ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we initiate the study of the class of cubic Kummer type towers considered by Garcia, Stichtenoth and Thomas in 1997 by classifying the asymptotically good ones in this class.
We revisit the neutrino and ultra high-energy cosmic ray (UHECR) production from gamma-ray bursts (GRBs) with time-dependent simulations for the proton-induced cascades. This method can generate self-consistent photon, neutrino and escaped neutron spectra. To obtain the integrated background spectra, we take into account the distributions of the burst luminosity and pulse duration timescale. A benchmark case with standard GRB luminosity function, a bulk Lorentz factor $\Gamma=300$ and a proton to gamma-ray luminosity fraction $f_{\rm p}=10$, is consistent with both the neutrino upper-limits and the observed UHECR intensity at $\sim 10^{20}$ eV, while requiring a different type of UHECR source at the ankle. For the benchmark case the GRBs in the bright end of the luminosity function, which contribute most of the neutrinos, have their photon spectrum substantially distorted by secondary photons. Such bright GRBs are few in number, and reducing their $f_p$ eliminates the distortion, while reducing the neutrino production. Even if we neglect the contribution of the brightest GRBs, the UHECR production rate at GZK energies is almost unchanged. These nominal GRB models, especially with $L_{\rm iso} \lesssim 10^{53} ~\mbox{erg} ~\mbox{s}^{-1}$, appear to meet the current constraints as far as being candidate UHECR sources above the ankle energy.
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that these operators reduce to the conventional ones which are the starting point in standard supersymmetric quantum mechanics. In this context, we argue furthermore that supersymmetry does not only connect Schr\"odinger-like operators, but also a more general class of differential operators. Second, we revisit the supersymmetric $\varepsilon$-system recently introduced in the literature by exploiting its intrinsic supersymmetry. Specifically, combining the Hamilton hierarchy method and the $\delta$-expansion method, we determine an energy for the first excited state of the bosonic Hamiltonian close to that calculated in earlier works.
In this work we propose a car cellular automaton model that reproduces the experimental behavior of traffic flows in Bogot\'a. Our model includes three elements: hysteresis between the acceleration and brake gaps, a delay time in the acceleration, and an instantaneous brake. The parameters of our model were obtained from direct measurements inside a car on motorways in Bogot\'a. Next, we simulated with this model the flux-density fundamental diagram for a single-lane traffic road and compared it with experimental data. Our simulations are in very good agreement with the experimental measurements, not just in the shape of the fundamental diagram, but also in the numerical values for both the road capacity and the density of maximal flux. Our model reproduces, too, the qualitative behavior of shock waves. In addition, our work identifies the periodic boundary conditions as the source of false peaks in the fundamental diagram, when short roads are simulated, that have been also found in previous works. The phase transition between free and congested traffic is also investigated by computing both the relaxation time and the order parameter. Our work shows how different the traffic behavior from one city to another can be, and how important is to determine the model parameters for each city.
The Chamaeleon molecular cloud complex is one of the nearest star-forming sites encompassing three molecular clouds with a different star-formation history, from quiescent (Cha III) to actively forming stars (Cha II), and reaching the end of star-formation (Cha I). To charactize its large-scale structure, we derived column density and temperature maps using PACS and SPIRE observations from the Herschel Gould Belt Survey, and applied several tools, such as filament tracing, power-spectra, \Delta-variance, and probability distribution functions of column density (PDFs), to derive physical properties. The column density maps reveal a different morphological appearance for the three clouds, with a ridge-like structure for Cha I, a clump-dominated regime for Cha II, and an intricate filamentary network for Cha III. The filament width is measured to be around 0.12\pm0.04 pc in the three clouds, and the filaments found to be gravitationally unstable in Cha I and II, but mostly subcritical in Cha III. Faint filaments (striations) are prominent in Cha I showing a preferred alignment with the large-scale magnetic field. The PDFs of all regions show a lognormal distribution at low column densities. For higher densities, the PDF of Cha I shows a turnover indicative of an extended higher density component, culminating with a power-law tail. Cha II shows a power-law tail with a slope characteristic of gravity. The PDF of Cha III can be best fit by a single lognormal. The turbulence properties of the three regions are found to be similar, pointing towards a scenario where the clouds are impacted by large-scale processes. The magnetic field could possibly play an important role for the star-formation efficiency in the Chamaeleon clouds if proven that it can effectively channel material on Cha I, and possibly Cha II, but probably less efficiently on the quiescent Cha III cloud.
