ShantanuT01/DACTYL-Pretraining huggingface dataset:
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be related by a canonical transformation. In its turn, it raises a question about the equivalence of these two Hamiltonian formulations and their equivalence to the original formulation of General Relativity. We argue that, since the transformation from components of metric tensor to the ADM variables touches gauge degrees of freedom, which are non-canonical from the point of view of Dirac, the problem cannot be resolved in the limits of the Dirac approach. The proposed solution requires the extension of phase space by treating gauge degrees of freedom on an equal footing with other variables and introducing missing velocities into the Lagrangian by means of gauge conditions in differential form. We illustrate with a simple cosmological model the features of Hamiltonian dynamics in extended phase space. Then, we give a clear proof for the full gravitational theory that the ADM-like transformation is canonical in extended phase space in a wide enough class of possible parametrizations.
We prove that the coindex of the box complex $\mathrm{B}(H)$ of a graph $H$ can be measured by the generalised Mycielski graphs which admit a homomorphism to it. As a consequence, we exhibit for every graph $H$ a system of linear equations solvable in polynomial time, with the following properties: If the system has no solutions, then $\mathrm{coind}(\mathrm{B}(H)) + 2 \leq 3$; if the system has solutions, then $\chi(H) \geq 4$. We generalise the method to other bounds on chromatic numbers using linear algebra.
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.
We present a catalogue of RIZ photometry over an area of 0.855 square degrees, centred on NGC 2547. The survey is substantially complete to limits of R_c=21.5, I_c=19.5, Z=19.5. We use the catalogue to define NGC 2547 candidates with masses of about 0.05-1.0 M_sun. After correcting for incompleteness and contamination by foreground field dwarfs, we investigate the mass function of the cluster, its binary content, and search for evidence of mass segregation among lower mass stars. There is evidence for mass segregation between high (>3 M_sun) and lower mass stars, but over the range 0.1<M<0.7 M_sun, the data are consistent with no further mass segregation. By fitting King profiles we conclude that at least 60 percent of the low-mass stellar population are contained in our survey. The cluster mass function is remarkably similar to the Pleiades for 0.075<M<0.7 M_sun. Because of its age (~30 Myr), we demonstrate that this mass function is robust to several systematic uncertainties likely to affect older and younger clusters and is therefore one of the best available estimates for the initial mass function in young disc populations. For 0.05<M<0.075 M_sun there is some evidence for a deficit of brown dwarfs in NGC 2547 compared with other clusters. This deficit may extend to lower masses or may only be a dip, perhaps caused by an imperfect understanding of the mass-magnitude relationship at temperatures of 2800K.Incompleteness in our survey, and the luminosity functions from which we estimate contamination, leave this question open. The binary fraction for systems with mass ratios greater than about 0.5 is 20-35 per cent for M-dwarfs in NGC 2547, quite consistent with that found in the field (abridged).
The properties of dust change during the transition from diffuse to dense clouds as a result of ice formation and dust coagulation, but much is still unclear about this transformation. We present 2-20 micron spectra of 49 field stars behind the Perseus and Serpens Molecular Clouds and establish relationships between the near-infrared continuum extinction (AK) and the depths of the 9.7 micron silicate (tau97) and 3.0 micron H2O ice (tau30) absorption bands. The tau97/AK ratio varies from large, diffuse interstellar medium-like values (~0.55), to much lower ratios (~0.26). Above extinctions of AK~1.2 (AV~10; Perseus, Lupus, dense cores) and ~2.0 (AV~17; Serpens), the tau97/AK ratio is lowest. The tau97/AK reduction from diffuse to dense clouds is consistent with a moderate degree of grain growth (sizes up to ~0.5 micron), increasing the near-infrared color excess (and thus AK), but not affecting ice and silicate band profiles. This grain growth process seems to be related to the ice column densities and dense core formation thresholds, highlighting the importance of density. After correction for Serpens foreground extinction, the H2O ice formation threshold is in the range of AK=0.31-0.40 (AV=2.6-3.4) for all clouds, and thus grain growth takes place after the ices are formed. Finally, abundant CH3OH ice (~21% relative to H2O) is reported for 2MASSJ18285266+0028242 (Serpens), a factor of >4 larger than for the other targets.
We present a combined analysis of all publicly available, visible HST observations of transits of the planet HD 209458b. We derive the times of transit, planet radius, inclination, period, and ephemeris. The transit times are then used to constrain the existence of secondary planets in the system. We show that planets near an Earth mass can be ruled out in low-order mean-motion resonance, while planets less than an Earth mass are ruled out in interior, 2:1 resonance. We also present a combined analysis of the transit times and 68 high precision radial velocity measurements of the system. These results are compared to theoretical predictions for the constraints that can be placed on secondary planets.
