ShantanuT01/DACTYL-Pretraining huggingface dataset:
The pulsar current, in the $P$--$ {\dot P}$ plane where $P$ is the pulsar period and ${\dot P}$ is the period derivative, is used as a supposedly ``model free'' way to estimate the pulsar birthrate from statistical data on pulsars. We reconsider the derivation of the kinetic equation on which this is based, and argue that the interpretation of the pulsar current is strongly model dependent, being sensitive to the form of the assumed evolution law for pulsars. We discuss the case where the trajectory of a pulsar is assumed to be of the form ${\dot P}=KP^{2-n}$ with $K$ and $n$ constant, and show that (except for $n=2$) one needs to introduce a pseudo source term in order to infer the birthrate from the pulsar current. We illustrate the effect of this pseudo source term using pulsar data to estimate the birthrate for different choices of $n$. We define and discuss an alternative ``potential'' class of evolution laws for which this complication is avoided due to the pseudo source term being identically zero.
We present brane constructions in Type IIA string theory for N=1 supersymmetric SO and Sp gauge theories with tensor representations using an orientifold 6-plane. One limit of these set-ups corresponds to N=2 theories previously constructed by Landsteiner and Lopez, while a different limit yields N=1 SO or Sp theories with a massless tensor and no superpotential. For the Sp-type orientifold projection comparison with the field theory moduli space leads us to postulate two new rules governing the stability of configurations of D-branes intersecting the orientifold. Lifting one of our configurations to M-theory by finding the corresponding curves, we re-derive the N=1 dualities for SO and Sp groups using semi-infinite D4 branes.
In this letter we present an expression relating the cohesive energy for the A3B5 and A2B6 semiconductors with the product of their ionic charges and nearest neighbor distance. The cohesive energy values of these solids exhibits a linear relationship when plotted on a log-log scale against the nearest neighbor distance, but fall on different straight lines according to the ionic charge product of the solids. A good agreement has been found between the experimental and calculated values of the cohesive energy for A3B5 and A2B6 semiconductors.
We study the derivative nonlinear wave equation \( - \partial_{tt} u + \Delta u = |\nabla u|^2 \) on \( \mathbb{R}^{1+3} \). The deterministic theory is determined by the Lorentz-critical regularity \( s_L = 2 \), and both local well-posedness above \( s_L \) as well as ill-posedness below \( s_L \) are known. In this paper, we show the local existence of solutions for randomized initial data at the super-critical regularities \( s\geq 1.984\). In comparison to the previous literature in random dispersive equations, the main difficulty is the absence of a (probabilistic) nonlinear smoothing effect. To overcome this, we introduce an adaptive and iterative decomposition of approximate solutions into rough and smooth components. In addition, our argument relies on refined Strichartz estimates, a paraproduct decomposition, and the truncation method of de Bouard and Debussche.
We present the last version of {\scshape{Hyperion}} (HYdrodynamic Ppm Explosion with Radiation diffusION), a hydrodynamic code designed to calculate the explosive nucleosynthesis, remnant mass and light curve associated to the explosion of a massive star. By means of this code we compute the explosion of a subset of red supergiant models, taken from the database published by \cite{lc18}, for various explosion energies in the range $\rm \sim 0.20-2.00~10^{51}~erg$. The main outcomes of these simulations, i.e., remnant mass, $\rm ^{56}Ni$ synthesized, luminosity and length of the plateau of the bolometric light curve, are analyzed as a function of the initial parameters of the star (mass and metallicity) and of the explosion energy. As a first application of {\scshape{Hyperion}} we estimated the mass and the metallicity of the progenitor star of SN 1999em, a well studied SN IIP, by means of the light curve fitting. In particular, if the adopted distance to the host galaxy NGC 1637 is $\rm 7.83~Mpc$, the properties of the light curve point toward a progenitor with an initial mass of $\rm 13~M_\odot$ and a metallicity [Fe/H]=-1. If, on the contrary, the adopted distance modulus is $\rm 11.7~Mpc$, all the models with initial mass $13\leq M/M_\odot\leq 15$ and metallicities $\rm -1\leq [Fe/H] \leq 0$ are compatible with the progenitor of SN 1999em.
