ShantanuT01/DACTYL-Pretraining huggingface dataset:
We explore differences in Galactic halo kinematic properties derived from two commonly employed Galactic potentials: the St$\ddot{a}$ckel potential and the default Milky Way-like potential used in the "Galpy" package (MWPotential2014), making use of stars with available metallicities, radial velocities, and proper motions from Sloan Digital Sky Survey Data Release 12. Adopting the St$\ddot{a}$ckel potential, we find that the shape of the metallicity distribution function (MDF) and the distribution of orbital rotation abruptly change at $Z_{\rm max}$ = 15 kpc and $r_{\rm max}$ = 30 kpc (where $Z_{\rm max}$ and $r_{\rm max}$ are the maximum distances reached by a stellar orbit from the Galactic plane and from the Galactic center, respectively), indicating that the transition from dominance by the inner-halo stellar population to the outer-halo population occurs at those distances. Stars with $Z_{\rm max}$ $>$ 15 kpc show an average retrograde motion of $V_{\rm \phi}$ = $-$60 km s$^{-1}$, while stars with $r_{\rm max}$ $>$ 30 kpc exhibit an even larger retrograde value, $V_{\rm \phi}$ = $-$150 km s$^{-1}$. This retrograde signal is also confirmed using the sample of stars with radial velocities obtained by $Gaia$ Data Release 2, assuming the St$\ddot{a}$ckel potential. In comparison, when using the shallower Galpy potential, a noticeable change in the MDF occurs only at $Z_{\rm max}$ = 25 kpc, and a much less extreme retrograde motion is derived. This difference arises because stars with highly retrograde motions in the St$\ddot{a}$ckel potential are unbound in the shallower Galpy potential, and stars with lower rotation velocities reach larger $Z_{\rm max}$ and $r_{\rm max}$. The different kinematic characteristics derived from the two potentials suggest that the nature of the adopted Galactic potential can strongly influence interpretation of the properties of the Galactic halo.
The present paper is a natural continuation of our previous paper: "Teleparallel Lagrange geometry and a unified field theory, Class. Quantum Grav., 27 (2010), 045005 (29pp)" \cite{WNA}. In this paper, we apply a linearization scheme on the field equations obtained in \cite{WNA}. Three important results under the linearization assumption are accomplished. First, the vertical fundamental geometric objects of the EAP-space loose their dependence on the positional argument $x$. Secondly, our linearized theory in the Cartan-type case coincides with the GFT in the first order of approximation. Finally, an approximate solution of the vertical field equations is obtained.
Na5Cu3O6, a new member of one dimensional charge ordered chain cuprates, was synthesized via the azide/nitrate route by reacting NaN3, NaNO3 and CuO. According to single crystal X-ray analysis, one dimensional CuO2 chains built up from planar, edge-sharing CuO4 squares are a dominant feature of the crystal structure. From the analysis of the Cu-O bond lengths we find that the system forms a Wigner lattice. The commensurate charge order allows to explicitly assign the valence states of either +2 or +3 to each copper atom resulting in a repetition according to Cu(2+)-Cu(3+)-Cu(2+)-Cu(2+)-Cu(3+)-Cu(2+). Following the theoretical analysis of the previously synthesized compounds Na3Cu2O4 and Na8Cu5O10, the magnetic susceptibility was expected to show a large dimer gap. Surprisingly, this is not the case. To resolve this puzzle, we show that the magnetic couplings in this compound are strongly affected by excitations across the Wigner charge gap. By including these contributions, which are distinct from conventional superexchange in Mott-insulators, we obtain a quantitative satisfying theoretical description of the magnetic susceptibility data.
We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open questions.
