace by exploiting the relation to minisuperspace Killing tensors. A classification of exact solutions having the full number of integrations constants is given according to their minisuperspace symmetry properties. In particular it is shown that Schwarzschild's exterior solution and Buchdahl's n=1 polytrope solution correspond to minisuperspaces with a Killing vector symmetry while Schwarzschild's interior solution, Whittaker's solution and Buchdahl's n=5 polytrope solution correspond to minisuperspaces with a second rank Killing tensor. New solutions filling in empty slots in this classification scheme are also given. One of these new solutions has a physically reasonable equation of state and is a generalization of Buchdahl's n=1 polytrope model.
Magnetic topological quantum materials have attracted great attention due to their exotic topological quantum physics induced by the interplay among crystalology, magnetism, and topology, which is of profound importance to fundamental research and technology applications. However, limited materials are experimentally available, most of whom are realized by magnetic impurity doping or heterostructural constructions. In this work, based on the first-principles calculations, we predict that double perovskite Ba2CdReO6 is an intrinsic ferromagnetic topological semi-half-metal, while the ferrimagnetic double perovskite with space group symmetry Fm-3m, such as Ba2FeMoO6, belongs to a topological half-metal. One pair of Weyl points and fully spin-polarized nodal-ring states are found in the vicinity of the Fermi level in Ba2CdReO6. Its two-dimensional nearly flat drumhead surface states are fully spin-polarized. In Ba2FeMoO6, however, there exist four pairs of Weyl points and two fully spin-polarized nodal-rings near the Fermi level. These topological properties are stable in the presence of spin-orbit coupling. This makes these materials be an appropriate platform for studying the emerging intriguing properties, especially for the applications in spintronics, information technology, and topological superconductivity.
Increasing evidence for coronal heating contributions from cooler solar atmospheric layers, notably quiet Sun (QS) conditions, challenges standard solar atmospheric descriptions of bright transition region (TR) emission. As such, questions to the role of dynamic QS transients in contributing to the total coronal energy budget are elevated. Using observations from the {\it Atmospheric Imaging Assembly} and {\it Heliosemic Magnetic Imager} on board the {\it Solar Dynamics Observatory}, and numerical model extrapolations of coronal magnetic fields, we investigate a dynamic QS transient energetically isolated to the TR and extruding from a common footpoint shared with two heated loop arcades. A non-casual relationship is established between episodic heating of the QS transient and wide-spread magnetic field re-organization events, while evidence is found favoring a magnetic topology typical of eruptive processes. Quasi-steady interchange reconnection events are implicated as a source of the transient's visibly bright radiative signature. We consider the QS transient's temporally stable ($\approx$\,35\,min) radiative nature occurs as a result of the large-scale magnetic field geometries of the QS and/or relatively quiet nature of the magnetic photosphere, which possibly act to inhibit energetic buildup processes required to initiate a catastrophic eruption phase. This work provides insight to the QS's thermodynamic and magnetic relation to eruptive processes quasi-steadily heating a small-scale dynamic and TR transient. This work elevates arguments of non-negligible coronal heating contributions from cool atmospheric layers in QS conditions, and increases evidence for solar wind mass feeding of dynamic transients therein.
Ideal graphene antidot lattices are predicted to show promising band gap behavior (i.e., $E_G\simeq 500$ meV) under carefully specified conditions. However, for the structures studied so far this behavior is critically dependent on superlattice geometry and is not robust against experimentally realistic disorders. Here we study a rectangular array of triangular antidots with zigzag edge geometries and show that their band gap behavior qualitatively differs from the standard behavior which is exhibited, e.g, by rectangular arrays of armchair-edged triangles. In the spin unpolarized case, zigzag-edged antidots give rise to large band gaps compared to armchair-edged antidots, irrespective of the rules which govern the existence of gaps in armchair-edged antidot lattices. In addition the zigzag-edged antidots appear more robust than armchair-edged antidots in the presence of geometrical disorder. The inclusion of spin polarization within a mean-field Hubbard approach gives rise to a large overall magnetic moment at each antidot due to the sublattice imbalance imposed by the triangular geometry. Half-metallic behavior arises from the formation of spin-split dispersive states near the Fermi energy, reducing the band gaps compared to the unpolarized case. This behavior is also found to be robust in the presence of disorder. Our results highlight the possibilities of using triangular perforations in graphene to open electronic band gaps in systems with experimentally realistic levels of disorder, and furthermore, of exploiting the strong spin dependence of the system for spintronic applications.
The aim of these notes is to generalize Laumon's construction [18] of automorphic sheaves corresponding to local systems on a smooth, projective curve $C$ to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article "On the geometric Langlands conjecture" by Frenkel, Gaitsgory and Vilonen [10] carry over to our situation. We show that our sheaves descend to the moduli space of parabolic bundles if the rank is $\leq 3$ and that the general case can be deduced form a generalization of the vanishing conjecture of [10].