The contribution of the tensor meson $K_2^*(1430)$ exchange in the process $\gamma p\to K^+\Lambda(\Sigma^0)$ is investigated within the Regge framework. Inclusion of the $K_2^*$ exchange in the $K(494)+K^*(892)$ exchanges with the coupling constants chosen from the SU(3) symmetry leads to a better description of the production mechanism without referring to any fitting procedure. This shows the significance of the role of the tensor meson exchange to have the Regge theory basically free of parameters with the SU(3) symmetry a good approximation for the meson-baryon couplings.
In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial density is a small perturbation of a constant state, we recover in the limit the convergence to the homogeneous incompressible Navier-Stokes equations (up to an additional term, due to density fluctuations). For general non-homogeneous fluids, the limit equations are instead linear, and the limit dynamics is described in terms of the vorticity and the density oscillation function: we lack enough regularity on the latter to prove convergence on the momentum equation itself. The proof of both results relies on a compensated compactness argument, which enables one to treat also the possible presence of vacuum.
The $\gamma$-ray flares from the Crab nebula observed by {\it AGILE} and {\it Fermi}-LAT between 2007-2013 reached GeV photon energies and lasted several days. The strongest emission, observed during the 2011 April "super-flare," exceeded the quiescent level by more than an order of magnitude. These observations challenge the standard models for particle acceleration in pulsar wind nebulae, because the radiating electrons have energies exceeding the classical radiation-reaction limit for synchrotron. Particle-in-cell simulations have suggested that the classical synchrotron limit can be exceeded if the electrons also experience electrostatic acceleration due to shock-driven magnetic reconnection. In this paper, we revisit the problem using an analytic approach based on solving a fully time-dependent electron transport equation describing the electrostatic acceleration, synchrotron losses, and escape experienced by electrons in a magnetically confined plasma "blob" as it encounters and passes through the pulsar-wind termination shock. We show that our model can reproduce the $\gamma$-ray spectra observed during the rising and decaying phases of each of the two sub-flare components of the 2011 April super-flare. We integrate the spectrum for photon energies $\ge 100\,$MeV to obtain the light curve for the event, which agrees with the observations. We find that strong electrostatic acceleration occurs on both sides of the termination shock, driven by magnetic reconnection. We also find that the dominant mode of particle escape changes from diffusive escape to advective escape as the blob passes through the shock.
Let $(X_n)_{n \in\mathbb{N}}$ be a $V$-geometrically ergodic Markov chain on a measurable space $\mathbb{X}$ with invariant probability distribution $\pi$. In this paper, we propose a discretization scheme providing a computable sequence $(\widehat\pi_k)_{k\ge 1}$ of probability measures which approximates $\pi$ as $k$ growths to infinity. The probability measure $\widehat\pi_k$ is computed from the invariant probability distribution of a finite Markov chain. The convergence rate in total variation of $(\widehat\pi_k)_{k\ge 1}$ to $\pi$ is given. As a result, the specific case of first order autoregressive processes with linear and non-linear errors is studied. Finally, illustrations of the procedure for such autoregressive processes are provided, in particular when no explicit formula for $\pi$ is known.
A dissipative Lorentz-covariant Ohm's law which uses only the electromagnetic degrees of freedom is proposed. For large conductivity, Maxwell equations equipped with this Ohm's law reduce to the equations of Force-Free Electrodynamics (FFE) with small dissipative corrections, but only in the regions where the ideal FFE 4-current is space-like. This might indicate that the pulsar emission comes primarily from the magnetic separartrix.
Bethe-Salpeter equation is applied to nucleon-nucleon elastic scattering at the intermediate energy. The differential cross section and the polarization are calculated in terms of the phase shift analysis method using the two-body potential derived from the Bethe-Salpeter equation. The lowest-order Born approximation for the K-matrix is corrected by including the inverse square part of the potential.
An integrable quantum spin ladder based on the SU(4) symmetry algebra with boundary defects is studied in the framework of boundary integrability. Five nontrivial solutions of the reflection equations lead to different boundary impurities. In each case the energy spectrum is determined using the quantum inverse scattering method. The thermodynamic properties are investigated by means of the thermodynamic Bethe ansatz. In particular, the susceptibility and the magnetization of the model in the vicinity of the critical points are derived along with differing magnetic properites for antiferromagnetic and ferromagnetic impurity couplings at the edges. The results are applicable to the strong coupling ladder compounds, such as Cu_2(C_5 H_12 N_2)_2 Cl_4.
