ShantanuT01/DACTYL-Pretraining huggingface dataset:
We discuss chemical enrichments of ~4000 SDSS early-type galaxies using as tracers the element abundance ratios [C/Fe], [N/Fe], [O/Fe], [Mg/Fe], [Ca/Fe] and [Ti/Fe]. We utilise the stellar population models of absorption line indices from Thomas, Maraston & Johansson (2011) which are based on the MILES stellar library. We confirm previous results of increasing age, [Z/H] and [O/Fe] ratios (most often represented by [{\alpha}/Fe] in the literature) with velocity dispersion. We further derive identical correlations with velocity dispersion for the abundance ratios [O/Fe], [Mg/Fe] and [C/Fe], implying that C/Mg and C/O are close to solar values. This sets a lower limit on the formation time-scales and star-burst components of early-type galaxies to ~0.4 Gyr, which is the lifetime of a 3Msun star, since the full C enrichment must be reached. [N/Fe] correlates with velocity dispersion, but offset to lower values and with a steeper slope compared to the other element ratios. We do not find any environmental dependencies for the abundances of C and N, contrary to previous reports in the literature. [Fe/H] does not correlate with velocity dispersion over the entire parameter range covered, but for fixed age we find a steep trend for the [Fe/H]-{\sigma} relation. This trend is weaker than the analogous for total metallicity (which also shows steeper trends at fixed age) owing to the lower Fe contribution from SN Ia for more massive early-type galaxies. We find [Ca/Fe] ratios that are close to solar values over the entire velocity dispersion range covered. Tentative, due to large scatter, the results for [Ti/Fe] indicate that Ti follows the trends of Ca. This implies a significant contribution from SN Ia to the enrichment of heavy {\alpha}-elements and puts strong constraints on supernova nucleosynthesis and models of galactic chemical evolution.
It is known that Nambu-Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri equation [Rh] for membranes to determine if there are cusps and kinks in the world-sheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu-Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.
Any Zariski dense countable subgroup of $SL(d,R)$ is shown to carry a non-degenerate finitely supported symmetric random walk such that its harmonic measure on the flag space is singular. The main ingredients of the proof are: (1) a new upper estimate for the Hausdorff dimension of the projections of the harmonic measure onto Grassmannians in $R^d$ in terms of the associated differential entropies and differences between the Lyapunov exponents; (2) an explicit construction of random walks with uniformly bounded entropy and Lyapunov exponents going to infinity.
In this paper we consider the multi-dimensional pressureless Euler system and we tackle the problem of existence and uniqueness of sticky particle solutions for general measure-type initial data. Although explicit counterexamples to both existence and uniqueness are known since \cite{Bressan-Nguyen}, the problem of whether one can still find sticky particle solutions for a large set of data and of how one can select them was up to our knowledge still completely open.   In this paper we prove that for a comeager set of initial data in the weak topology the pressureless Euler system admits a unique sticky particle solution given by a free flow where trajectories are disjoint straight lines.   Indeed, such an existence and uniqueness result holds for a broader class of solutions decreasing their kinetic energy, which we call dissipative solutions, and which turns out to be the compact weak closure of the classical sticky particle solutions. Therefore any scheme for which the energy is l.s.c. and is dissipated will converge, for a comeager set of data, to our solution, i.e. the free flow.
We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.
One of the fundamental ground-state properties of nuclei is binding energy. In this study, we have employed artificial neural networks (ANNs) to obtain binding energies based on the data calculated from Hartree-Fock-Bogolibov (HFB) method with the two SLy4 and SKP Skyrme forces. Also, ANNs have been employed to obtain two-neutron and two-proton separation energies of nuclei. Statistical modeling of nuclear data using ANNs has been seen as to be successful in this study. Such a statistical model can be possible tool for searching in systematics of nuclei beyond existing experimental nuclear data.
Bolton et al. (2007) have derived a mass-based fundamental plane using photometric and spectroscopic observations of 36 strong gravitational lenses. The lensing allows a direct determination of the mass-surface density and so avoids the usual dependence on mass-to-light ratio. We consider this same sample in the context of modified Newtonian dynamics (MOND) and demonstrate that the observed mass-based fundamental plane coincides with the MOND fundamental plane determined previously for a set of high-order polytropic spheres chosen to match the observed range of effective radii and velocity dispersions in elliptical galaxies. Moreover, the observed projected mass within one-half an effective radius is consistent with the mass in visible stars plus a small additional component of ``phantom dark matter'' resulting from the MOND contribution to photon deflection.
