ShantanuT01/DACTYL-Pretraining huggingface dataset:
The GW method is a many-body approach capable of providing quasiparticle bands for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to large complex materials due to its computational expense. We perform an exact recasting of the GW polarizability and the self-energy as Laplace integrals over imaginary time propagators. We then "shred" the propagators (via energy windowing) and approximate them in a controlled manner by using Gauss-Laguerre quadrature and discrete variable methods to treat the imaginary time propagators in real space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems (>=10 atoms) and also represents a substantial improvement over several other cubic methods tested. This approach is useful for evaluating quantum mechanical response function involving large sums containing energy (difference) denominators.
Both the three-dimensional density of red clump giants and the gas kinematics in the inner Galaxy indicate that the pattern speed of the Galactic bar could be much lower than previously estimated. Here, we show that such slow bar models are unable to reproduce the bimodality observed in local stellar velocity space. We do so by computing the response of stars in the Solar neighbourhood to the gravitational potential of slow and fast bars, in terms of their perturbed distribution function in action-angle space up to second order, as well as by identifying resonantly trapped orbits. We also check that the bimodality is unlikely to be produced through perturbations from spiral arms, and conclude that, contrary to gas kinematics, local stellar kinematics still favour a fast bar in the Milky Way, with a pattern speed of the order of almost twice (and no less than 1.8 times) the circular frequency at the Sun's position. This leaves open the question of the nature of the long flat extension of the bar in the Milky Way.
A significant frequency dependence of the ESR line width is found in NaV_2O_5 between 34-100 K and the line width increases as the resonance frequency is increased from 95 GHz to 760 GHz. The observed frequency dependence is qualitatively explained in terms of the dynamical charge disproportionation. The present results show the essential role of the internal charge degree of freedom in a V-O-V bond. We have also proposed the existence of the Dzyaloshinsky-Moriya interaction in the low temperature charge ordered phase considering the breaking of the selection rule of ESR realized as the direct observation of the spin gap excitation.
We deeply appreciate the papers of Ivi\'c on the links between the $2k-$th moments of the Riemann zeta function and, say, $d_k$, the $k-$divisor function. More specifically, both the one bounding the $2k-$th moment with a simple average of correlations of the $d_k$ (Palanga 1996 Conference Proceedings) and the more recent (arXiv:0708.1601v2 to appear on JTNB), which bounds the Selberg integral of $d_k$ applying the $2k-$th moment of the zeta. Building on the former paper, we apply an elementary approach (based on arithmetic averages) in order to get information on the reverse link to the second work.
We investigate the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided into two chambers by a movable adiabatic piston of mass $M\gg m$. Using a two-time-scale perturbation approach in terms of the small parameter $\alpha=2m/(M+m)$, we show that the evolution towards thermal equilibrium proceeds in two stages. The first stage is a fast, deterministic, adiabatic relaxation towards mechanical equilibrium. The second stage, which takes place at times ${\cal O}(M)$, is a slow fluctuation-driven, diathermic relaxation towards thermal equilibrium. A very simple equation is derived which shows that in the second stage, the position of the piston is given by $X_M(t)=L[1/2-\xi(\alpha t)]$ where the function $\xi$ is independent of $M$. Numerical simulations support the assumptions underlying our analytical derivations and illustrate the large mass range in which the picture holds.
In this overview paper, presented at the meeting DANS14, Novi Sad, July3-7, 2014, we give some applications of Laplace transforms to analytic number theory. These include the classical circle and divisor problem, moments of $|\zeta(1/2+it)|$, and a discussion of two functional equations connected to a work of Prof. Bogoljub Stankovi\'c.
The deuteron wave function can be presented as the table through the respective massifs of numerically values of radial wave functions. In calculations such arrays of numbers in the texts of programs to operate quite difficult. Therefore a used simpler analytical forms is expedient. In the received analytical forms of deuteron wave function in coordinate representation it is necessary to calculate density distribution in the deuteron and transition density and compare them among themselves. On the received coefficients of the four analytical forms for deuteron wave function for the nucleon-nucleon potential Reid93 are calculated density distribution and transition density. For comparison, similar results are given for Moscow potential. Such calculations help to evaluate the correctness of the choice of the analytical form for approximation of the wave function, and also to obtain information about such characteristics of the deuteron as charge form factor, tensor polarization and momentum distribution.
Molecular dynamics (MD) simulations have been performed to investigate the mechanical properties of hydrogen functionalized graphene allotropes (GAs) for H-coverage spanning the entire range (0-100%). Four allotropes (graphyne, cyclic graphene, octagonal graphene, and biphenylene) with larger unit lattice size than graphene are considered. The effect of the degree of functionalization and molecular structure on the Young's modulus and strength are investigated, and the failure processes of some new GAs are reported for the first time. We show that the mechanical properties of the hydrogenated GAs deteriorate drastically with increasing H-coverage within the sensitive threshold, beyond which the mechanical properties remain insensitive to the increase in H-coverage. This drastic deterioration arises both from the conversion of sp2 to sp3 bonding and easy rotation of unsupported sp3 bonds. Allotropes with different lattice structures correspond to different sensitive thresholds. The Young's moduli deterioration of fully hydrogenated allotropes can be up to 70% smaller than that of the corresponding pristine structure. Moreover the tensile strength shows an even larger drop of about 90% and higher sensitivity to H-coverage even if it is small. Our results suggest that the unique coverage-dependent deterioration of the mechanical properties must be taken into account when analyzing the performance characteristics of nanodevices fabricated from functionalized GAs.
