ShantanuT01/DACTYL-Pretraining huggingface dataset:
The study of Ly-alpha emission in the high-redshift universe is a useful probe of the epoch of reionization, as the Ly-alpha line should be attenuated by the intergalactic medium (IGM) at low to moderate neutral hydrogen fractions. Here we present the results of a deep and wide imaging search for Ly-alpha emitters in the COSMOS field. We have used two ultra-narrowband filters (filter width of ~8-9 {\deg}A) on the NEWFIRM camera, installed on the Mayall 4m telescope at Kitt Peak National Observatory, in order to isolate Ly-alpha emitters at z = 7.7; such ultra-narrowband imaging searches have proved to be excellent at detecting Ly-alpha emitters. We found 5-sigma detections of four candidate Ly-alpha emitters in a survey volume of 2.8 x 10^4 Mpc^3 (total survey area ~760 arcmin^2). Each candidate has a line flux greater than 8 x 10^-18 erg s^-1 cm^-2. Using these results to construct a luminosity function and comparing to previously established Ly-alpha luminosity functions at z = 5.7 and z = 6.5, we find no conclusive evidence for evolution of the luminosity function between z = 5.7 and z = 7.7. Statistical Monte Carlo simulations suggest that half of these candidates are real z = 7.7 targets, and spectroscopic follow-up will be required to verify the redshift of these candidates. However, our results are consistent with no strong evolution in the neutral hydrogen fraction of the IGM between z = 5.7 and z = 7.7, even if only one or two of the z = 7.7 candidates are spectroscopically confirmed.
In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.
Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables. Earlier work on the subject, which traced back the quantum qroup symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic form, left some open questions: - How to reconcile the monodromy invariance of the local 2D group valued field (i.e., equality of the left and right monodromies) with the fact that the latter obey different exchange relations? - What is the status of the quantum group symmetry in the 2D theory in which the chiral fields commute? - Is there a consistent operator formalism in the chiral and in the extended 2D theory in the continuum limit? We propose a constructive affirmative answer to these questions for G=SU(2) by presenting the chiral quantum fields as sums of chiral vertex operators and q-Bose creation and annihilation operators.
We propose a method for obtaining the Schmidt decomposition of bipartite systems with continuous variables. It approximates the modes to the prescribed accuracy by well known orthogonal functions. We give some criteria for the control of errors. We illustrate the method comparing its results with the already published analysis for entanglement of biphotons. The agreement is excellent.
We make a comparison for thirteen dark energy (DE) models by using current cosmological observations, including type Ia supernova, baryon acoustic oscillations, and cosmic microwave background. To perform a systematic and comprehensive analysis, we consider three statistics methods of SNIa, including magnitude statistic (MS), flux statistic (FS), and improved flux statistic (IFS), as well as two kinds of BAO data. In addition, Akaike information criteria (AIC) and Bayesian information criteria (BIC) are used to assess the worth of each model. We find that: (1) The thirteen models can be divided into four grades by performing cosmology-fits. The cosmological constant model, which is most favored by current observations, belongs to grade one; $\alpha$DE, constant $w$ and generalized Chaplygin gas models belong to grade two; Chevalliear-Polarski-Linder (CPL) parametrization, Wang parametrization, doubly coupled massive gravity, new generalized Chaplygin gas and holographic DE models belong to grade three; agegraphic DE, Dvali-Gabadadze-Porrati, Vacuum metamorphosis and Ricci DE models, which are excluded by current observations, belong to grade four. (2) For parameter estimation, adopting IFS yields the biggest $\Omega_m$ and the smallest $h$ for all the models. In contrast, using different BAO data does not cause significant effects. (3) IFS has the strongest constraint ability on various DE models. For examples, adopting IFS yields the smallest value of $\Delta$AIC for all the models; in addition, making use of this technique yields the biggest figure of merit for CPL and Wang parametrizations.
In this paper we consider an optimal control problem for a large population of interacting agents with deterministic dynamics, aggregating potential and constraints on reciprocal distances, in dimension 1. We study existence and qualitative properties of periodic in time optimal trajectories of the finite agents optimal control problem, with particular interest on the compactness of the solutions' support and on the saturation of the distance constraint. Moreover, we prove, through a $\Gamma$-convergence result, the consistency of the mean-field optimal control problem with density constraints with the corresponding underlying finite agent one and we deduce some qualitative results for the time periodic equilibria of the limit problem.
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative scheme thus obtained allows to pre-select a quantum number of one of the two commuting operators and then calculate a corresponding eigenvalue of the other operator. The result is the common eigenvector of the eigenvalue pair. Among others the method may be used to calculate excited states, cope with degeneracy and/or accelerate convergence. Small example calculations are presented as a 'Proof-of-Concept' and to reveal some properties of the new method.