Solutions in the form of series expansion, as the Born approximation, are very useful for describing time-independent scattering of quantum particles. In this work, it is mathematically demonstred that such solutions, when applied to multiple beam scattering phenomena, can lead to energy violation where the number of incident and scattered particles is not preserved. General basic conditions for developing consistent solutions of time-dependent multiple beam scattering problems are outlined.
We investigate non-thermal electron and nuclei energy losses within the binary neutron star merger remnant produced by the event GW170817. The lack of a cooling feature within the detected synchrotron emission from the source is used to constrain the magnetic field at the mG level, assuming that this emission is electron synchrotron in origin, and that the accelerated spectrum in the electrons follows the form $dN/dE_e \propto E_e^{-2}$. The level of subsequent gamma-ray emission from the source is demonstrated to provide a further constraint on the source magnetic field strength. We also put forward alternative strong ($\sim$G) magnetic field scenarios able to support this emission. For such stronger fields, the photo-disintegration of non-thermal nuclei within the source is considered, and a bottleneck period of $\sim$5-30 days is found when this process peaks. We find that this class of source is in principle able to support the population of cosmic rays detected at Earth below the "ankle".
We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of individuals to infinity, we derive the macroscopic system of nonlinear differential equations describing the evolution of trait distributions in male and female subpopulations. We study solutions, give criteria for persistence or extinction, and state theorem on asymptotic stability, which we apply later to particular examples of trait inheritance.
We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2.
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common properties.   We propose a unified abstract treatment of slope filtrations, and survey how new ties between different domains have been woven by dint of deep correspondences between different concrete slope filtrations.
We present a theoretical study of the structural, electronic and transport properties of bulk Bi2Te3 within density functional theory taking into account the van der Waals interactions (vdW) and the quasiparticle self-energy corrections. It is found that the optB86b-vdW functional can well reproduce the experimental lattice constants and interlayer distances for Bi2Te3. Based on the fully optimized structure, the band structure of Bi2Te3 is obtained from first-principles calculations with the GW approximation and the Wannier function interpolation method. The global band extrema are found to be off the high-symmetry lines, and the real energy band calculated is in good agreement with that measured experimentally. In combination with the Boltzmann theory, the GW calculations also give accurate prediction of the transport properties, and the calculated thermoelectric coefficients of Bi2Te3 almost coincide with the experimental data.
In this paper, we calculate the next to the leading order Casimir energy for real massive and massless scalar fields within $\lambda\phi^{4}$ theory, confined between two parallel plates with the Dirichlet boundary condition in two spatial dimensions. Our results are finite in both cases, in sharp contrast to the infinite result reported previously for the massless case. In this paper we use a renormalization procedure introduced earlier, which naturally incorporates the boundary conditions. As a result our radiative correction term is different from the previously calculated value. We further use a regularization procedure which help us to obtain the finite results without resorting to any analytic continuation techniques.
We study mesoscopic resonant tunneling as well as multichannel Kondo problems by mapping them to a first-quantized quantum mechanical model of a particle moving in a multi-dimensional periodic potential with Ohmic dissipation. From a renormalization group analysis, we obtain phase diagrams of the quantum Brownian motion model with various lattice symmetries. For a symmorphic lattice, there are two phases at T=0: a localized phase in which the particle is trapped in a potential minimum, and a free phase in which the particle is unaffected by the periodic potential. For a non-symmorphic lattice, however, there may be an additional intermediate phase in which the particle is neither localized nor completely free. The fixed point governing the intermediate phase is shown to be identical to the well-known multichannel Kondo fixed point in the Toulouse limit as well as the resonance fixed point of a quantum dot model and a double-barrier Luttinger liquid model. The mapping allows us to compute the fixed-poing mobility $\mu^*$ of the quantum Brownian motion model exactly, using known conformal-field-theory results of the Kondo problem. From the mobility, we find that the peak value of the conductance resonance of a spin-1/2 quantum dot problem is given by $e^2/2h$. The scaling form of the resonance line shape is predicted.
We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which attempts to provide a "scalable" implementation on an expectation-value NMR quantum computer. We show that this ensemble implementation of the DJ algorithm is at best as efficient as the classical random algorithm. As soon as any attempt is made to classify all possible functions with certainty, the implementation requires an exponentially large number of molecules. The discrepancies arise out of the interpretation of mixed state density matrices.