The amount of training data that is required to train a classifier scales with the dimensionality of the feature data. In hyperspectral remote sensing, feature data can potentially become very high dimensional. However, the amount of training data is oftentimes limited. Thus, one of the core challenges in hyperspectral remote sensing is how to perform multi-class classification using only relatively few training data points.   In this work, we address this issue by enriching the feature matrix with synthetically generated sample points. This synthetic data is sampled from a GMM fitted to each class of the limited training data. Although, the true distribution of features may not be perfectly modeled by the fitted GMM, we demonstrate that a moderate augmentation by these synthetic samples can effectively replace a part of the missing training samples. We show the efficacy of the proposed approach on two hyperspectral datasets. The median gain in classification performance is $5\%$. It is also encouraging that this performance gain is remarkably stable for large variations in the number of added samples, which makes it much easier to apply this method to real-world applications.
The stability of skyrmions in various environments is estimated by analyzing the multidimensional surface describing the energy of the system as a function of the directions of the magnetic moments in the system. The energy is given by a Heisenberg-like Hamiltonian that includes Dzyaloshinskii-Moriya interaction, anisotropy and external magnetic field. Local minima on this surface correspond to the ferromagnetic and skyrmion states. Minimum energy paths (MEP) between the minima are calculated using the geodesic nudged elastic band method. The maximum energy along an MEP corresponds to a first order saddle point on the energy surface and gives an estimate of the activation energy for the magnetic transition, such as creation and annihilation of a skyrmion. The pre-exponential factor in the Arrhenius law for the rate, the so-called attempt frequency, is estimated within harmonic transition state theory where the eigenvalues of the Hessian at the saddle point and the local minima are used to characterize the shape of the energy surface. For some degrees of freedom, so-called 'zero modes', the energy of the system remains invariant. They need to be treated separately and give rise to temperature dependence of the attempt frequency. As an example application of this general theory, the lifetime of a skyrmion in a track of finite width for a PdFe overlayer on a Ir(111) substrate is calculated as a function of track width and external magnetic field. Also, the effect of non-magnetic impurities is studied. Various MEPs for annihilation inside a track, via the boundary of a track and at an impurity are presented. The attempt frequency as well as the activation energy has been calculated for each mechanism to estimate the transition rate as a function of temperature.
In Lorentz violating theories of gravitation with a preferred foliation a notion of black hole is still possible, despite the presence of infinitely fast propagating modes. Such event horizons are known as universal horizons. Their discovery poses the question of whether they satisfy mechanical laws, analogous to the ones of Killing horizons in Lorentz symmetric theories, and whether they admit a thermodynamical interpretation. In this paper we study the viability of the first law for several exact universal horizon solutions previously derived in the literature. Our results show that a simple mechanical and thermodynamical interpretation is problematic in these cases, and call for a more systematic study of rotating universal horizons.
We perform a measurement of the Hubble constant, $H_0$, using the latest baryonic acoustic oscillations (BAO) measurements from galaxy surveys of 6dFGS, SDSS DR7 Main Galaxy Sample, BOSS DR12 sample, and eBOSS DR14 quasar sample, in the framework of a flat $\Lambda$CDM model. Based on the Kullback-Leibler (KL) divergence, we examine the consistency of $H_0$ values derived from various data sets. We find that our measurement is consistent with that derived from Planck and with the local measurement of $H_0$ using the Cepheids and type Ia supernovae. We perform forecasts on $H_0$ from future BAO measurements, and find that the uncertainty of $H_0$ determined by future BAO data alone, including complete eBOSS, DESI and Euclid-like, is comparable with that from local measurements.
We consider the production of a single top quark in association with a Higgs boson at the LHC. In particular, we compute the cross sections for the processes $ p p \to t h j$, $t h b$, $t h W$, $t h j j$, $t h j b$, $t h W j$, $t h W b$ in the presence of the anomalous $Wtb, WWh$ and $tth$ couplings. We find that the anomalous $Wtb$ and $tth$ couplings can enhance the cross sections significantly. We also analyze a few signatures and show that, if these couplings are indeed anomalous, then with enough data, one should be able to observe the production of the Higgs boson in association with single top quark.
The well-known middle levels problem is to find a Hammiltonian cycle in the graph induced from the binary Hamming graph $\cH_2(2k+1)$ by the words of weight $k$ or $k+1$. In this paper we define the $q$-analog of the middle levels problem. Let $n=2k+1$ and let $q$ be a power of a prime number. Consider the set of $(k+1)$-dimensional subspaces and the set of $k$-dimensional subspaces of $\F_q^n$. Can these subspaces be ordered in a way that for any two adjacent subspaces $X$ and $Y$, either $X \subset Y$ or $Y \subset X$? A construction method which yields many Hamiltonian cycles for any given $q$ and $k=2$ is presented.