An essentially "complete" description of the low-energy nuclear structure of the superfluid nucleus $^{120}$Sn and of its odd-$A$ neighbors is provided by the observations carried out with the help of Coulomb excitation and of one-- and of two-- particle transfer reactions, specific probes of vibrations, quasiparticle and pairing degrees of freedom respectively, and of their mutual couplings. These experimental findings are used to stringently test the predictions of a similarly "complete" description of $^{119,120,121}$Sn carried out in terms of elementary modes of excitation which, through their interweaving, melt together into effective fields, each displaying properties reflecting that of all others, there individuality resulting from the actual relative importance of each one. Its implementation is done by solving the Nambu-Gor'kov equations including, for the first time, all medium polarization effects resulting from the interweaving of quasiparticles, spin and surface vibrations, taking into account, within the framework of nuclear field theory (NFT), the variety of processes leading to self-energy, vertex and Pauli principle corrections, and to the induced pairing interaction. Theory provides an overall quantitative account of the experimental findings. From these results one can, not only obtain strong circumstantial evidence for the inevitability for the dual origin of pairing in nuclei but also, extract information which can be used at profit to quantitatively disentangle the contributions to pairing correlations in general and to the pairing gap in particular, arising from the bare and from the induced pairing interactions.
We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$, where $p$ is an odd prime. The isomorphisms are given by twisted sums of the components of vector-valued modular forms. Our results generalize work of Bruinier and Bundschuh to the case that the components $F_{\gamma}$ of the vector-valued modular form are antisymmetric in the sense that $F_{\gamma} = -F_{-\gamma}$ for all $\gamma \in A$. As an application, we compute restrictions of Doi-Naganuma lifts of odd weight to components of Hirzebruch-Zagier curves.
Shear viscosity $\eta$ is calculated for the nuclear matter described as a system of interacting nucleons with the van der Waals (VDW) equation of state. The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of the collective overdamped motion. In the frequent-collision regime, the shear viscosity depends on the particle-number density $n$ through the mean-field parameter $a$, which describes attractive forces in the VDW equation. In the temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the entropy density $s$ is smaller than 1 at the nucleon number density $n =(0.5 - 1.5)\,n^{}_0$, where $n^{}_0=0.16\,$fm$^{-3}$ is the particle density of equilibrium nuclear matter at zero temperature. A minimum of the $\eta/s$ ratio takes place somewhere in a vicinity of the critical point of the VDW system. Large values of $\eta/s\gg 1$ are, however, found in both the low-density, $n\ll n^{}_0$, and high-density, $n>2n^{}_0$, regions. This makes the ideal hydrodynamic approach inapplicable for these densities.
Rotational glitches in some rotation-powered pulsars display power-law size and exponential waiting time distributions. These statistics are consistent with a state-dependent Poisson process, where the glitch rate is an increasing function of a global stress variable (e.g. crust-superfluid angular velocity lag), diverges at a threshold stress, increases smoothly while the star spins down, and decreases step-wise at each glitch. A minimal, seven-parameter, maximum likelihood model is calculated for PSR J1740-3015, PSR J0534+2200, and PSR J0631+1036, the three objects with the largest samples whose glitch activity is Poisson-like. The estimated parameters have theoretically reasonable values and contain useful information about the glitch microphysics. It is shown that the maximum likelihood, state-dependent Poisson model is a marginally (23-27 per cent) better post factum "predictor" of historical glitch epochs than a homogeneous Poisson process for PSR J1740-3015 and PSR J0631+1036 and a comparable predictor for PSR J0534+2200. Monte Carlo simulations imply that > 50 glitches are needed to test reliably whether one model outperforms the other. It is predicted that the next glitch will occur at Modified Julian Date (MJD) 57784 +/- 256.8, 60713 +/- 1935, and 57406 +/- 1444 for the above three objects respectively. The analysis does not apply to quasiperiodic glitchers like PSR J0537-6910 and PSR J0835-4510, which are not described accurately by the state-dependent Poisson model in its original form.
One-dimensional spin-1/2 systems are well-known candidates to study the quantum correlations between particles. In the condensed matter physics, studies often are restricted to the 1st neighbor particles. In this work, we consider the 1D XXZ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature, using an analytical approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the efficiency of the QD with respect to the entanglement in the detection of critical points (CPs) as the neighboring spin pairs go farther than the next nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the 2nd neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast to the pairwise entanglement, two-site quantum discord is effectively long-range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal quantum discord between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.
Magnetic massive stars comprise approximately 10% of the total OB star population. Modern spectropolarimetry shows these stars host strong, stable, large-scale, often nearly dipolar surface magnetic fields of 1 kG or more. These global magnetic fields trap and deflect outflowing stellar wind material, forming an anisotropic magnetosphere that can be probed with wind-sensitive UV resonance lines. Recent HST UV spectra of NGC 1624-2, the most magnetic O star observed to date, show atypically unsaturated P-Cygni profiles in the Civ resonant doublet, as well as a distinct variation with rotational phase. We examine the effect of non-radial, magnetically-channeled wind outflow on P-Cygni line formation, using a Sobolev Exact Integration (SEI) approach for direct comparison with HST UV spectra of NGC 1624-2. We demonstrate that the addition of a magnetic field desaturates the absorption trough of the P-Cygni profiles, but further efforts are needed to fully account for the observed line profile variation. Our study thus provides a first step toward a broader understanding of how strong magnetic fields affect mass loss diagnostics from UV lines.
