ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the framework of gravitational models obtained from the Geometric Inflation's proposal, where an infinite tower of curvature scalars are included into the action, we compute the slow-roll parameters by the Hubble slow-roll approach. We test the viability of such models as inflationary scenarios, focusing on the tensor-to-scalar ratio, $r$, and spectral scalar index, $n_s$, relation. We find that all models considered here produce inflation and, most of them coincide, some better than others, with the marginalized 95$\%$ CL region given by Planck's data collaboration.
We examine statistical properties of the Calkin--Wilf tree and give number-theoretical applications.
We analyze the physical parameters of interstellar filaments that we describe by an idealized model of isothermal self-gravitating infinite cylinder in pressure equilibrium with the ambient medium. Their gravitational state is characterized by the ratio f_cyl of their mass line density to the maximum possible value for a cylinder in a vacuum. Equilibrium solutions exist only for f_cyl < 1. This ratio is used in providing analytical expressions for the central density, the radius, the profile of the column density, the column density through the cloud centre, and the fwhm. The dependence of the physical properties on external pressure and temperature is discussed and directly compared to the case of pressure-confined isothermal self-gravitating spheres.   Comparison with recent observations of the fwhm and the central column density N_H(0) show good agreement and suggest a filament temperature of ~10 K and an external pressure p_ext/k in the range 1.5x10^4 K/cm^3 to 5x10^4 K/cm^3.   Stability considerations indicate that interstellar filaments become increasingly gravitationally unstable with mass line ratio f_cyl approaching unity. For intermediate f_cyl>0.5 the instabilities should promote core formation through compression, with a separation of about five times the fwhm. We discuss the nature of filaments with high mass line densities and their relevance to gravitational fragmentation and star formation.
The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions are obtained and characterize this system as a two-dimensional quantum spin liquid. Spin-spin correlation functions decay exponentially with distance down to low temperature and the calculated missing entropy at T=0 is found to be $0.46\ln{2}$. Within the present scheme, the specific heat exhibits a single peak structure and a $T^2$ dependence at low temperature.
Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding $G$-invariant pencils of surfaces in $\mathbb{P}_3$ which we started in math. AG/0106080. It turns out that we have five more pencils, two of them containing surfaces with nodes.
Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Recently, several authors have shown that the invariant distribution of such networks admits a product form distribution under critical loading. Assuming exponential job size distributions, they leave the case of general job size distributions as an open question. In this paper we show the conjecture holds for a dense class of distributions. This yields a key example of a stochastic network in which the heavy traffic limit has an invariant distribution that does not depend on second moments. Our analysis relies on a uniform convergence result for a fluid model which may be of independent interest.
Au+Au, $s^{1/2} = 200$ A GeV measurements at RHIC, obtained with the PHENIX, STAR, PHOBOS and BRAHMS detectors, have all indicated a suppression of neutral pion production, relative to an appropriately normalized NN level. For central collisions and vanishing pseudo-rapidity these experiments exhibit suppression in charged meson production, especially at medium to large transverse momenta. In the PHENIX experiment similar behavior has been reported for $\pi^0$ spectra.   In a recent work on the simpler D+Au interaction, to be considered perhaps as a tune-up for Au+Au, we reported on a pre-hadronic cascade mechanism which explains the mixed observation of moderately reduced $p_\perp$ suppression at higher pseudo-rapidity as well as the Cronin enhancement at mid-rapidity. Here we present the extension of this work to the more massive ion-ion collisions.   Our major thesis is that much of the suppression is generated in a late stage cascade of colourless pre-hadrons produced after an initial short-lived coloured phase. We present a pQCD argument to justify this approach and to estimate the time duration $\tau_p$ of this initial phase. Of essential importance is the brevity in time of the coloured phase existence relative to that of the strongly interacting pre-hadron phase. The split into two phases is of course not sharp in time, but adequate for treating the suppression of moderate and high $p_\perp$ mesons.
In this paper we answer a question posed by R. Stanley in his collection of Bijection Proof Problems (Problem 240). We present a bijective proof for the enumeration of walks of length $k$ a chess rook can move along on an $m\times n$ board starting and ending on the same square.