Let $E$ be an elliptic curve defined over $\mathbb Q$. Let $\Gamma$ be a subgroup of $E(\mathbb Q)$ and $P\in E(\mathbb Q)$. In [1], it was proved that if $E$ has no nontrivial rational torsion points, then $P\in\Gamma$ if and only if $P\in \Gamma$ mod $p$ for finitely many primes $p$. In this note, assuming the General Riemann Hypothesis, we provide an explicit upper bound on these primes when $E$ does not have complex multiplication and either $E$ is a semistable curve or $E$ has no exceptional prime.
It is known that the strength of neutral oxygen triplet lines at 7771-5 A shows a luminosity effect in evolved A through G stars. However, its general behavior across the HR diagram is not yet well understood, since the applicability limit of the relations proposed by various previous work (tending to be biased toward supergiants) still remains unclear. Besides, our understanding on the nature of atmospheric micro-scale turbulence, which is considered to play a significant role (along with the non-LTE line intensification) for the cause of this effect, is still insufficient. Towards clarifying these problems, we carried out an extensive non-LTE spectrum-fitting analysis of O I 7771--5 lines for unbiased sample of 75 evolved A-, F,- and G-type stars over wide luminosity classes (from subgiants through supergiants) including rapid rotators, from which the total equivalent width (W_77) was derived and the microturbulence (xi) was determined by two different (profile- and abundance-based) methods for each star. While we confirmed that W_77 tends to increase in the global sense as a star's absolute magnitude (M_V) becomes more luminous, distinctly different trends were found between lower-gravity (log g <~ 2.5) and higher-gravity (log g >~ 2.5) stars, in the sense that the M_V vs. W_77 formulas proposed by past studies are applicable only to the former supergiant group. In case of using W_77 for empirical M_V evaluation by such simple formulas, it is recommended to confine only to supergiants of -5 > M_V > -10. Regarding the microturbulence significantly controlling W_77, it roughly shows an increasing tendency with a decrease in surface gravity. However, the trend is not monotonic but rather intricate (e.g., hump, stagnation, or discontinuously large increase) depending on the stellar type and evolutionary stage.
Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markov switching in additive noises is studied for incompressible fluid flow in a bounded domain in the three-dimensional space. To study such a system, we introduce a family of regularized equations and investigate the asymptotic behavior of the regularized equations first. The existence an ergodic measure for the regularized system is established via the Krylov-Bogolyubov method. Then the existence of an stationary measure to the original system is obtained by extracting a limit from the ergodic measures of the family of the regularized system.
In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of the force vector resulting from the interaction of two agents. In this way the anisotropy is leading to a smooth evasion behaviour. In fact, the proposed model generalizes the standard models, and compensates their drawback of not being able to avoid collisions. Moreover, the model allows for formal passage to the limit 'number of particles to infinity', leading to a mesoscopic description in the mean-field sense. Possible applications are autonomous traffic, swarming or pedestrian motion. Here, we focus on the latter, as the model is validated numerically using two scenarios in pedestrian dynamics. The first one investigates the pattern formation in a channel, where two groups of pedestrians are walking in opposite directions. The second experiment considers a crossing with one group walking from left to right and the other one from bottom to top. The well-known pattern of lanes in the channel and travelling waves at the crossing can be reproduced with the help of this anisotropic model at both, the microscopic and the mesoscopic level. In addition, the 'right-before-left' and 'left-before-right' rule appear intrinsically for different anisotropy parameters.
We utilize state-of-the-art 3D hydrodynamical and classical 1D stellar model atmospheres to study the influence of convection on the formation properties of various atomic and molecular spectral lines in the atmospheres of four red giant stars, located close to the base of the red giant branch, RGB ($T_{\mathrm eff}\approx5000$ K, $\log g=2.5$), and characterized by four different metallicities, [M/H] = 0.0, -1.0, -2.0, -3.0. The role of convection in the spectral line formation is assessed with the aid of abundance corrections, i.e., the differences in abundances predicted for a given equivalent width of a particular spectral line with the 3D and 1D model atmospheres. We find that for lines of certain neutral atoms the abundance corrections strongly depend both on metallicity of a given model atmosphere and the line excitation potential. While abundance corrections for all lines of both neutral and ionized elements tend to be small at solar metallicity, for lines of neutral elements with low ionization potential and low-to-intermediate $\chi$ they quickly increase with decreasing metallicity, reaching in their extremes to -0.6...-0.8 dex. In all such cases the large abundance corrections are due to horizontal temperature fluctuations in the 3D hydrodynamical models. Abundance corrections of molecular lines are very sensitive to metallicity of the underlying model atmosphere and may be larger (in absolute value) than -0.5 dex at [M/H] = -3.0 (-1.5 dex in the case of CO). We also find that an approximate treatment of scattering in the 3D model calculations leads to the abundance corrections that are altered by less than ~0.1 dex, both for atomic and molecular (CO) lines, with respect to the model where scattering is treated as true absorption throughout the entire atmosphere, with the largest differences for the resonance and low-excitation lines.