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all alpha > 0 in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite size scaling implications of this are characterized. The exponents characterizing the steady state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean field approximation and found to compare well with the results from numerical simulations in one dimension.
Motivated by independent results of Bizley and Duchon, we study rational Dyck paths and their subset of factor-free elements. On the one hand, we give a bijection between rational Dyck paths and regular Dyck paths with ascents colored by factor-free words. This bijection leads to a new statistic based on the reducibility level of the paths for which we provide a corresponding formula. On the other hand, we prove an inverse relation for certain sequences defined via partial Bell polynomials, and we use it to derive a formula for the enumeration of factor-free words. In addition, we give alternative formulas for various enumerative sequences that appear in the context of rational Dyck paths.
In this paper we study the class of backward doubly stochastic differential equations (BDSDEs, for short) whose terminal value depends on the history of forward diffusion. We first establish a probabilistic representation for the spatial gradient of the stochastic viscosity solution to a quasilinear parabolic SPDE in the spirit of the Feynman-Kac formula, without using the derivatives of the coefficients of the corresponding BDSDE. Then such a representation leads to a closed-form representation of the martingale integrand of BDSDE, under only standard Lipschitz condition on the coefficients.
The goal of this article is to define an analogue of the Weil-pairing for Drinfeld modules using explicit formulas and to deduce its main properties from these formulas. Our result generalizes the formula currently known for rank 2 Drinfeld modules and works as a more explicit, elementary proof of the Weil-pairing's existence than the one appearing in the current literature.
This paper shows the first synthetic tomography of the quiet solar chromosphere formed by spatial maps of scattering polarization. It has been calculated for the CaII 8498, 8542 and 3934 A lines by solving the NLTE (non-local thermodynamical equilibrium) RT (radiative transfer) problem of the second kind in a 3D atmosphere model obtained from realistic MHD (magneto-hydrodynamical) simulations. Maps of circular polarization were calculated neglecting atomic polarization. Our investigation focuses on the linear polarization signals induced by kinematics, radiation field anisotropy and Hanle effect in forward-scattering geometry. Thus, instead of considering slit profiles at the limb as normally done in the study of the second solar spectrum, we synthetize and analyze spatial maps of polarization at disk center. It allows us to understand the spatial signatures of dynamics and magnetic field in the linear polarization for discriminating them observationally. Our results suggest new ideas for chromospheric diagnosis that will be developed throughout a serie of papers. In particular, Hanle Polarity Inversion Lines and dynamic Hanle diagrams are two concepts introduced in the present work. We find that chromospheric dynamics and magnetic field topology create spatial fingerprints in the polarization maps that trace the dynamic situation of the plasma and the magnetic field. Based on such spatial features we reconstruct the magnetic field intensity in the middle chromosphere along grooves of null linear polarization. We finally address the problems of diagnosing Hanle saturation and kinematic amplification of scattering signals using Hanle diagrams.
Quasi-one-dimensional iron-based ladders and chains, with the 3$d$ iron electronic density $n = 6$, are attracting considerable attention. Recently, a new iron chain system Ba$_2$FeS$_3$, also with $n = 6$, was prepared under high-pressure and high-temperature conditions. Here, the magnetic and electronic phase diagrams are theoretically studied for this quasi-one-dimensional compound. Based on first-principles calculations, a strongly anisotropic one-dimensional electronic band behavior near the Fermi level was observed. In addition, a three-orbital electronic Hubbard model for this chain was constructed. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group (DMRG) method, we studied the ground-state phase diagram. A robust staggered $\uparrow$-$\downarrow$-$\uparrow$-$\downarrow$ AFM region was unveiled in the chain direction, consistent with our density functional theory (DFT) calculations. Furthermore, at intermediate Hubbard $U$ coupling strengths, this system was found to display an orbital selective Mott phase (OSMP) with one localized orbital and two itinerant metallic orbitals. At very large $U/W$ ($W$ = bandwidth), the system displays Mott insulator characteristics, with two orbitals half-filled and one doubly occupied. Our results for high pressure Ba$_2$FeS$_3$ provide guidance to experimentalists and theorists working on this one-dimensional iron chalcogenide chain material.