Finite convex geometries are combinatorial structures. It follows from a recent result of M.\ Richter and L.G.\ Rogers that there is an infinite set $T_{rr}$ of planar convex polygons such that $T_{rr}$ with respect to geometric convex hulls is a locally convex geometry and every finite convex geometry can be represented by restricting the structure of $T_{rr}$ to a finite subset in a natural way. An \emph{almost-circle of accuracy} $1-\epsilon$ is a differentiable convex simple closed curve $S$ in the plane having an inscribed circle of radius $r_1>0$ and a circumscribed circle of radius $r_2$ such that the ratio $r_1/r_2$ is at least $1-\epsilon$. % Motivated by Richter and Rogers' result, we construct a set $T_{new}$ such that (1) $T_{new}$ contains all points of the plane as degenerate singleton circles and all of its non-singleton members are differentiable convex simple closed planar curves; (2) $T_{new}$ with respect to the geometric convex hull operator is a locally convex geometry; (3) as opposed to $T_{rr}$, $T_{new}$ is closed with respect to non-degenerate affine transformations; and (4) for every (small) positive $\epsilon\in\real $ and for every finite convex geometry, there are continuum many pairwise affine-disjoint finite subsets $E$ of $T_{new}$ such that each $E$ consists of almost-circles of accuracy $1-\epsilon$ and the convex geometry in question is represented by restricting the convex hull operator to $E$. The affine-disjointness of $E_1$ and $E_2$ means that, in addition to $E_1\cap E_2=\emptyset$, even $\psi(E_1)$ is disjoint from $E_2$ for every non-degenerate affine transformation $\psi$.
During the last two decades, the focus of star formation research has shifted from understanding the collapse of a single dense core into a star to studying the formation hundreds to thousands of stars in molecular clouds. In this chapter, we overview recent observational and theoretical progress toward understanding star formation on the scale of molecular clouds and complexes, i.e the macrophysics of star formation. We begin with an overview of recent surveys of young stellar objects (YSOs) in molecular clouds and embedded clusters, and we outline an emerging picture of cluster formation. We then discuss the role of turbulence to both support clouds and create dense, gravitationally unstable structures, with an emphasis on the role of magnetic fields (in the case of distributed stars) and feedback (in the case of clusters) to slow turbulent decay and mediate the rate and density of star formation. The discussion is followed by an overview of how gravity and turbulence may produce observed scaling laws for the properties of molecular clouds, stars and star clusters, and how the observed, low star formation rate may result from self regulated star formation. We end with some concluding remarks, including a number of questions to be addressed by future observations and simulations.
We study the essentially isolated determinantal singularities (EIDS), defined by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity. We prove in dimension $3$ a minimality theorem for the Milnor number of a generic hyperplane section of an EIDS, generalizing previous results by J. Snoussi in dimension $2$. We define strongly generic hyperplane sections of an EIDS and show that they are still EIDS.   Using strongly general hyperplanes, we extend a result of L\^e D. T. concerning constancy of the Milnor number.
QCD sum rules are used to calculate the contribution of short-distance single-quark transition $s\rightarrow d \gamma$, to the amplitudes of the hyperon radiative decay, $\Omega^-\rightarrow \Xi^-\gamma$. We re-evaluate the Wilson coefficient of the effective operator responsible for this transition. We obtain a branching ratio which is comparable to the unitarity limit.
We study the integro-differential operators $L$ with kernels $K(y) = a(y) J(y)$, where $J(y)dy$ is a L\'evy measure on $\bR^d$ (i.e. $\int_{\bR^d}(1\wedge |y|^2)J(y)dy<\infty$) and $a(y)$ is an only measurable function with positive lower and upper bounds. Under few additional conditions on $J(y)$, we prove the unique solvability of the equation $Lu-\lambda u=f$ in $L_p$-spaces and present some $L_p$-estimates of the solutions.
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. While the mean-square displacement of the particle shows the expected anomalous diffusion behavior $\langle x^2 \rangle \sim t^\alpha$, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case, $\alpha> 1$, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion, $\alpha < 1$, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular for applications that are dominated by rare events.
Detecting companions to Cepheids is difficult. In most cases the bright pulsator overshines the fainter secondary. Since Cepheids play a key role in determining the cosmic distance scale it is crucial to find binaries among the calibrating stars of the period-luminosity relation. Here we present an ongoing observing project of searching for faint and close companions of Galactic Cepheids using lucky imaging technique.
In January 2009, multiple short bursts of soft gamma-rays were detected from the direction of the anomalous X-ray pulsar 1E 1547.0-5408 by different satellites. Here we report on the observations obtained with the INTEGRAL SPI-ACS detector during the period with the strongest bursting activity. More than 200 bursts were detected at energies above 80 keV in a few hours on January 22. Among these, two remarkably bright events showed pulsating tails lasting several seconds and modulated at the 2.1 s spin period of 1E 1547.0-5408. The energy released in the brightest of these bursts was of a few 10^43 erg, for an assumed distance of 10 kpc. This is smaller than that of the three giant flares seen from soft gamma-ray repeaters, but higher than that of typical bursts from soft gamma-ray repeaters and anomalous X-ray pulsars.