We present a comprehensive study of star-forming (SF) regions in the nearest large spiral galaxy M31. We use GALEX far-UV (1344-1786 \AA, FUV) and near-UV (1771-2831 \AA, NUV) imaging to detect young massive stars and trace the recent star formation across the galaxy. The FUV and NUV flux measurements of the SF regions, combined with ground-based data for estimating the reddening by interstellar dust from the massive stars they contain, are used to derive their ages and masses. The GALEX imaging, combining deep sensitivity and coverage of the entire galaxy, provides a complete picture of the recent star formation in M31 and its variation with environment throughout the galaxy. The FUV and NUV measurements are sensitive to detect stellar populations younger than a few hundred Myrs. We detected 894 SF regions, with size > 1600 pc^{2} above an average FUV flux limit of ~ 26 ABmag arcsecond^{-2}, over the whole 26 kpc galaxy disk. We derive the star-formation history of M31 within this time span. The star formation rate (SFR) from the youngest UV sources (age < 10 Myr) is comparable to that derived from H_{alpha}, as expected. We show the dependence of the results on the assumed metallicity. When star formation detected from IR measurements of the heated dust is added to the UV-measured star formation (from the unobscured populations) in the recent few Myrs, we find the SFR has slightly decreased in recent epochs, with a possible peak between 10 and 100 Myrs, and an average value of SFR ~ 0.6 or 0.7 M_{sun} yr^{-1} (for metallicity Z=0.02 or 0.05 respectively) over the last 400 Myrs.
Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X.
We consider the Cauchy problem for an equation of Korteweg-de Vries-Kawahara type with initial data in the analytic Gevrey spaces. By using linear, bilinear and trilinear estimates in analytic Bourgain spaces, we establish the local well-posedness for this problem. By using an approximate conservation law, we extend this to a global result in such a way that the radius of analyticity of solutions is uniformly bounded below by a fixed positive number for all time.
Cold Dark Matter (CDM) is a crucial constituent of the current concordance cosmological model. Having a vanishing equation of state (EoS), its energy density scales with the inverse cosmic volume and is thus uniquely described by a single number, its present abundance. We test the inverse cosmic volume law for Dark Matter (DM) by allowing its EoS to vary independently in eight redshift bins in the range $z=10^5$ and $z=0$. We use the latest measurements of the Cosmic Microwave Background radiation from the Planck satellite and supplement them with Baryon Acoustic Oscillation (BAO) data from the 6dF and SDSS-III BOSS surveys, and with the Hubble Space Telescope (HST) key project data. We find no evidence for nonzero EoS in any of the eight redshift bins. With Planck data alone, the DM abundance is most strongly constrained around matter-radiation equality $\omega^{\rm eq}_g = 0.1193^{+0.0036}_{-0.0035}$ (95% c.l.), whereas its present day value is more weakly constrained $\omega^{(0)}_g = 0.16^{+0.12}_{-0.10}$ (95% c.l.). Adding BAO or HST data does not significantly change the $\omega^{\rm eq}_g$ constraint, while $\omega^{(0)}_g$ tightens to $0.160^{+0.069}_{-0.065} $ (95% c.l.) and $0.124^{+0.081}_{-0.067}$ (95% c.l.) respectively. Our results constrain for the first time the level of "coldness" required of the DM across various cosmological epochs and show that the DM abundance is strictly positive at all times.
A famous conjecture attributed to Kodaira asks whether any compact Kaehler manifold can be approximated by projective manifolds. We confirm this conjecture on projectivized direct sums of three line bundles on three-dimensional complex tori which appears rather surprising in view of expected dimensions of certain families of tori. We also discuss possible counter examples.
We build a sample of distant (D > 80 kpc) stellar halo stars with measured radial velocities. Faint ($20 < g <22$) candidate blue horizontal branch (BHB) stars were selected using the deep, but wide, multi-epoch Sloan Digital Sky Survey photometry. Follow-up spectroscopy for these A-type stars was performed using the VLT-FORS2 instrument. We classify stars according to their Balmer line profiles, and find 7 are bona fide BHB stars and 31 are blue stragglers (BS). Owing to the magnitude range of our sample, even the intrinsically fainter BS stars can reach out to D ~ 90 kpc. We complement this sample of A-type stars with intrinsically brighter, intermediate-age, asymptotic giant branch stars. A set of 4 distant cool carbon stars is compiled from the literature and we perform spectroscopic follow-up on a further 4 N-type carbon stars using the WHT-ISIS instrument. Altogether, this provides us with the largest sample to date of individual star tracers out to r ~ 150 kpc. We find that the radial velocity dispersion of these tracers falls rapidly at large distances and is surprisingly cold (sigma_r ~ 50-60 km/s) between 100-150 kpc. Relating the measured radial velocities to the mass of the Milky Way requires knowledge of the (unknown) tracer density profile and anisotropy at these distances. Nonetheless, by assuming the stellar halo stars between 50-150 kpc have a moderate density fall-off (with power-law slope alpha < 5) and are on radial orbits (sigma^2_t/sigma^2_r < 1), we infer that the mass within 150 kpc is less than 10^12 M_solar and suggest it probably lies in the range (5-10) x 10^11 M_solar. We discuss the implications of such a low mass for the Milky Way.
