ShantanuT01/DACTYL-Pretraining huggingface dataset:
Motivated by a question of van der Poorten about the existence of infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen consecutively from a sequence in a finite field of odd prime characteristic. We study the arithmetic of such sequences, including bounds for the largest degree of irreducible factors, the number of irreducible factors, as well as for the number of such sequences of fixed length in which all the polynomials are irreducible.
Using the Bond Operator Technique (BOT), we have studied the low energy excitationspectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalizations (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.
The cosmological constant problem is examined under the assumption that the extrinsic curvature of the space-time contributes to the vacuum. A compensation mechanism based on a variable cosmological term is proposed. Under a suitable hypothesis on the behavior of the extrinsic curvature, we find that an initially large $\Lambda(t)$ rolls down rapidly to zero during the early stages of the universe. Using perturbation analysis, it is shown that such vacuum behaves essentially as a spin-2 field which is independent of the metric.
We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.
From experimental and theoretical analyses of magnetic and specific-heat properties, we present the complete magnetic phase diagram of the quasi-one-dimensional antiferromagnet Cu(N$_2$H$_5$)$_2$(SO$_4$)$_2$. On cooling and at zero magnetic field this compound enters a one-dimensional regime with short-range magnetic correlations, marked by a broad maximum in the specific heat and magnetic susceptibility at $T_\mathrm{max}\sim 2\,\mathrm{K}$, followed by an ordered antiferromagnetic phase below $T_\mathrm{N}\sim 1\,\mathrm{K}$ induced by small interchain couplings. The intermediate-temperate one-dimensional regime can be modeled using exact quantum-transfer-matrix calculations, which perfectly describe the nonmonotonic behavior of T_max as a function of the magnetic field, giving $J = 4.25\,\mathrm{K}$ for the intrachain exchange parameter. The analysis of magnetic specific-heat and susceptibility data at low temperature indicates that the interchain exchange couplings are an order of magnitude smaller than the coupling inside the chains.
Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state with the correct multi-component structure. (iii) Close to critical points, plait points, and consolute points, the correct universality and scaling behavior is guaranteed.   This paper discusses semiempirical equations of state for mixtures that express the pressure as an explicit function of temperature and the chemical potentials. In the first part, expressions are derived for the most important thermodynamic quantities. The main result of the second part is the construction of a large family of equations of state with the properties (i)--(iii).
Pinning of magnetic-field induced Wigner molecules (WMs) confined in parabolic two-dimensional quantum dots by a charged defect is studied by an exact diagonalization approach. We found a re-entrant pinning of the WMs as function of the magnetic field, a magnetic field induced re-orientation of the WMs and a qualitatively different pinning behaviour in the presence of a positive and negative Coulomb impurity.
Over the past six years, the Fermi Large Area Telescope has detected more than 150 gamma-ray pulsars, discovering a variety of light curve trends and classes. Such diversity hints at distinct underlying magnetospheric and/or emission geometries. We implemented an offset-dipole magnetic field, with an offset characterised by parameters epsilon and magnetic azimuthal angle, in an existing geometric pulsar modelling code which already includes static and retarded vacuum dipole fields. We use these different magnetic field solutions in conjunction with standard emission geometries, namely the two-pole caustic and outer gap models (the latter only for non-offset dipoles), and construct intensity maps and light curves for several pulsar parameters. We compare our model light curves to the Vela data from the second pulsar catalogue of Fermi. We use a refined chi-square grid search method for finding best-fit light curves for each of the different models. Our best fit is for the retarded vacuum dipole field and the outer gap model.