For a family of random walks $\{S^{(a)}\}$ satisfying $\mathbf{E}S_1^{(a)}=-a<0$ we consider ladder epochs $\tau^{(a)}=\min\{k\geq1: S_k^{(a)}<0\}$. We study the asymptotic, as $a\to0$, behaviour of $\mathbf{P}(\tau^{(a)}>n)$ in the case when $n=n(a)\to\infty$. As a consequence we obtain also the growth rates of the moments of $\tau^{(a)}$.
To characterize the absorption properties of this circumgalactic medium (CGM) and its relation to the LG we present the so-far largest survey of metal absorption in Galactic high-velocity clouds (HVCs) using archival ultraviolet (UV) spectra of extragalactic background sources. The UV data are obtained with the Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope (HST) and are supplemented by 21 cm radio observations of neutral hydrogen. Along 270 sightlines we measure metal absorption in the lines of SiII, SiIII, CII, and CIV and associated HI 21 cm emission in HVCs in the velocity range |v_LSR|=100-500 km s^-1. With this unprecedented large HVC sample we were able to improve the statistics on HVC covering fractions, ionization conditions, small-scale structure, CGM mass, and inflow rate. For the first time, we determine robustly the angular two point correlation function of the high-velocity absorbers, systematically analyze antipodal sightlines on the celestial sphere, and compare the absorption characteristics with that of Damped Lyman alpha absorbers (DLAs) and constrained cosmological simulations of the LG. Our study demonstrates that the Milky Way CGM contains sufficient gaseous material to maintain the Galactic star-formation rate at its current level. We show that the CGM is composed of discrete gaseous structures that exhibit a large-scale kinematics together with small-scale variations in physical conditions. The Magellanic Stream clearly dominates both the cross section and mass flow of high-velocity gas in the Milky Way's CGM. The possible presence of high-velocity LG gas underlines the important role of the local cosmological environment in the large-scale gas-circulation processes in and around the Milky Way (abridged).
Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with its environment in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. Finally, this TSS-based approach also leads to some new insights about the origin of the second law of thermodynamics.
We study Cox rings of K3-surfaces. A first result is that a K3-surface has a finitely generated Cox ring if and only if its effective cone is polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3-surfaces of Picard number two, and explicitly compute the Cox rings of generic K3-surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.
Low-energy lepton observables are discussed in the Minimal R-symmetric Supersymmetric Standard Model. We present comprehensive numerical analyses and the analytic one-loop results for $(g-2)_\mu$, $\mu \to e \gamma$, and $\mu \to e$ conversion. The interplay between the three observables is investigated as well as the parameter regions with large $g-2$. A striking difference to the MSSM is the absence of $\tan\beta$ enhancements; however we find smaller enhancements governed by MRSSM-specific R-Higgsino couplings $\lambda_d$ and $\Lambda_d$. As a result we find significant contributions to $g-2$ only in a small parameter space with several SUSY masses below $200$ GeV, compressed spectra and large $\lambda_d$, $\Lambda_d$. In this parameter space there is a correlation between all three considered observables. In the parameter region with small $(g-2)_\mu$ the SUSY masses can be larger and the correlation between $\mu\to e\gamma$ and $\mu\to e$ conversion is weak. Therefore already COMET Phase 1 has a promising sensitivity to the MRSSM.
The FORS Deep Field project is a multi-colour, multi-object spectroscopic investigation of an approx. 7 times 7 region near the south galactic pole based mostly on observations carried out with the FORS instruments attached to the VLT telescopes. It includes the QSO Q 0103-260 (z = 3.36). The goal of this study is to improve our understanding of the formation and evolution of galaxies in the young Universe. In this paper the field selection, the photometric observations, and the data reduction are described. The source detection and photometry of objects in the FORS Deep Field is discussed in detail. A combined B and I selected UBgRIJKs photometric catalog of 8753 objects in the FDF is presented and its properties are briefly discussed. The formal 50% completeness limits for point sources, derived from the co-added images, are 25.64, 27.69, 26.86, 26.68, 26.37, 23.60 and 21.57 in U, B, g, R, I, J and Ks (Vega-system), respectively. A comparison of the number counts in the FORS Deep Field to those derived in other deep field surveys shows very good agreement.