The stellar content of the spiral galaxy NGC 247 is investigated. The main sequence turn-off (MSTO) in the inner 12 kpc of the disk corresponds to an age of 6 Myr. A mean star formation rate (SFR) of 0.1 solar masses per year during the past 16 Myr is computed from star counts. The color of the red supergiant plume does not change with radius, suggesting that the mean metallicity of young stars does not vary by more than 0.1 dex. The number of bright main sequence stars per local stellar mass density climbs towards larger radii out to a distance of 12 kpc; the scale lengths that characterize the radial distributions of young and old stars in the disk thus differ. The density of bright main sequence stars with respect to projected HI mass gradually drops with increasing radius. The population of very young stars disappears in the outer disk; the MSTO at galactocentric radii between 12 and 15 kpc corresponds to 16 Myr, while between 15 and 18 kpc the age is > 40 Myr. Red giant branch (RGB) stars are resolved at a projected minor axis galactocentric distance of 12 kpc. There is a broad spread in metallicity among the RGB stars, with a mean [M/H] = -1.2. The RGB-tip occurs at i' = 24.5 +/- 0.1, indicating that the distance modulus is 27.9 +/- 0.1. Luminous AGB stars with an age 3 Gyr are also seen in this field.
We present new, multiwavelength Very Large Array observations of the 3 radio galaxies in the cluster Abell 119: 0053-015, 0053-016 and 3C 29. The first two radio galaxies, which lie close to the cluster center, show a narrow-angle-tailed structure, with many twists in the tails. The third radio source is located at the cluster periphery, and shows an undistorted FR I morphology. All three radio sources are strongly polarized at the highest frequencies, and all three show both more depolarization and higher Faraday Rotation Measures with increasing proximity to the cluster center. We interpret this polarization behaviour as induced by the magneto-ionized intracluster medium, whose magnetic field is estimated to be in the range 5-10 microG.
This paper is devoted to the problem of blob detection in manifold-valued images. Our solution is based on new definitions of blob response functions. We define the blob response functions by means of curvatures of an image graph, considered as a submanifold. We call the proposed framework Riemannian blob detection. We prove that our approach can be viewed as a generalization of the grayscale blob detection technique. An expression of the Riemannian blob response functions through the image Hessian is derived. We provide experiments for the case of vector-valued images on 2D surfaces: the proposed framework is tested on the task of chemical compounds classification.
We present a deep, wide-field photometric survey of the newly-discovered Hercules dwarf spheroidal galaxy, based on data from the Large Binocular Telescope. Images in B, V and r were obtained with the Large Binocular Camera covering a 23' times 23' field of view to a magnitude of ~25.5 (5 sigma). This permitted the construction of colour-magnitude diagrams that reach approximately 1.5 magnitudes below the Hercules main sequence turnoff. Three-filter photometry allowed us to preferentially select probable Hercules member stars, and examine the structure of this system at a previously unattained level. We find that the Hercules dwarf is highly elongated (3:1), considerably more so than any other dSph satellite of the Milky Way except the disrupting Sagittarius dwarf. While we cannot rule out that the unusual structure is intrinsic to Hercules as an equilibrium system, our results suggest tidal disruption as a likely cause of this highly elliptical structure. Given the relatively large Galactocentric distance of this system (132 +/- 12 kpc), signs of tidal disruption would require the Hercules dwarf to be on a highly eccentric orbit around the Milky Way.
High levels of horizontal magnetic flux have been reported in the quiet-Sun internetwork, often based on Stokes profile inversions. Here we introduce a new method for deducing the inclination of magnetic elements and use it to test magnetic field inclinations from inversions. We determine accurate positions of a set of small, bright magnetic elements in high spatial resolution images sampling different photospheric heights obtained by the Sunrise balloon-borne solar observatory. Together with estimates of the formation heights of the employed spectral bands, these provide us with the inclinations of the magnetic features. We also compute the magnetic inclination angle of the same magnetic features from the inversion of simultaneously recorded Stokes parameters. Our new, geometric method returns nearly vertical fields (average inclination of around 14 deg with a relatively narrow distribution having a standard deviation of 6 deg). In strong contrast to this, the traditionally used inversions give almost horizontal fields (average inclination of 75+-8 deg) for the same small magnetic features, whose linearly polarised Stokes profiles are adversely affected by noise. The almost vertical field of bright magnetic features from our geometric method is clearly incompatible with the nearly horizontal magnetic fields obtained from the inversions. This indicates that the amount of magnetic flux in horizontal fields deduced from inversions is overestimated in the presence of weak Stokes signals, in particular if Stokes Q and U are close to or under the noise level. By combining the proposed method with inversions we are not just improving the inclination, but also the field strength. This technique allows us to analyse features that are not reliably treated by inversions, thus greatly extending our capability to study the complete magnetic field of the quiet Sun.