We present a post-processing catalog of globular clusters (GCs) for the $39$ most massive groups and clusters in the TNG50 simulation of the IlllustrisTNG project (virial masses $M_{200} =[5\times 10^{12} \rm - 2 \times 10^{14}$] M$_{\odot}$). We tag GC particles to all galaxies with stellar mass $M_* \geq 5\times10^6$ M$_{\odot}$, and we calibrate their masses to reproduce the observed power-law relation between GC mass and halo mass for galaxies with $M_{200} \geq 10^{11}$ M$_{\odot}$ (corresponding to $M_* \sim 10^9$ $M_{\odot}$). Here we explore whether an extrapolation of this $M_{\rm GC}$-$M_{200}$ relation to lower-mass dwarfs is consistent with current observations. We find a good agreement between our predicted number and specific frequency of GCs in dwarfs with $\rm M_*=[5 \times 10^6 \rm - 10^9]$ M$_{\odot}$ and observations. Moreover, we predict a steep decline in the GC occupation fraction for dwarfs with $M_*<10^9$ M$_{\odot}$ which agrees well with current observational constraints. This declining occupation fraction is due to a combination of tidal stripping in all dwarfs plus a stochastic sampling of the GC mass function for dwarfs with $M_* < 10^{7.5}$ M$_{\odot}$. Our simulations also reproduce available constraints on the abundance of intra-cluster GCs in Virgo and Centaurus A. These successes provide support to the hypothesis that the $M_{\rm GC}$-$M_{200}$ relation holds, albeit with more scatter, all the way down to the regime of classical dwarf spheroidals in these environments. Our GC catalogs are publicly available as part of the IllustrisTNG data release.
We consider, in normal-gauge Lyra's geometry, evolution of a homogeneous isotropic universe in a gravitational model involving only the standard matter in interaction with a displacement vector field $\phi_{\mu}$. Considering both constant and time-dependent displacement vector field we show that the observed cosmic acceleration could be explained without considering an alien energy component with a negative pressure.
Let $p$ be a prime integer, $k$ be a $p$-closed field of characteristic $\neq p$, $T$ be a torus defined over $k$, $F$ be a finite $p$-group, and $1\to T \to G \to F \to 1$ be an exact sequence of algebraic groups. Extending earlier work of N. Karpenko and A. Merkurjev, R. L\"otscher, M. MacDonald, A. Meyer, and the first author showed that \[\min\dim(V) - \min\dim(G) \leqslant \text{ed}(G; p) \leqslant \min \dim(W) - \dim(G),\] where $V$ and $W$ range over the $p$-faithful and $p$-generically free $k$-representations of $G$, respectively. They conjectured that the upper bound is, in fact, sharp. This conjecture has remained open for some time. We prove it in the case, where $F$ is diagonalizable.
For $m \in \mathbb{N}$, we determine the irreducible components of the $m$-th Jet Scheme of a complex branch $C$ and give formulas for their number $N(m)$ and for their codimensions, in terms of $m$ and the generators of the semigroup of $C$. This structure of the Jet Schemes determines and is determined by the topological type of $C$.
In a recent paper, Merca posed three conjectures on congruences for specific convolutions of a sum of odd divisor functions with a generating function for generalized $m$-gonal numbers. Extending Merca's work, we complete the proof of these conjectures.
Context: Galactic abundance gradients set strong constraints to chemo-dynamical evolutionary models of the Milky Way. Given the PL relations that provide accurate distances and the large number of spectral lines, Cepheids are excellent tracers of the present-day abundance gradients. Aims: We want to measure the Galactic abundance gradient of several chemical elements. While the slope of the Cepheid iron gradient did not vary much from the very first studies, the gradients of the other elements are not that well constrained. In this paper we focus on the inner and outer regions of the Galactic thin disk. Methods: We use HR spectra (FEROS, ESPADONS, NARVAL) to measure the abundances of several light (Na, Al), alpha (Mg, Si, S, Ca), and heavy elements (Y, Zr, La, Ce, Nd, Eu) in a sample of 65 Milky Way Cepheids. Combining these results with accurate distances from period-Wesenheit relations in the NIR enables us to determine the abundance gradients in the Milky Way. Results: Our results are in good agreement with previous studies on either Cepheids or other tracers. In particular, we confirm an upward shift of approximatively 0.2 dex for the Mg abundances, as has recently been reported. We also confirm the existence of a gradient for all the heavy elements studied in the context of a LTE analysis. However, for Y, Nd, and especially La, we find lower abundances for Cepheids in the outer disk than reported in previous studies, leading to steeper gradients. This effect can be explained by the differences in the line lists used by different groups. Conclusions: Our data do not support a flattening of the gradients in the outer disk, in agreement with recent Cepheid studies and chemo-dynamical simulations. This is in contrast to the open cluster observations but remains compatible with a picture where the transition zone between the inner disk and the outer disk would move outward with time.