Fiber-fed multi-object spectroscopic surveys, with their ability to collect an unprecedented number of redshifts, currently dominate large-scale structure studies. However, physical constraints limit these surveys from successfully collecting redshifts from galaxies too close to each other on the focal plane. This ultimately leads to significant systematic effects on galaxy clustering measurements. Using simulated mock catalogs, we demonstrate that fiber collisions have a significant impact on the power spectrum, $P(k)$, monopole and quadrupole that exceeds sample variance at scales smaller than $k\sim0.1~h/Mpc$.   We present two methods to account for fiber collisions in the power spectrum. The first, statistically reconstructs the clustering of fiber collided galaxy pairs by modeling the distribution of the line-of-sight displacements between them. It also properly accounts for fiber collisions in the shot-noise correction term of the $P(k)$ estimator. Using this method, we recover the true $P(k)$ monopole of the mock catalogs with residuals of $<0.5\%$ at $k=0.3~h/Mpc$ and $<4\%$ at $k=0.83~h/Mpc$ -- a significant improvement over existing correction methods. The quadrupole, however, does not improve significantly.   The second method models the effect of fiber collisions on the power spectrum as a convolution with a configuration space top-hat function that depends on the physical scale of fiber collisions. It directly computes theoretical predictions of the fiber-collided $P(k)$ multipoles and reduces the influence of smaller scales to a set of nuisance parameters. Using this method, we reliably model the effect of fiber collisions on the monopole and quadrupole down to the scale limits of theoretical predictions. The methods we present in this paper will allow us to robustly analyze galaxy power spectrum multipole measurements to much smaller scales than previously possible.
We obtained [O III] narrow-band imaging and multi-slit MXU spectroscopy of the blue compact dwarf (BCD) galaxy NGC 1705 with FORS2@VLT to derive chemical abundances of PNe and H II regions and, more in general, to characterize the properties of the ionized gas. The auroral [O III]\lambda4363 line was detected in all but one of the eleven analyzed regions, allowing for a direct estimate of their electron temperature. The only object for which the [O III]\lambda4363 line was not detected is a possible low-ionization PN, the only one detected in our data. For all the other regions, we derived the abundances of Nitrogen, Oxygen, Neon, Sulfur and Argon out to ~ 1 kpc from the galaxy center. We detect for the first time in NGC 1705 a negative radial gradient in the oxygen metallicity of -0.24 \pm 0.08 dex kpc^{-1}. The element abundances are all consistent with values reported in the literature for other samples of dwarf irregular and blue compact dwarf galaxies. However, the average (central) oxygen abundance, 12 + log(O/H)=7.96 \pm 0.04, is ~0.26 dex lower than previous literature estimates for NGC 1705 based on the [O III]\lambda4363 line. From classical emission-line diagnostic diagrams, we exclude a major contribution from shock excitation. On the other hand, the radial behavior of the emission line ratios is consistent with the progressive dilution of radiation with increasing distance from the center of NGC 1705. This suggests that the strongest starburst located within the central $\sim$150 pc is responsible for the ionization of the gas out to at least $\sim$1 kpc. The gradual dilution of the radiation with increasing distance from the center reflects the gradual and continuous transition from the highly ionized H II regions in the proximity of the major starburst into the diffuse ionized gas.
Intense work studying the ballistic regime of electron transport in two dimensional systems based on semiconductors and graphene had been thought to have established most of the key experimental facts of the field. In recent years, however, new forms of ballistic transport have become accessible in the quasi-two-dimensional delafossite metals, whose Fermi wavelength is a factor of 100 shorter than those typically studied in the previous work, and whose Fermi surfaces are nearly hexagonal in shape, and therefore strongly faceted. This has some profound consequences for results obtained from the classic ballistic transport experiment of studying bend and Hall resistances in mesoscopic squares fabricated from delafossite single crystals. We observe pronounced anisotropies in bend resistances and even a Hall voltage that is strongly asymmetric in magnetic field. Although some of our observations are non-intuitive at first sight, we show that they can be understood within a non-local Landauer-B\"uttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of non-local transport can be resolved for squares of linear dimension of nearly 100 $\mu$m, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated.
Gravitational Waves (GW's) can determine the luminosity distance of the progenitor directly from the amplitude of the wave, without assuming any specific cosmological model. Thus, it can be considered as a standard siren. The coalescence of binary neutron stars (BNS) or neutron star-black hole pair (NSBH) can generate GW's as well as the electromagnetic counterpart, which can be detected in a form of Gamma-Ray Bursts (GRB) and can be used to determine the redshift of the source. Consequently, such a standard siren can be a very useful probe to constrain the cosmological parameters. In this work, we consider an interacting Dark Matter-Dark Energy (DM-DE) model. Assuming some fiducial values for the parameters of our model, we simulate the luminosity distance for a "realistic" and "optimistic" GW+GRB events , which can be detected by the third-generation GW detector Einstein Telescope (ET). Using these simulated events, we perform a Monte Carlo Markov Chain (MCMC) to constrain the DM-DE coupling constant and other model parameters in $1\sigma$ and $2\sigma$ confidence levels. We also investigate how GW's can improve the constraints obtained by current cosmological probes.