The gauge dependence of the effective action of composite fields for general gauge theories in the framework of the quantization method by Batalin, Lavrov and Tyutin is studied. The corresponding Ward identities are obtained. The variation of composite fields effective action is found in terms of new set of operators depending on composite field. The theorem of the on-shell gauge fixing independence for the effective action of composite fields in such formalism is proved. brief discussion of gravitational-vector induced interaction for Maxwell theory with composite fields is given.
We consider the lightest Kaluza-Klein particle at N=1 mode (LKP) of universal extra dimension to be the candidate for Dark Matter and predict the detection rates for such particles for Germenium and NaI detectors. We have also calculated the nature of annual modulation for the signals in these two types of detectors for LKP Dark Matter. The rates with different values of speed of solar system in the Galactic rest frame are also evaluated.
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite, background independent, and diffeomorphism-invariant, and therefore well defined on the space of diffeomorphism invariant states (knot states). We find that the spectrum of the volume of any physical region is discrete. A family of eigenstates are in one to one correspondence with the spin networks, which were introduced by Penrose in a different context. We compute the corresponding component of the spectrum, and exhibit the eigenvalues explicitly. The other eigenstates are related to a generalization of the spin networks, and their eigenvalues can be computed by diagonalizing finite dimensional matrices. Furthermore, we show that the eigenstates of the volume diagonalize also the area operator. We argue that the spectra of volume and area determined here can be considered as predictions of the loop-representation formulation of quantum gravity on the outcomes of (hypothetical) Planck-scale sensitive measurements of the geometry of space.
We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package \textsc{SeaSyde}. The implementation solves by series expansions the system of differential equations satisfied by the Master Integrals. At variance with respect to other existing codes, the analytical continuation of the solution is performed in the complex plane associated to each kinematical invariant. We present the results of the evaluation of the Master Integrals relevant for the NNLO QCD-EW corrections to the neutral-current Drell-Yan processes.
The uniaxial elastic-plastic deformation process is considered. Mathematical model of this process was built. According to this model all stable static states form the lattice, which is called the delta-lattice.
Transport equations for quark matter are derived in the mean field approximation for the Nambu -- Jona-Lasinio Lagrangian. Emphasis is put on the chiral limit (zero current quark masses) and the consequences of the chiral symmetry are investigated in detail. Our approach is based on the spinor decomposition of the Wigner function. Kinetic equations for the quark densities and for the spin are derived. We find that the latter is constrained by the requirement of the axial current conservation.
We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems:   v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx}   The conservative case is, in particular, included in the previous formulation.   We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit.   The most interesting points are the following two.   First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$.   Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.
We extend the Zamolodchikov-Faddeev algebra for the superstring sigma model on $AdS_{5}\times S^{5}$, which was formulated by Arutyunov, Frolov and Zamaklar, to the case of open strings attached to maximal giant gravitons, which was recently considered by Hofman and Maldacena. We obtain boundary $S$-matrices which satisfy the standard boundary Yang-Baxter equation.
We study experimentally the fracture dynamics during the peeling at a constant velocity of a roller adhesive tape mounted on a freely rotating pulley. Thanks to a high speed camera, we measure, in an intermediate range of peeling velocities, high frequency oscillations between phases of slow and rapid propagation of the peeling fracture. This so-called stick-slip regime is well known as the consequence of a decreasing fracture energy of the adhesive in a certain range of peeling velocity coupled to the elasticity of the peeled tape. Simultaneously with stick-slip, we observe low frequency oscillations of the adhesive roller angular velocity which are the consequence of a pendular instability of the roller submitted to the peeling force. The stick-slip dynamics is shown to become intermittent due to these slow pendular oscillations which produce a quasi-static oscillation of the peeling angle while keeping constant the peeling fracture velocity (averaged over each stick-slip cycle). The observed correlation between the mean peeling angle and the stick-slip amplitude questions the validity of the usually admitted independence with the peeling angle of the fracture energy of adhesives.