We extend a result of Griggs and Yeh about the maximum possible value of the L(2,1)-labeling number of a graph in terms of its maximum degree to oriented graphs. We consider the problem both in the usual definition of the oriented L(2,1)-labeling number and in some variants we introduce.
Reliable evaluation of the lattice thermal conductivity is of importance for optimizing the figure-of-merit of thermoelectric materials. Traditionally, when deriving the phonon mediated thermal conductivity $\kappa_{ph} = \kappa - \kappa_{el}$ from the measured total thermal conductivity $\kappa$ the constant Lorenz number $L_0$ of the Wiedemann-Franz law \mbox{$\mathbf{\kappa_{el}}=T L_0 \sigma$} is chosen. The present study demonstrates that this procedure is not reliable when the Seebeck coefficient $|S|$ becomes large which is exactly the case for a thermoelectric material of interest. Another approximation using $L_0-S^2$, which seem to work better for medium values of $S^2$ also fails when $S^2$ becomes large, as is the case when the system becomes semiconducting/insulating. For a reliable estimation of $\kappa_{el}$ it is proposed, that a full first-principles calculations by combining density functional theory with Boltzmann's transport theory has to be made. For the present study such an approach was chosen for investigating the clathrate type-I compound Ba$_8$Au$_{6-x}$Ge$_{40+x}$ for a series of dopings or compositions $x$. For a doping of $0.8$ electrons corresponding to $x=0.27$ the calculated temperature dependent Seebeck coefficient agrees well with recent experiments corroborating the validity of the density functional theory approach.
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the time-derivative with power-law kernels, are typical for memory effects in complex systems. In this paper we consider a nonlinear transport equation with a fractional time-derivative. We provide a well-posedness theory for weak measure solutions of the problem and an integral formula which generalizes the classical push-forward representation formula to this setting.
Even though the observed spectra for GRB prompt emission is well constrained, no single radiation mechanism can robustly explain its distinct non-thermal nature. Here we explore the radiation mechanism with the photospheric emission model using our Monte Carlo Radiative Transfer (MCRaT) code. We study the sub-photospheric Comptonization of fast cooled synchrotron photons while the Maxwellian electrons and mono-energetic protons are accelerated to relativistic energies by repeated dissipation events. Unlike previous simulations, we implement a realistic photon to electron number ratio $N_{\gamma}/N_{e} \sim 10^5$ consistent with the observed radiative efficiency of a few percent. We show that it is necessary to have a critical number of episodic energy injection events $N_{rh,cr} \sim {\rm few}\ 10{\rm s}-100$ in the jet in addition to the electron-proton Coulomb coupling in order to inject sufficient energy $E_{inj,cr} \sim 2500-4000\ m_e c^2$ per electron and produce an output photon spectrum consistent with observations. The observed GRB spectrum can be generated when the electrons are repeatedly accelerated to highly relativistic energies $\gamma_{e,in} \sim {\rm few}\ 10{\rm s}-100$ in a jet with bulk Lorentz factor $\Gamma \sim 30-100$, starting out from moderate optical depths $\tau_{in} \sim 20-40$. The shape of the photon spectrum is independent of the initial photon energy distribution and baryonic energy content of the jet and hence independent of the emission mechanism, as expected for photospheric emission.
We present moderate resolution data for 39 QSOs at z $\approx$ 2 obtained at the Multiple Mirror Telescope. These data are combined with spectra of comparable resolution of 60 QSOs with redshifts greater than 1.7 found in the literature to investigate the distribution of Ly-alpha forest lines in redshift and equivalent width. We find a value for $\gamma$, the parameter describing the number distribution of Ly-alpha forest lines in redshift, of $1.88\pm0.22$ for lines stronger than a rest equivalent width of 0.32 $\AA$, in good agreement with some previous studies. The Kolmogorov-Smirnov test was applied to the data and it is found that this single power law is a good fit over the relevant redshift ranges. Simulations of the Lyman alpha forest were performed to determine the completeness of the line lists and to test how well the analysis the underlying line statistics, given this level of completeness.
A role of the multipole interaction in the description of the $\triangle I$=4 staggering phenomenon is investigated in a model consisting of a single-$j$ shell filled by identical nucleons. Exact diagonalization of the quadrupole-plus-hexadecapole Hamiltonian shows that the hexadecapole-hexadecapole interaction can produce a $\triangle I$=4 periodicity in the yrast sequence.
We present an analysis of the variability of the solar oscillation spectrum during solar cycle 23 and its extended minimum. We use simultaneous observations of the low-degree solar p modes collected by the space-based, Sun-as-a-star GOLF (radial velocity) and VIRGO (intensity) instruments, and by the ground-based, multi-site network GONG. We investigate in particular the response of the p-mode eigenfrequencies to the observed peculiar deep solar minimum of surface activity of 2007-2009 as compared with the previous solar cycle 23. We study the different temporal variations of the p-mode frequencies with individual angular degrees.