We present the first successful demonstration of multi-object near-infrared spectroscopy on high redshift galaxies. Our objective is to address the true star formation history of the universe at z~1, a crucial epoch which some have suggested is the peak of star formation activity. By using H-alpha -the same robust star formation indicator used at low-z - redshifted into the J- and H-bands, we can trace star formation without the systematic uncertainties of different calibrators, or the extreme dust extinction in the rest-UV, which have plagued previous efforts. We are using the instrument CIRPASS (the Cambridge Infra-Red PAnoramic Survey Spectrograph), in multi-object mode, which has been successfully demonstrated on the Anglo-Australian Telescope (AAT) and the William Herschel Telescope (WHT). CIRPASS has 150 fibres deployable over \~40arcmin on the AAT and ~15arcmin on the WHT. Here we present preliminary results from one of our fields observed with the WHT: H-alpha detections of z~1 galaxies in the Hubble Deep Field North.
In this paper, we transform compressible MHD system written in Euler coordinate to Lagrange coordinate in critical Besov space. Then we construct unique local solutions for compressible MHD system. Our results improve the range of Lebesgue exponent in Besov space from $[2, N)$ to $[2, 2N)$ with $N$ stands for dimension. In addition, we give a lower bound for the maximal existence time which is important for our construction of global solutions. Based on the local solution, we obtain a unique global solution with high oscillating initial velocity and density by using effective viscous flux and Hoff's energy methods to explore the structure of compressible MHD system.
The internal rotation of low mass stars all along their evolution is of primary interest when studying their rotational dynamics, internal mixing and magnetic fields generation. In this context, helio- and asteroseismology probe angular velocity gradients deep within solar type stars. Still the rotation of the close center of such stars on the main sequence is hardly detectable and the dynamical interactions of the radiative core with the surface convective envelope is not well understood. Among them, the influence of the differential rotation profile sustained by convection and applied as a boundary condition to the radiation zone may be very important leading to the formation of tachoclines. In the solar convective region, the equator is rotating faster than the pole while numerical simulations predict either a solar or an anti-solar rotation in other low mass stars envelopes depending on their convective Rossby number. In this work, we therefore build for the first time 2D steady hydrodynamical models of low mass stars radiation zone providing a full 2D description of their dynamics and studying the influence of a general shear boundary condition accounting for a solar or an anti-solar differential rotation in the convective envelope. We compute coherently differential rotation and the associated meridional circulation using the Boussinesq approximation.
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube. These solutions are applicable to jets launched from a small region (e.g., near the inner edge of an accretion disk). As implied by earlier work, the flow can converge onto the rotation axis, potentially creating a collimation shock.   In this first version of the method, we derive the gravitational contribution to the relativistic equations by analogy with non-relativistic flow. This approach captures the relativistic kinetic gravitational mass of the flowing plasma, but not that due to internal thermal and magnetic energies. A more sophisticated treatment, derived from the basic general relativistic magnetohydrodynamical equations, is currently being developed.   Here we present an initial exploration of parameter space, describing the effects the model parameters have on flow solutions and the location of the collimation shock. These results provide the groundwork for new, semi-analytic models of relativistic jets which can constrain conditions near the black hole by fitting the jet break seen increasingly in X-ray binaries.