We present the non-linear theory of shock acceleration applied to SNRs expanding into partially neutral plasma. Using this theory we show how the Balmer lines detected from young SNRs can be used to test the efficiency of shocks in the production of cosmic rays. In particular we investigate the effect of charge-exchange between protons and neutral hydrogen occurring in the precursor formed ahead of the shock. In this precursor the CR pressure accelerate the ionized component of the plasma and a relative velocity between protons and neutral hydrogen is established. On the other hand the charge-exchange process tends to equilibrate ions and neutrals resulting in the heating of both components. We show that even when the shock converts only a few per cent of the total bulk kinetic energy into CRs, the heating is efficient enough to produce a detectable broadening of the narrow Balmer lines emitted by the neutral hydrogen.
The HEGRA system of 4 Imaging Atmospheric Cherenkov Telescopes (IACTs) has been used to determine the flux and the spectrum of cosmic ray protons over a limited energy range around 1.5 TeV. Although the IACT system is designed for the detection of gamma-rays with energies above 500 GeV, it has also a large detection area of $ \simeq 10^6 m^2 \cdot 3 msr$ for primary protons of energies above 1 TeV and the capability to reconstruct the primary proton energy with a reasonable accuracy $\Delta$E/E of 50% near this threshold. Furthermore, the principle of stereoscopic detection of air showers permits the effective suppression of air showers induced by heavier primaries already on the trigger level, and in addition on the software level by analysis of the stereoscopic images. The combination of both capabilities permits a determination of the proton spectrum almost independently of the cosmic ray chemical composition. The accuracy of our estimate of the spectral index at 1.5 TeV is limited by systematic uncertainties and is comparable to the accuracy achieved with recent balloon and space borne experiments. In this paper we describe in detail the analysis tools, namely the detailed Monte Carlo simulation, the analysis procedure and the results. We determine the local (i.e. in the range of 1.5 to 3 TeV) differential spectral index to be $\gamma_p = 2.72\pm 0.02_{stat.}{\pm 0.15}_{syst.}$ and obtain an integral flux above 1.5 TeV of $F(> 1.5 TeV) =3.1\pm 0.6_{stat.}\pm 1.2_{syst.} 10^{-2}/s sr m^2$.
We consider a second-order parabolic equation in $\bR^{d+1}$ with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally H\"older continuous in the space variables. We show that global Schauder estimates hold even in this case. The proof introduces a new localization procedure. Our results show that the constant appearing in the classical Schauder estimates is in fact independent of the $L_{\infty}$-norms of the lower order coefficients. We also give a proof of uniqueness which is of independent interest even in the case of bounded coefficients.
The repulsive-potential Kronig-Penney (KP) model for a one-dimensional band structure is well known. However, real metals contain positively-charged ions resulting in attractive potential wells seen by the metallic electrons. Here we consider the latter case in detail. The square-well version of the KP model is considered first, for which the band structure and wave functions for different potential-well depths are derived. Then an extended treatment of the attractive Dirac-comb version of the KP model is presented. For the nearly-free-electron case, the band structure exhibits a negative-energy band in addition to positive-energy bands. The wave functions, electron densities of states, effective masses, and group velocities are derived for the positive-energy band states. The wave functions of the negative-energy band states are also calculated and found to be quite different from the sinusoidal wave functions for the positive-energy band and band-gap states. High-degeneracy bound states are found at negative energies and their wave functions are derived.
We carry out numerical simulations of the gravitational collapse of a rotating perfect fluid with the ultrarelativistic equation of state $P=\kappa\rho$, in axisymmetry in $2+1$ spacetime dimensions with $\Lambda<0$. We show that for $\kappa \lesssim 0.42$, the critical phenomena are type I and the critical solution is stationary. The picture for $\kappa \gtrsim 0.43$ is more delicate: for small angular momenta, we find type II phenomena and the critical solution is quasistationary, contracting adiabatically. The spin-to-mass ratio of the critical solution increases as it contracts, and hence so does that of the black hole created at the end as we fine-tune to the black-hole threshold. Forming extremal black holes is avoided because the contraction of the critical solution smoothly ends as extremality is approached.
In this paper we count the number of some particular quadruple persymmetric rank i matrices over F_2.