In this note we prove that for every integer $d \geq 1$, there exists an explicit constant $B_d$ such that the following holds. Let $K$ be a number field of degree $d$, let $q > \max\{d-1,5\}$ be any rational prime that is totally inert in $K$ and $E$ any elliptic curve defined over $K$ such that $E$ has potentially multiplicative reduction at the prime $\mathfrak q$ above $q$. Then for every rational prime $p> B_d$, $E$ has an irreducible mod $p$ Galois representation. This result has Diophantine applications within the "modular method". We present one such application in the form of an Asymptotic version of Fermat's Last Theorem that has not been covered in the existing literature.
We investigate the topological insulating states of the $p$-band systems in optical lattices induced by the onsite orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises from the energy level splitting between the onsite $p_x+ip_y$ and $p_x-ip_y$ orbitals by rotating each optical lattice site around its own center. At large rotation angular velocities, this model naturally reduces to two copies of Haldane's quantum Hall model without Landau levels. The distribution of Berry curvature in the momentum space and the quantized Chern numbers are calculated. The experimental realization is also discussed.
Motivated by recent suggestions that many Be stars form through binary mass transfer, we searched the APOGEE survey for Be stars with bloated, stripped companions. From a well-defined parent sample of 297 Be stars, we identified one mass-transfer binary, HD 15124. The object consists of a main-sequence Be star ($M_{\rm Be}=5.3\pm 0.6 \,M_{\odot}$) with a low-mass ($M_{\rm donor}=0.92\pm 0.22\,M_{\odot}$), subgiant companion on a 5.47-day orbit. The emission lines originate in an accretion disk caused by ongoing mass transfer, not from a decretion disk as in classical Be stars. Both stars have surface abundances bearing imprint of CNO processing in the donor's core: the surface helium fraction is $Y_{\rm He}\approx 0.6$, and the nitrogen-to-carbon ratio is 1000 times the solar value. The system's properties are well-matched by binary evolution models in which mass transfer begins while a $3-5\,M_{\odot}$ donor leaves the main sequence, with the secondary becoming the Be star. These models predict that the system will soon become a detached Be + stripped star binary like HR 6819 and LB-1, with the stripped donor eventually contracting to become a core helium-burning sdOB star. Discovery of one object in this short-lived ($\sim$1 Myr) evolutionary phase implies the existence of many more that have already passed through it and are now Be + sdOB binaries. We infer that $(28_{-16}^{+27})\,\%$ of Be stars have stripped companions, most of which are faint. Together with the dearth of main-sequence companions to Be stars and recent discovery of numerous Be + sdOB binaries in the UV, our results imply that binarity plays an important role in the formation of Be stars.
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that it gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure, and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field, and show that the full time-evolution of the control problem can be analytically solved.
Materials with tunable charge and lattice degrees of freedom provide excellent platforms for investigating multiple phases that can be controlled via external stimuli. We show how the charge-ordered ferroelectric oxide Ag$_2$BiO$_3$, which has been realized experimentally, presents a unique exemplar of a metal-insulator transition under an external electric field. Our first-principles calculations, combined with a symmetry analysis, reveal the presence of a nearly ideal hourglass-Dirac-semimetal state in the nonpolar structure of Ag$_2$BiO$_3$. The low-energy band structure consists of two hourglasslike nodal lines located on two mutually orthogonal glide-mirror planes in the absence of spin-orbit coupling (SOC) effects. These lines cross at a common point and form an interlinked chainlike structure, which extends beyond the first Brillouin zone. Inclusion of the SOC opens a small gap in the nodal lines and results in two symmetry-enforced hourglasslike Dirac points on the $\tilde{\mathcal{C}}_{2y}$ screw rotation axis. Our results indicate that Ag$_2$BiO$_3$ will provide an ideal platform for exploring the ferroelectric-semiconductor to Dirac-semimetal transition by the application of an external electric field.
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra $SU(3)_X$ gauge factor gets completely broken by the vacuum expectation values of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic $Z_2\times Z_2'$ discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.
The distinguishing number of a graph $G$ is the smallest $k$ such that $G$ admits a $k$-colouring for which the only colour-preserving automorphism of $G$ is the identity. We determine the distinguishing number of finite $4$-valent vertex-transitive graphs. We show that, apart from one infinite family and finitely many examples, they all have distinguishing number $2$.