In shell model calculations for the yrast even spin states of 50Cr, the static quadrupole moments of the low spin states 2+_1 and 4+_1 are negative but those of the high spin states 10+_1, 12+_1 and 14+_1 are positive. Even spin states beyond the single j shell limit, J_max=14, again have negative moments. While the B(E2)'s for the J -> J-2 transitions are strongest along the yrast path for J <= 8, it is found that the transition from the second J=10 state to the first J=8 state (10+_2 -> 8+_1) is much stronger than the 10+_1 -> 8+_1 transition. We also note that while the 16+_1 -> 14+_1 transition is weak, the 16+_1 -> 14+_2 is quite strong.
We have proposed a method to calculate the relative magnetic helicity in a finite volume as given the magnetic field in the former paper (Yang et al. {\it Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic flux to be balanced on all the side boundaries of the considered volume. In this paper, we propose a scheme to obtain the vector potentials at the boundaries to remove the above restriction. We also used a theoretical model (Low and Lou, {\it Astrophys. J.} {\bf 352}, 343, 1990) to test our scheme.
We perform photoluminescence excitation measurements on individual CdSe/ZnS nanocrystal quantum dots (NCQDs) at room temperature to study optical transition energies and broadening. The observed features in the spectra are identified and compared to calculated transition energies using an effective mass model. The observed broadening is attributed to phonon broadening, spectral diffusion and size and shape inhomogeneity. The former two contribute the broadening transitions in individual QDs while the latter contributes to the QD-to-QD variation. We find that phonon broadening is often not the dominant contribution to transition line widths, even at room temperature, and that broadening does not necessarily increase with transition energy. This may be explained by differing magnitude of spectral diffusion for different quantum-confined states.
We present a comparative analysis of atmospheric parameters obtained with the so-called photometric and spectroscopic techniques. Photometric and spectroscopic data for 1360 DA white dwarfs from the Sloan Digital Sky Survey (SDSS) are used, as well as spectroscopic data from the Villanova White Dwarf Catalog. We first test the calibration of the ugriz photometric system by using model atmosphere fits to observed data. Our photometric analysis indicates that the ugriz photometry appears well calibrated when the SDSS to AB_95 zeropoint corrections are applied. The spectroscopic analysis of the same data set reveals that the so-called high-log g problem can be solved by applying published correction functions that take into account 3D hydrodynamical effects. However, a comparison between the SDSS and the White Dwarf Catalog spectra also suggests that the SDSS spectra still suffer from a small calibration problem. We then compare the atmospheric parameters obtained from both fitting techniques and show that the photometric temperatures are systematically lower than those obtained from spectroscopic data. This systematic offset may be linked to the hydrogen line profiles used in the model atmospheres. We finally present the results of an analysis aimed at measuring surface gravities using photometric data only.
For fixed integers $p$ and $q$, let $f(n,p,q)$ denote the minimum number of colors needed to color all of the edges of the complete graph $K_n$ such that no clique of $p$ vertices spans fewer than $q$ distinct colors. Any edge-coloring with this property is known as a $(p,q)$-coloring. We construct an explicit $(5,5)$-coloring that shows that $f(n,5,5) \leq n^{1/3 + o(1)}$ as $n \rightarrow \infty$. This improves upon the best known probabilistic upper bound of $O\left(n^{1/2}\right)$ given by Erd\H{o}s and Gy\'{a}rf\'{a}s, and comes close to matching the best known lower bound $\Omega\left(n^{1/3}\right)$.
Thermodynamics on the cosmological apparent horizon of a flat Friedmann-Lemaitre-Robertson-Walker metric has been investigated with Bekenstein entropy and Hawking temperature on the horizon, and Unruh temperature for the fluid inside the horizon. This temperature is experienced by a radial comoving observer infinitesimally close to the horizon due to the pressure exerted by the fluid bounded by the horizon. An expression for the entropy of the fluid has been obtained which is found to be proportional to the volume of the thermodynamic system which implies that the Unruh temperature of the fluid is inconsistent with the holographic principle. Further, we have been able to find an expression for the effective entropy of the system. Finally, assuming a barotropic equation of state $p=w\rho$ ($w$ constant) for the fluid, it has been shown that the generalized second law holds good for a non-phantom w, while thermodynamic equilibrium is never possible for such a scenario.
In this note we show that the standard \mbox{Rayleigh-Schr\"odinger} (RS) perturbation method gives the same result as the hypervirial pertubative method (HPM), for an approximate analytic expression for the energy eigenvalues of the bounded quartic oscillator. This connection between the HPM and the RS method went unnoticed for a long time, apparently because it was not obvious that the resulting polygamma sums to be evaluated in the RS method could, in fact, be expressed in closed form.