We evaluate within the LO DGLAP approximation the dependence on energy of the cross section of the photo(electro)production of vector meson V ($V=J/\psi,...$) in the hard elastic processes off a parton $\gamma^*+g\to V=J/\psi+g$ as the function of momentum transfer $t=(q_{\gamma}-p_V)^2$. We demonstrate that in the limit $-t \ge m_V^2 +Q^2$ the cross section does not contain double logarithmic terms in any order of the DGLAP approximation leading to the energy independent cross section. Thus the energy dependence of cross section $\gamma^*+p\to J/\psi+{\rm rapidity ~gap} +X$ is governed at large $t$ by the gluon distribution within a proton, i.e. it is unambiguously predicted within the DGLAP approximation including the stronger $W_{\gamma N}$ dependence at larger $-t$ . This prediction explains recent HERA data. The calculations which follow perturbative Pomeron logic predict opposite trend of a weaker $W_{\gamma N}$ dependence at larger $t$. We explain that at the HERA energies double logarithmic terms characteristic for DGLAP approximation dominate in the hard processes as the consequence of constraints due to energy-momentum conservation. We give predictions for ultraperipheral hard diffractive processes at the LHC and show that these processes are well suited for looking for the contribution of the single logarithmic terms due to the gluon emission in the multiRegge kinematics. We also comment on the interrelation between energy and $t$ dependence of the cross sections of the hard exclusive processes.
Globular clusters are among the oldest structures in the Universe and they host today low-mass stars and no gas. However, there has been a time when they formed as gaseous objects hosting a large number of short-lived, massive stars. Many details on this early epoch have been depicted recently through unprecedented dissection of low-mass globular cluster stars via spectroscopy and photometry. In particular, multiple populations have been identified, which bear the nucleosynthetic fingerprints of the massive hot stars long disappeared. Here we discuss how massive star archeology can been done through the lens of these multiple populations.
Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical divisor $D$ on ${\cal M}_{\xi}$. So $D$ is a Calabi-Yau variety. We compute the number of moduli of $D$, namely $\dim H^1(D, T_D)$, to be $3g-4 + \dim H^0({\cal M}_{\xi}, K^{-1}_{{\cal M}_{\xi}})$. Denote by $\cal N$ the moduli space of all such pairs $(X',D')$, namely $D'$ is a smooth anticanonical divisor on a smooth moduli space of semistable vector bundles over the Riemann surface $X'$. It turns out that the Kodaira-Spencer map from the tangent space to $\cal N$, at the point represented by the pair $(X,D)$, to $H^1(D, T_D)$ is an isomorphism. This is proved under the assumption that if $g =2$, then $n\neq 2,3$, and if $g=3$, then $n\neq 2$.
Far-UV photons (E<13.6 eV) from hot massive stars regulate, or at least influence, the heating, ionization, and chemistry of most of the neutral interstellar medium. Investigating the interaction between FUV radiation and interstellar matter thus plays an important role in astrochemistry. We have used ALMA to mosaic a small field of the Orion Bar where the critical transition from atomic to molecular gas takes place. These observations provide an unprecedented sharp view of this transition layer (~1" resolution or ~414 AU). The resulting images (so far in the rotational emission of CO, HCO+, H13CO+, SO+, SO, and reactive ions SH+ and HOC+) show the small-scale structure in gas density and temperature, and the steep abundance gradients. The images reveal a pattern of high-density substructures, photo-ablative gas flows and instabilities at the edge of the molecular cloud. We have also used the IRAM 30m telescope to carry out a line-survey of the illuminated edge of the Bar in the mm domain. Our observations reveal the presence of complex organic molecules that were not expected in such a harsh environment. In particular, we have reported the first detection of the unstable cis conformer of formic acid (HCOOH) in the ISM. The energy barrier to internal rotation (the conversion from trans to cis) is approximately 4827 cm-1. Hence, this detection is surprising. The low inferred trans-to-cis abundance ratio of 2.8+/-1.0 supports a photoswitching mechanism: a given conformer absorbs a FUV stellar photon that radiatively excites the molecule to electronic states above the interconversion barrier. Subsequent fluorescent decay leaves the molecule in a different conformer form. This mechanism, which we have specifically studied with ab initio quantum calculations, was not considered so far in astrochemistry although it can affect the structure of a variety of molecules in PDRs. (abridged)
We relate the equianalytic and the equisingular deformations of a reduced complex plane curve to the Jacobian syzygies of its defining equation. Several examples and conjectures involving rational cuspidal curves are discussed.
Let $T$ be a tile in $\mathbb{Z}^n$, meaning a finite subset of $\mathbb{Z}^n$. It may or may not tile $\mathbb{Z}^n$, in the sense of $\mathbb{Z}^n$ having a partition into copies of $T$. However, we prove that $T$ does tile $\mathbb{Z}^d$ for some $d$. This resolves a conjecture of Chalcraft.