The radial motion of massive particles in the equatorial plane of the Kerr black hole is considered. Screening of the Hawking radiation and shielding of the Penrose process are examined (both insides and outside the ergosphere) and their effects on the evaporation of the black hole is studied. In particular, the locus and width of a classically forbidden region and their dependence on the particle's angular momentum and energy is analysed. Tunneling of particles between the boundaries of this region is considered and the transmission coefficient is determined.
Whole-body 3D human mesh estimation aims to reconstruct the 3D human body, hands, and face simultaneously. Although several methods have been proposed, accurate prediction of 3D hands, which consist of 3D wrist and fingers, still remains challenging due to two reasons. First, the human kinematic chain has not been carefully considered when predicting the 3D wrists. Second, previous works utilize body features for the 3D fingers, where the body feature barely contains finger information. To resolve the limitations, we present Hand4Whole, which has two strong points over previous works. First, we design Pose2Pose, a module that utilizes joint features for 3D joint rotations. Using Pose2Pose, Hand4Whole utilizes hand MCP joint features to predict 3D wrists as MCP joints largely contribute to 3D wrist rotations in the human kinematic chain. Second, Hand4Whole discards the body feature when predicting 3D finger rotations. Our Hand4Whole is trained in an end-to-end manner and produces much better 3D hand results than previous whole-body 3D human mesh estimation methods. The codes are available here at https://github.com/mks0601/Hand4Whole_RELEASE.
[Abridged] Context. The high-energy radiation from black-hole binaries may be due to the reprocessing of a lamp located on the black hole axis, emitting X-rays. The observed spectrum is made of 3 components: the direct spectrum; the thermal bump; and the reflected spectrum made of the Compton hump and the iron-line complex.   Aims. We aim at computing accurately the complete reprocessed spectrum (thermal bump + reflected) of black-hole binaries over the entire X-ray band. We also determine the strength of the direct component. Our choice of parameters is adapted to a source showing an important thermal component.   Methods. We compute in full GR the illumination of a thin disk by a lamp along the rotation axis. We use the ATM21 radiative transfer code to compute the spectrum emitted along the disk. We ray trace this local spectrum to determine the reprocessed spectrum as observed at infinity. We discuss the dependence of the local and ray-traced spectra on the emission angle and spin.   Results. We show the importance of the angle dependence of the total disk specific intensity spectrum emitted by the illuminated atmosphere when the thermal disk emission if fully taken into account. High spin implies high temperature in the inner regions, so the emitted thermal disk spectrum covers the iron-line complex. As a result we locally observe absorption lines produced in the hot disk atmosphere. Absorption lines are narrow and disappear after ray tracing the local spectrum.   Conclusions. Our results mainly highlight the importance of considering the angle dependence of the local spectrum when computing reprocessed spectra, as was already found in a recent study. The main new result of our work is to show the importance of computing the thermal bump of the spectrum, as this feature can change considerably the observed iron-line complex.
Recent experimental measurements of magnetoresistance in dual spin valves [A. Aziz et al., Phys. Rev. Lett. 103, 237203 (2009)] reveal some nonlinear features of transport, which have not been observed in other systems. We propose a phenomenological model describing current-dependent resistance (and giant magnetoresistance) in double spin valves. The model is based on a modified Valet-Fert approach, and takes into account the dependence of bulk/interface resistance and bulk/interface spin asymmetry parameters for the central magnetic layer on spin accumulation, and consequently on charge current. Such a nonlinear model accounts for recent experimental observations.