We review the status of a class of gauge unified models based on SO(10) group and discuss the main phenomenological implications of these models in particular for neutrino masses.
A large fraction of Gamma Ray Bursts (GRBs) displays an X-ray plateau phase within <10^{5} s from the prompt emission, proposed to be powered by the spin-down energy of a rapidly spinning newly born magnetar. In this work we use the properties of the Galactic neutron star population to constrain the GRB-magnetar scenario. We re-analyze the X-ray plateaus of all Swift GRBs with known redshift, between January 2005 and August 2014. From the derived initial magnetic field distribution for the possible magnetars left behind by the GRBs, we study the evolution and properties of a simulated GRB-magnetar population using numerical simulations of magnetic field evolution, coupled with Monte Carlo simulations of Pulsar Population Synthesis in our Galaxy. We find that if the GRB X-ray plateaus are powered by the rotational energy of a newly formed magnetar, the current observational properties of the Galactic magnetar population are not compatible with being formed within the GRB scenario (regardless of the GRB type or rate at z=0). Direct consequences would be that we should allow the existence of magnetars and "super-magnetars" having different progenitors, and that Type Ib/c SNe related to Long GRBs form systematically neutron stars with higher initial magnetic fields. We put an upper limit of <16 "super-magnetars" formed by a GRB in our Galaxy in the past Myr (at 99% c.l.). This limit is somewhat smaller than what roughly expected from Long GRB rates, although the very large uncertainties do not allow us to draw strong conclusion in this respect.
We describe a new class of instanton effects in string compactifications that preserve only N=1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective superpotential for the moduli of the compactification. We generalize this phenomenon by showing that such instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low-energy effective action. We consider in most detail the example of heterotic compactification on a Calabi-Yau threefold X with gauge bundle V, in which case we study worldsheet instanton effects that deform the complex structure of the moduli space associated to X and V. We also give new, slightly more economical derivations of some previous results about worldsheet instantons in Type IIA Calabi-Yau compactifications.
Magnetic droplets are dynamical solitons that can be generated by locally suppressing the dynamical damping in magnetic films with perpendicular anisotropy. To date, droplets have been observed only in nanocontact spin-torque oscillators operated by spin-polarized electrical currents. Here, we experimentally demonstrate that magnetic droplets can be nucleated and sustained by pure spin currents in nanoconstriction-based spin Hall devices. Micromagnetic simulations support our interpretation of the data, and indicate that in addition to the stationary droplets, propagating solitons can be also generated in the studied system, which can be utilized for the information transmission in spintronic applications.
In this paper we will apply the modified potential well method and variational method to the study of the long time behaviors of solutions to a class of parabolic equation of Kirchhoff type. Global existence and blow up in finite time of solutions will be obtained for arbitrary initial energy. To be a little more precise, we will give a threshold result for the solutions to exist globally or to blow up in finite time when the initial energy is subcritical and critical, respectively. The decay rate of the $L^2(\Omega)$ norm is also obtained for global solutions in these cases. Moreover, some sufficient conditions for the existence of global and blow-up solutions are also derived when the initial energy is supercritical.
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the sense that a pure bipartite quantum state, having nonvanishing entanglement, always violates a Bell inequality. We construct Bell-type inequalities for product states in quantum coherence theory for different measures of coherence, and find that the maximally entangled states violate these inequalities. We further show that Bell-type inequalities for relative entropy of coherence is violated by all two-qubit pure entangled states, serving as an entanglement witness.
This paper studies visual search using structured queries. The structure is in the form of a 2D composition that encodes the position and the category of the objects. The transformation of the position and the category of the objects leads to a continuous-valued relationship between visual compositions, which carries highly beneficial information, although not leveraged by previous techniques. To that end, in this work, our goal is to leverage these continuous relationships by using the notion of symmetry in equivariance. Our model output is trained to change symmetrically with respect to the input transformations, leading to a sensitive feature space. Doing so leads to a highly efficient search technique, as our approach learns from fewer data using a smaller feature space. Experiments on two large-scale benchmarks of MS-COCO and HICO-DET demonstrates that our approach leads to a considerable gain in the performance against competing techniques.
We obtain the persistence exponents for an antiferromagnetic Ising system in which the magnetisation is kept constant. This system belongs to Model C (system with non-conserved order parameter with a conserved density) and is expected to have persistence exponents different from that of Model A (system with no conservation) but independent of the conserved density. Our numerical results for both local persistence at zero temperature and global persistence at the critical temperature however indicate that the exponents are dependent on the conserved magnetisation in both two and three dimensions. This nonuniversal feature is attributed to the presence of the conserved field and is special to the persistence phenomena.