Compact star-forming clumps observed in distant galaxies are often suggested to play a crucial role in galaxy assembly. In this paper, we use a novel approach of applying finite resolution deconvolution on ground-based images of the COSMOS field to resolve 20,185 star-forming galaxies (SFG) at 0.5<z<2 to an angular resolution of 0.3", and study their clumpy fractions. A comparison between the deconvolved and HST images across four different filters shows good agreement and validates the deconvolution. We model spectral energy distributions using the deconvolved 14-band images to provide resolved surface brightness and stellar mass density maps for these galaxies. We find that the fraction of clumpy galaxies decreases with increasing stellar masses, and with increasing redshift: from ~30% at z ~ 0.7 to ~50% at z ~ 1.7. Using abundance matching, we also trace the progenitors for galaxies at z ~ 0.7 and measure the fractional mass contribution of clumps toward their total mass budget. Clumps are observed to have a higher fractional mass contribution toward galaxies at higher redshift: increasing from ~1% at z ~ 0.7 to ~5% at z ~ 1.7. Finally, the majority of clumpy SFGs have higher specific star formation rates (sSFR) compared to the average SFGs at fixed stellar mass. We discuss the implication of this result to in-situ clump formation due to disk instability.
We employ spectral analysis and compressed sensing to identify settings where a variational algorithm's cost function can be recovered purely classically or with minimal quantum computer access. We present theoretical and numerical evidence supporting the viability of sparse recovery techniques. To demonstrate this approach, we use basis pursuit denoising to efficiently recover simulated Quantum Approximate Optimization Algorithm (QAOA) instances of large system size from very few samples. Our results indicate that sparse recovery can enable a more efficient use and distribution of quantum resources in the optimisation of variational algorithms.
It is known that the special values of multiple zeta functions at non-positive arguments are indeterminate in most cases due to the occurrences of infinitely many singularities. In order to give a suitable rigorous meaning of the special values there, Furusho, Komori, Matsumoto and Tsumura introduced the desingularized values by the desingularization method to resolve all singularities. While, Ebrahimi-Fard, Manchon and Singer introduced the renormalized values to keep the "shuffle" relation by the renormalization procedure \`a la Connes and Kreimer. In this paper, we reveal an equivalence, that is, an explicit interrelationship between these two values. As a corollary, we also obtain an explicit formula to describe renormalized values in terms of Bernoulli numbers.
Keldysh nonequilibrium Green's function method is utilized to study theoretically the spin polarized transport through a graphene spin valve irradiated by a monochromatic laser field. It is found that the bias dependence of the differential conductance exhibits successive peaks corresponding to the resonant tunneling through the photon-assisted sidebands. The multi photon processes originate from the combined effects of the radiation field and the graphene tunneling properties, and are shown to be substantially suppressed in a graphene spin valve which results in a decrease of the differential conductance for a high bias voltage. We also discussed the appearance of a dynamical gap around zero bias due to the radiation field. The gap width can be tuned by changing the radiation electric field strength and the frequency. This leads to a shift of the resonant peaks in the differential conductance. We also demonstrate numerically the dependencies of the radiation and spin valve effects on the parameters of the external fields and those of the electrodes. We find that the combined effects of the radiation field, the graphene, and the spin valve properties bring about an oscillatory behavior in the tunnel magnetoresistance (TMR), and this oscillatory amplitude can be changed by scanning the radiation field strength and/or the frequency.