The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.
Falsification of medicines is a big problem in many developing countries, where technological infrastructure is inadequate to detect these harmful products. We have developed a set of inexpensive paper cards, called Paper Analytical Devices (PADs), which can efficiently classify drugs based on their chemical composition, as a potential solution to the problem. These cards have different reagents embedded in them which produce a set of distinctive color descriptors upon reacting with the chemical compounds that constitute pharmaceutical dosage forms. If a falsified version of the medicine lacks the active ingredient or includes substitute fillers, the difference in color is perceivable by humans. However, reading the cards with accuracy takes training and practice, which may hamper their scaling and implementation in low resource settings. To deal with this, we have developed an automatic visual recognition system to read the results from the PAD images. At first, the optimal set of reagents was found by running singular value decomposition on the intensity values of the color tones in the card images. A dataset of cards embedded with these reagents is produced to generate the most distinctive results for a set of 26 different active pharmaceutical ingredients (APIs) and excipients. Then, we train two popular convolutional neural network (CNN) models, with the card images. We also extract some "hand-crafted" features from the images and train a nearest neighbor classifier and a non-linear support vector machine with them. On testing, higher-level features performed much better in accurately classifying the PAD images, with the CNN models reaching the highest average accuracy of over 94\%.
Modeling properly the interface between convective cores and radiative interiors is one the most challenging and important open questions in modern stellar physics. The rapid development of asteroseismology, with the advent of space missions partly dedicated to this discipline, has provided new constraints to progress on this issue. We here give an overview of the information that can be obtained from pressure modes, gravity modes and mixed modes. We also review some of the most recent constraints obtained from space-based asteroseismology on the nature and the amount of mixing beyond convective cores.
In this paper we consider all possible 1D and 2P ccbar assignments for the recently discovered X(3872). Taking the experimental mass as input, we give numerical results for the E1 radiative widths as well as the three principal types of strong decays; open-charm, ccbar annihilation and closed-charm hadronic transitions. We find that many assignments may be immediately eliminated due to the small observed total width. The remaining viable ccbar assignments are 3D3, 3D2, 1D2, 2 3P1 and 2 1P1. A search for the mode J/psi pi0 pi0 can establish the C-parity of the X(3872), which will eliminate many of these possibilities. Radiative transitions can then be used to test the remaining assignments, as they populate characteristic final states. The 3D2 and 1D2 states are predicted to have large (ca.50%) radiative branching fractions to chi_1 gamma and h_c gamma respectively. We predict that the 3D3 will also be relatively narrow and will have a significant (ca.10%) branching fraction to chi_2 gamma, and should also be observable in B decay. Tests for non-ccbar X(3872) assignments are also discussed.
We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness of the results obtained in a full general relativistic approach in comparison with the ones obtained when the electric charge is assumed to be orbiting a massive object due to a Newtonian force.
The manifestation of exceptional points in the scattering continuum of atomic nucleus is studied using the real-energy continuum shell model. It is shown that low-energy exceptional points appear for realistic values of coupling to the continuum and, hence, could be accessible experimentally. Experimental signatures are proposed which include the jump by $2\pi$ of the elastic scattering phase shift and a salient energy dependence of cross-sections in the vicinity of the exceptional point.
A general method is presented to build all gauge-invariant terms in gauge field theories, including quantum electrodynamics and quantum chromodynamics. It is applied to two experiments, light-by-light scattering and deep inelastic scattering, to extract first bounds on certain nonminimal coefficients for Lorentz violation.
We explore physical properties of the shocked external medium (i.e., a shell) in 3C 84 associated with the recurrent radio lobe born around 1960. In the previous work of Ito et al., we investigated a dynamical and radiative evolution of such a shell after the central engine stops the jet launching and we found that a fossil shell emission overwhelms that of the rapidly fading radio lobe. We apply this model to 3C 84 and find the followings: (i) The fossil shell made of shocked diffuse ambient matter with the number density of 0.3 cm$^{-3}$ radiates bright Inverse-Compton (IC) emission with the seed photons of the radio emission from the central compact region and the IC emission is above the sensitivity threshold of the Cherenkov Telescope Array (CTA). (ii) When the fossil shell is produced in a geometrically thick ionized plasma with the number density of $10^{3}$ cm$^{-3}$ and the field strength in the shell may reach about 17 mG in the presence of magnetic fields amplification and the radio emission becomes comparable to the sensitivity of deep imaging VLBI observations. A possible production of ultra high energy cosmic-rays (UHECRs) in the dense shocked plasma is also argued.