We employ optical and UV observations to present SEDs for two reverberation-mapped samples of super-Eddington and sub-Eddington AGN with similar luminosity distributions. The samples are fitted with accretion disc models in order to look for SED differences that depend on the Eddington ratio. The fitting takes into account measured BH mass and accretion rates, BH spin and intrinsic reddening of the sources. All objects in both groups can be fitted by thin AD models over the range 0.2-1$\,\mu$m with reddening as a free parameter. The intrinsic reddening required to fit the data are relatively small, $E(B-V)\leq0.2$~mag, except for one source. Super-Eddington AGN seem to require more reddening. The distribution of $E(B-V)$ is similar to what is observed in larger AGN samples. The best fit disc models recover very well the BH mass and accretion for the two groups. However, the SEDs are very different, with super-Eddington sources requiring much more luminous far-UV continuum. The exact amount depends on the possible saturation of the UV radiation in slim discs. In particular, we derive for the super-Eddington sources a typical bolometric correction at 5100\AA{} of 60-150 compared with a median of $\sim$20 for the sub-Eddington AGN. The measured torus luminosity relative to $\lambda L_{\lambda}(5100\AA{}$) are similar in both groups. The $\alpha_{OX}$ distribution is similar too. However, we find extremely small torus covering factors for super-Eddington sources, an order of magnitude smaller than those of sub-Eddington AGN. The small differences between the groups regarding the spectral range 0.2-22$\,\mu$m, and the significant differences related to the part of the SED that we cannot observed may be consistent with some slim disc models. An alternative explanation is that present day slim-disc models over-estimate the far UV luminosity of such objects by a large amount.
We are surrounded by radiation that originated from the big bang. It has traveled to us from the farthest reaches of the Universe, carrying with it an unaltered record of the beginning of time and space. The radiation is in the form of gravitational waves - propagating ripples in the curvature of spacetime. We describe a mission to detect these Gravitational Echos Across Time (GREAT) that would open up a new window on the very early universe. By studying the gravitational echoes of the big bang we will gain insight into the fundamental structure of matter, gravity, and how the Universe formed.
The "triple-Regge" analysis of subleading Reggeon contributions to the diffractive structure function in DIS at HERA is presented. The recently published data allow to estimate the only free parameter of the analysis related to the ratio of the RRP and PPP couplings. The large value of this ratio is prefered which is in agreement with analyses of soft hadronic interactions. The role of the subleading Reggeons as well as pions for the fast forward neutron production in diffractive processes is estimated. The forward piN state production is also discussed.
We investigate the properties of the intracluster medium (ICM) that forms within N-body/hydrodynamical simulations of galaxy clusters in a \LambdaCDM cosmology. When radiative cooling and a simple model for galactic feedback are included, our clusters have X-ray luminosities and temperatures in good agreement with observed systems, demonstrating the required excess entropy in their cores. More generally, cooling and feedback increases the entropy of the ICM everywhere, albeit without significantly affecting the slope of the profile (S prop. to r) at large radii. The temperature of the ICM is only modestly increased by these processes, with projected temperature profiles being in reasonable agreement with the observations. Star/galaxy formation is still too efficient in our simulations, however, and so our gas mass fractions are around 60 per cent of the observed value at r_{2500}. Finally, we examine the reliability of using the hydrostatic equilibrium equation to estimate cluster masses and find that it underpredicts the true mass of our clusters by up to 20 per cent, due to incomplete thermalisation of the gas. Feedback reduces this discrepancy, however, with estimates being accurate to within 10 per cent out to r_{500}.
Several deep observations such as those carried out at the Canada-France-Hawaii Telescope (CFHT) have revealed prominent Low Surface Brightness (LSB) fine structures that change the apparent morphology of galaxies. Previous photometry surveys have developed observational techniques which exploit the diffuse light detected in the external regions of galaxies. In these studies the outer perturbations have been identified and classified like tidal tails, stellar streams, and shells. These structures are tracers of interacting and merging events and they keep a memory of the mass assembly of galaxies. Cosmological numerical simulations are needed to estimate their visibility time-scale (among other properties) in order to reconstruct the past merger history of galaxies. In the present work, we analyze a hydrodynamical cosmological simulation to build a comprehensive interpretation of the properties of fine structures. We make a census of several types of LSB fine structures by visual inspection of individual snapshots at various time. We reconstruct the evolution of the number of fine structures detected around an early-type galaxy and we compare with the merger history of the galaxy. We find that most of fine structures are associated with major and intermediate mass merger events. Their survival time scale ranges between 0.7 and 4 Gyr. Shells and streams remain visible for a longer time than tidal tails. These estimates of survival times provide clues to interpret the shape and frequency of fine structures observed in deep images in terms of mass assembly. We find that the detectability of stellar streams is the most sensitive to the surface brightness limit. We see 2-3 times more streams with a surface brightness cut of 33 mag arcsec$^{-2}$ than with 29 mag arcsec$^{-2}$. The detection of shells display a strong dependence on the projection angle.