We examine the accuracy of estimation of parameters of the gravitational-wave signals from spinning neutron stars that can be achieved from observations by Earth-based laser interferometers. We consider a model of the signal consisting of two narrowband components and including both phase and amplitude modulation. We calculate approximate values of the rms errors of the parameter estimators using the Fisher information matrix. We carry out extensive Monte Carlo simulations and obtain cumulative distribution functions of rms errors of astrophysically interesting parameters: amplitude of the signal, wobble angle, position of the source in the sky, frequency, and spindown coefficients. We consider both all-sky searches and directed searches. We also examine the possibility of determination of neutron star proper motion. We perform simulations for all laser-interferometric detectors that are currently under construction and for several possible lengths of the observation time and sizes of the parameter space. We find that observations of continuous gravitational-wave signals from neutron stars by laser-interferometric detectors will provide a very accurate information about their astrophysical properties. We derive several simplified models of the signal that can be used in the theoretical investigations of the data analysis schemes independently of the physical mechanisms generating the gravitational-wave signal.
Using a recently developed variational quantum Monte Carlo method, magnetic properties of high-$T_{\rm C}$ superconductors are studied at zero temperature ($T$), by numerical simulations on the 2D t-J model. Our focus here is to explore the difference in the properties of $p$-type and $n$-type cuprates as a function of the carrier concentrations close to half filling. As observed experimentally, it is found that the antiferromagnetically ordered phase persists even for a small, yet finite amount of carrier doping, and that this phase is more robust in the electron doped case.
We study the embedding of D(8-p)-branes in the background geometry of parallel Dp-branes for $p\le 6$. The D(8-p)-brane is extended along the directions orthogonal to the Dp-branes of the background. The D(8-p)-brane configuration is determined by its Dirac-Born-Infeld plus Wess-Zumino-Witten action. We find a BPS condition which solves the equation of motion. The analytical solution of the BPS equation for the near-horizon and asymptotically flat geometries is given. The embeddings we obtain represent branes joined by tubes. By analyzing the energy of these tubes we conclude that they can be regarded as bundles of fundamental strings. Our solution provides an explicit realization of the Hanany-Witten effect. When $p=6$ the solution of the BPS equation must be considered separately and, in general, the embeddings of the D2-branes do not admit the same interpretation as in the $p<6$ case.
Accreting neutron stars (NS) can exhibit high-frequency modulations, known as burst oscillations, in their lightcurves during thermonuclear X-ray bursts. Their frequencies can be offset from the spin frequency of the NS (known independently) by several Hz, and can drift by 1-3 Hz. One plausible explanation for this phenomenon is that a wave is present in the bursting ocean that decreases in frequency (in the rotating frame) as the burst cools. The strongest candidate is the buoyant $r$-mode; however, models for the burning ocean background used in previous studies over-predict frequency drifts by several Hz. Using new background models (which include shallow heating, and burning in the tail of the burst) the evolution of the buoyant $r$-mode is calculated. The resulting frequency drifts are smaller, in line with observations. This illustrates the importance of accounting for the detailed nuclear physics in these bursts.
A method allowing studies of the hadronic matter at the early evolution stage in A+A collisions is developed. It is based on an interferometry analysis of approximately conserved values such as the averaged phase-space density (APSD) and the specific entropy of thermal pions. The plateau found in the APSD behavior vs collision energy at SPS is associated, apparently, with the deconfinement phase transition at low SPS energies; a saturation of this quantity at the RHIC energies indicates the limiting Hagedorn temperature for hadronic matter.
This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.
Large values of Born effective charges are generally considered as reliable indicators of the genuine tendency of an insulator towards ferroelectric instability. However, these quantities can be very much influenced by strong electron correlation and metallic behavior, which are not exclusive properties of ferroelectric materials. In this paper we compare the Born effective charges of some prototypical ferroelectrics with those of magnetic, non-ferroelectric compounds using a novel, self-interaction free methodology that improves on the local-density approximation description of the electronic properties. We show that the inclusion of strong-correlation effects systermatically reduces the size of the Born effective charges and the electron localization lengths. Furthermore we give an interpretation of the Born effective charges in terms of band energy structure and orbital occupations which can be used as a guideline to rationalize their values in the general case.
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the horizontal and vertical components are not asymptotically independent.