We study the phase space of the quintom cosmologies for a class of exponential potentials. We combine normal forms expansions and the center manifold theory in order to describe the dynamics near equilibrium sets. Furthermore, we construct the unstable and center manifold of the massless scalar field cosmology motivated by the numerical results given in Lazkoz and Leon (Phys Lett B 638:303. arXiv:astro-ph/0602590, 2006). We study the role of the curvature on the dynamics. Several monotonic functions are defined on relevant invariant sets for the quintom cosmology. Finally, conservation laws of the cosmological field equations and algebraic solutions are determined by using the symmetry analysis and the singularity analysis.
In recent years, massive new spectroscopic data sets, such as the over half million stellar spectra obtained during the course of SDSS (in particular its sub-survey SEGUE), have provided the quantitative detail required to formulate a coherent story of the assembly and evolution of the Milky Way. The disk and halo systems of our Galaxy have been shown to be both more complex, and more interesting, than previously thought. Here we concentrate on the halo system of the Milky Way. New data from SDSS/SEGUE has revealed that the halo system comprises at least two components, the inner halo and the outer halo, with demonstrably different characteristics (metallicity distributions, density distributions, kinematics, etc.). In addition to suggesting new ways to examine these data, the inner/outer halo dichotomy has enabled an understanding of at least one long-standing observational result, the increase of the fraction of carbon-enhanced metal-poor (CEMP) stars with decreasing metallicity.
Upcoming high spectral resolution telescopes, particularly Astro-H, are expected to finally deliver firm quantitative constraints on turbulence in the intra-cluster medium (ICM). We develop a new spectral analysis technique which exploits not just the line width but the entire line shape, and show how the excellent spectral resolution of Astro-H can overcome its relatively poor spatial resolution in making detailed infer- ences about the velocity field. The spectrum is decomposed into distinct components, which can be quantitatively analyzed using Gaussian mixture models. For instance, bulk flows and sloshing produce components with offset means, while partial volume- filling turbulence from AGN or galaxy stirring leads to components with different widths. The offset between components allows us to measure gas bulk motions and separate them from small-scale turbulence, while component fractions and widths con- strain the emission weighted volume and turbulent energy density in each component. We apply mixture modeling to a series of analytic toy models as well as numerical simu- lations of clusters with cold fronts and AGN feedback respectively. From Markov Chain Monte Carlo and Fisher matrix estimates which include line blending and continuum contamination, we show that the mixture parameters can be accurately constrained with Astro-H spectra: at a \sim 10% level when components differ significantly in width, and a \sim 1% level when they differ significantly in mean value. We also study error scalings and use information criteria to determine when a mixture model is preferred. Mixture modeling of spectra is a powerful technique which is potentially applicable to other astrophysical scenarios.
A systematic study of the ground-state properties of even-even rare earth nuclei has been performed in the framework of the Relativistic Mean-Field (RMF) theory using the parameter set NL-SH. Nuclear radii, isotope shifts and deformation properties of the heavier rare-earth nuclei have been obtained, which encompass atomic numbers ranging from Z=60 to Z=70 and include a large range of isospin. It is shown that RMF theory is able to provide a good and comprehensive description of the empirical binding energies of the isotopic chains. At the same time the quadrupole deformations $\beta_{2}$ obtained in the RMF theory are found to be in good agreement with the available empirical values. The theory predicts a shape transition from prolate to oblate for nuclei at neutron number N=78 in all the chains. A further addition of neutrons up to the magic number 82 brings about the spherical shape. For nuclei above N=82, the RMF theory predicts the well-known onset of prolate deformation at about N=88, which saturates at about N=102. The deformation properties display an identical behaviour for all the nuclear chains. A good description of the above deformation transitions in the RMF theory in all the isotopic chains leads to a successful reproduction of the anomalous behaviour of the empirical isotopic shifts of the rare-earth nuclei. The RMF theory exhibits a remarkable success in providing a unified and microscopic description of various empirical data.
Grand unified theories open the possibility to transfer the neutrino mixing matrix U_PMNS to the quark sector. This is accomplished in a controlled way in a supersymmetric grand-unified model proposed by Chang, Masiero and Murayama (CMM model) where the atmospheric neutrino mixing angle induces large new b -> s and tau -> mu transitions. Relating the supersymmetric low-energy parameters to seven new parameters a_0, m_0^2, m_tilde{g}, D, xi, tan beta and arg(mu) of this SO(10) model, we perform a correlated study of several flavour-changing neutral current (FCNC) processes. The CMM model can serve as an alternative benchmark scenario to the popular constraint MSSM.