CeAu2Ge2 single crystals (tetragonal ThCr2Si2 structure) have been grown in Au-Ge flux (AGF) as well as in Sn flux (SF). X-ray powder-diffraction and EDX measurements indicate that in the latter case Sn atoms from the flux are incorporated in the samples, leading to a decrease of the lattice constants by ~ 0.3% compared to AGF samples. For both types of samples, a strong anisotropy of the magnetization M for the magnetic field B parallel and perpendicular to the c direction is observed with M||/M^{\bot} ~ 6 - 7 in low fields just above 10 K. This anisotropy is preserved to high fields and temperatures and can be quantitatively explained by crystal electric field effects. Antiferromagnetic ordering sets in around 10 K as previously found for polycrystalline samples. From the magnetization data of our single crystals we obtain the phase diagrams for the AGF and SF samples. The magnetic properties depend strongly on the flux employed. While the AGF samples exhibit a complex behavior indicative of several magnetic transitions, the SF samples adopt a simpler antiferromagnetic structure with a single spin-flop transition. This effect of a more ordered state induced by disorder in form of Sn impurities is qualitatively explained within the ANNNI model, which assumes ferromagnetic and antiferromagnetic interactions in agreement with the magnetic structure previously inferred from neutron-scattering experiments on polycrystalline CeAu2Ge2 by Loidl et al. [Phys. Rev. B 46, 9341, (1992)].
We present Atacama Large Millimeter/Submillimeter Array observations of the rest-frame far-infrared (FIR) dust continuum emission of six bright Lyman-break galaxies (LBGs) at $z \simeq 7$. One LBG is detected ($5.2\sigma$ at peak emission), while the others remain individually undetected at the $3\sigma$ level. The average FIR luminosity of the sample is found to be $L_{\rm FIR} \simeq 2 \times 10^{11}\,{\rm L}_{\odot}$, corresponding to an obscured star-formation rate (SFR) that is comparable to that inferred from the unobscured UV emission. In comparison to the infrared excess (IRX$\,=L_{\rm FIR}/L_{\rm UV}$)-$\beta$ relation, our results are consistent with a Calzetti-like attenuation law (assuming a dust temperature of T = 40-50 K). We find a physical offset of 3 kpc between the dust continuum emission and the rest-frame UV light probed by Hubble Space Telescope imaging for galaxy ID65666 at $z = 7.17^{+0.09}_{-0.06}$. The offset is suggestive of an inhomogeneous dust distribution, where 75% of the total star formation activity (SFR$ \,\simeq 70\,{\rm M}_{\odot}/{\rm yr}$) of the galaxy is completely obscured. Our results provide direct evidence that dust obscuration plays a key role in shaping the bright-end of the observed rest-frame UV luminosity function at $z \simeq 7$, in agreement with cosmological galaxy formation simulations. The existence of a heavily-obscured component of galaxy ID65666 indicates that dusty star-forming regions, or even entire galaxies, that are "UV-dark" are significant even in the $z \simeq 7$ galaxy population.
We consider the Dirichlet series associated to the number of representations of an integer as the sum of primes. Assuming the Riemann hypothesis on the distribution of the zeros of the Riemann zeta function we obtain the domain of meromorphic continuation of this series.