We present Early Science observations with the Large Millimeter Telescope, AzTEC 1.1 mm continuum images and wide bandwidth spectra (73-111 GHz) acquired with the Redshift Search Receiver, towards four bright lensed submillimetre galaxies identified through the Herschel Lensing Survey-snapshot and the SCUBA-2 Cluster Snapshot Survey. This pilot project studies the star formation history and the physical properties of the molecular gas and dust content of the highest redshift galaxies identified through the benefits of gravitational magnification. We robustly detect dust continuum emission for the full sample and CO emission lines for three of the targets. We find that one source shows spectroscopic multiplicity and is a blend of three galaxies at different redshifts (z=2.040, 3.252 and 4.680), reminiscent of previous high-resolution imaging follow-up of unlensed submillimetre galaxies, but with a completely different search method, that confirm recent theoretical predictions of physically unassociated blended galaxies. Identifying the detected lines as 12CO (J_up=2-5) we derive spectroscopic redshifts, molecular gas masses, and dust masses from the continuum emission. The mean H_2 gas mass of the full sample is (2.0 +- 0.2) x 10^11 M_sun/\mu, and the mean dust mass is (2.0+-0.2) x 10^9 M_sun/\mu, where \mu=2-5 is the expected lens amplification. Using these independent estimations we infer a gas-to-dust ratio of \delta_GDR=55-75, in agreement with other measurements of submillimetre galaxies. Our magnified high-luminosity galaxies fall on the same locus as other high-redshift submillimetre galaxies, extending the L'_CO - L_FIR correlation observed for local luminous and ultraluminous infrared galaxies to higher FIR and CO luminosities.
In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n=3,4, we also give an almost sharp life span for the subcritical case $2\le p<p_c$ when n=3. The main ingredients include a KSS type estimate with $0<\mu<1/2$ and weighted Strichartz estimates of order two.
We present the first high time-resolution simultaneous X-ray, ultraviolet, and optical observations of X-ray bursts in UY Vol, the optical counterpart of the low mass X-ray binary EXO 0748-676, obtained with RXTE, HST, and Gemini-S. Strong reprocessed signals are present in the ultraviolet (a factor of 4) and optical (a factor of 2.5). These signals are lagged with respect to the X-rays and appear significantly smeared as well. The addition of far-ultraviolet coverage for one burst, together with the high quality of the dataset, allow much tighter constraints upon the temperature and geometry of the reprocessing region than previously possible. A single-zone black body reprocessing model for this burst suggests a rise in temperatures during the burst from 18,000 to 35,000K and an emitting area comparable to that expected for the disk and/or irradiated companion star. The lags, a mean of 4.0s and range of 2.5s, are consistent with those expected within the binary. The single-zone black body model cannot reproduce the ratio of optical to ultraviolet flux during the burst, however. The discrepancy, corresponding to underpredicting the optical by more than a factor of two, seems too large to explain with deviations from a local black body spectrum and more likely indicates that a range of reprocessing temperatures are required, as would be expected, with cooler regions not contributing to the UV. Comparable results are derived from other bursts, and in particular the lag and smearing both appear shorter when the companion star is on the near side of the disk as predicted. The burst observed by HST also yielded a spectrum of the reprocessed light. [Abridged]
We present a spectroscopic survey of known and candidate $\gamma$\,Doradus stars. The high-resolution, high signal-to-noise spectra of 52 objects were collected by five different spectrographs. The spectral classification, atmospheric parameters (\teff, $\log g$, $\xi$), $v\sin i$ and chemical composition of the stars were derived. The stellar spectral and luminosity classes were found between G0-A7 and IV-V, respectively. The initial values for \teff\ and \logg\ were determined from the photometric indices and spectral energy distribution. Those parameters were improved by the analysis of hydrogen lines. The final values of \teff, \logg\ and $\xi$ were derived from the iron lines analysis. The \teff\ values were found between 6000\,K and 7900\,K, while \logg\,values range from 3.8 to 4.5\,dex. Chemical abundances and $v\sin i$ values were derived by the spectrum synthesis method. The $v\sin i$ values were found between 5 and 240\,km\,s$^{-1}$. The chemical abundance pattern of $\gamma$\,Doradus stars were compared with the pattern of non-pulsating stars. It turned out that there is no significant difference in abundance patterns between these two groups. Additionally, the relations between the atmospheric parameters and the pulsation quantities were checked. A strong correlation between the $v\sin i$ and the pulsation periods of $\gamma$\,Doradus variables was obtained. The accurate positions of the analysed stars in the H-R diagram have been shown. Most of our objects are located inside or close to the blue edge of the theoretical instability strip of $\gamma$\,Doradus.