Doppler tomography is a well-known method in astrophysics to image the accretion flow, often in the shape of thin discs, in compact binary stars. As accretion discs rotate, all emitted line radiation is Doppler-shifted. In fast-ion D-alpha (FIDA) spectroscopy measurements in magnetically confined plasma, the D-alpha-photons are likewise Doppler-shifted ultimately due to gyration of the fast ions. In either case, spectra of Doppler-shifted line emission are sensitive to the velocity distribution of the emitters. Astrophysical Doppler tomography has lead to images of accretion discs of binaries revealing bright spots, spiral structures, and flow patterns. Fusion plasma Doppler tomography has lead to an image of the fast-ion velocity distribution function in the tokamak ASDEX Upgrade. This image matched numerical simulations very well. Here we discuss achievements of the Doppler tomography approach, its promise and limits, analogies and differences in astrophysical and fusion plasma Doppler tomography, and what can be learned by comparison of these applications.
We here report a spectroscopic identification of two new changing-look AGNs (CL-AGNs): SDSS\,J104705.16+544405.8 and SDSS\,J120447.91+170256.8 both with a "turn-off" type transition from type 1 to type 1.8/1.9. The identification is arrived by a follow-up spectroscopic observation of the five changing-look AGN (CL-AGN) candidates that are extracted from the sample recently released in Macleod et al. The candidates are extract by the authors from the Sloan Digit Sky Survey Data Release 7 spectroscopically confirmed quasars with large amplitude variability. By compiling a sample of 26 previously identified CL-AGNs, we confirm the claim in Macleod et al. that CL-AGNs tend to be biased against low Eddington ratio, and identify an overlap between the CL-AGNs at their dim state and the so-called intermediate-type AGNs. The overlap implies that there two populations of the intermediate-type AGNs with different origins. One is due to the torus orientation effect, and the another the intrinsic change of the accretion rate of the central supermassive blackholes.
We investigate numerically the magnetisation dynamics of an array of nano-disks interacting through the magneto-dipolar coupling. In the presence of a temperature gradient, the chain reaches a non-equilibrium steady state where energy and magnetisation currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schr\"odinger (DNLS) equation. This model makes transparent the transport properties of the system and allows for a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a novel setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model
In this paper we present our study of the gamma-ray emission from the microquasar SS433. Integrating over 9 years of Fermi-LAT \textsc{pass8} data, we detect SS433 with a significance of ~13$\sigma$ in the 200 to 500 MeV photon energy range, with evidence for an extension in the direction of the w1 X-ray `hotspot`. A temporal analysis reveals evidence for modulation of SS433's gamma-ray emission with the precession period of its relativistic jet. This suggests that at least some of SS433's gamma-ray emission originates close to the object rather than from the jet termination regions.
To investigate statistically whether magnetic fields in massive stars are ubiquitous or appear in stars with specific spectral classification, certain ages, or in a special environment, we acquired 41 new spectropolarimetric observations for 36 stars. Among the observed sample roughly half of the stars are probable members of clusters at different ages, whereas the remaining stars are field stars not known to belong to any cluster or association.   Spectropolarimetric observations were obtained during three different nights using the low-resolution spectropolarimetric mode of FORS2 (FOcal Reducer low dispersion Spectrograph) mounted on the 8-m Antu telescope of the VLT. To assess the membership in open clusters and associations, we used astrometric catalogues with the best currently available kinematic and photometric data.   A field at a significance level of 3sigma was detected in ten O-type stars. Importantly, the largest longitudinal magnetic fields were measured in two Of?p stars: <B_z>=-381+-122G for CPD-282561 and <B_z>=-297+-62G for HD148937, previously detected by us as magnetic. The obtained observations of HD148937 on three different nights indicate that the magnetic field is slightly variable. Our new measurements support our previous conclusion that large-scale organized magnetic fields with polar field strengths in excess of 1kG are not widespread among O-type stars. Among the stars with a detected magnetic field, only one star, HD156154, belongs to an open cluster at high membership probability. According to previous kinematic studies, four magnetic O-type stars in the sample are well-known candidate runaway stars.
In this paper, we study conditions under which the solutions of a backward stochastic differential equation with jump remains in a given set of constrains. This property is the so-called "viability property". As an application, we study the comparison theorem for multidimensional BSDEs with jumps.
The quantum diffusion approach is extended to low energy fusion (capture) reactions of light- and medium-mass nuclei. The dependence of the friction parameter on bombarding energy is taken into account. A simple analytic expression is obtained for the capture probability at extreme sub-barrier energies. The calculated cross-sections are in a good agreement with the experimental data. The fusion excitation functions calculated within the quantum diffusion and WKB approaches are compared and presented in the astrophysical $S$-factor representation.