In this paper, the effect of electromagnetic field has been investigated on the spherically symmetric collapse with the perfect fluid in the presence of positive cosmological constant. Junction conditions between the static exterior and non-static interior spherically symmetric spacetimes are discussed. We study the apparent horizons and their physical significance. It is found that electromagnetic field reduces the bound of cosmological constant by reducing the pressure and hence collapsing process is faster as compared to the perfect fluid case. This work gives the generalization of the perfect fluid case to the charged perfect fluid. Results for the perfect fluid case are recovered.
Lyman alpha halos are observed ubiquitously around star-forming galaxies at high redshift, but their origin is still a matter of debate. We demonstrate that the emission from faint unresolved satellite sources, $M_{\rm UV} \gtrsim -17$, clustered around the central galaxies may play a major role in generating spatially extended Ly$\alpha$, continuum (${\rm UV + VIS}$) and H$\alpha$ halos. We apply the analytic formalism developed in Mas-Ribas & Dijkstra (2016) to model the halos around Lyman Alpha Emitters (LAEs) at $z=3.1$, for several different satellite clustering prescriptions. In general, our UV and Ly$\alpha$ surface brightness profiles match the observations well at $20\lesssim r \lesssim 40$ physical kpc from the centers of LAEs. We discuss how our profiles depend on various model assumptions and how these can be tested and constrained with future H$\alpha$ observations by the James Webb Space Telescope (JWST). Our analysis shows how spatially extended halos constrain (i) the presence of otherwise undetectable satellite sources, (ii) the integrated, volumetric production rates of Ly$\alpha$ and LyC photons, and (iii) their population-averaged escape fractions. These quantities are all directly relevant for understanding galaxy formation and evolution and, for high enough redshifts, cosmic reionization.
Let G be a graph whose edges are labeled by positive integers. Label each vertex with an integer and suppose if two vertices are joined by an edge, the vertex labels are congruent to each other modulo the edge label. The set of vertex labels satisfying this condition is called a generalized spline. Gilbert, Polster, and Tymoczko recently defined generalized splines based on work on polynomial splines by Billera, Rose, Haas, Goresky-Kottwitz-Machperson, and many others. We focus on generalized splines on $n$-cycles. We construct a particularly nice basis for the module of splines on $n$-cycles. As an application, we construct generalized splines on star graphs, wheel graphs, and complete graphs.
Unpulsed, high-energy emission from pulsar binaries can be attributed to the interaction of a pulsar wind with that of a companion star. At the shock between the outflows, particles carried away from the pulsar magnetosphere are accelerated and radiate both in synchrotron and inverse Compton processes. This emission constitutes a significant fraction of the pulsar spin-down luminosity. It is not clear however, how the highly magnetized pulsar wind could convert its mainly electromagnetic energy into the particles with such high efficiency. Here we investigate a scenario in which a pulsar striped wind converts into a strong electromagnetic wave before reaching the shock. This mode can be thought of as a shock precursor that is able to accelerate particles to ultrarelativistic energies at the expense of the electromagnetic energy it carries. Radiation of the particles leads to damping of the wave. The efficiency of this process depends on the physical conditions imposed by the external medium. Two regimes can be distinguished: a high density one, where the EM wave cannot be launched at all and the current sheets in the striped wind are first compressed by an MHD shock and subsequently dissipate by reconnection, and a low density one, where the wind can first convert into an electromagnetic wave in the shock precursor, which then damps and merges into the surroundings. Shocks in binary systems can transit from one regime to another according to binary phase. We discuss possible observational implications for these objects.
The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with artificial operator. This paper introduces the development of this method to the inverse crack scattering problem. Our aim is to give the following two indicators: One (Theorem 1.1) is to determine whether an artificial small arc is contained in the unknown arc. The other one (Theorem 1.2) is whether an artificial large domain contain the unknown one. Finally, numerical examples based on Theorem 1.1 are given.
The existence of a dark energy component has usually been invoked as the most plausible way to explain the recent observational results. However, it is also well known that effects arising from new physics (e.g., extra dimensions) can mimic the gravitational effects of a dark energy through a modification of the Friedmann equation. In this paper we investigate some observational consequences of a flat, matter dominated and accelerating/decelerating scenario in which this modification is given by $H^{2} = g(\rho_m, n, q)$ where $g(\rho_m, n, q)$ is a new function of the energy density $\rho_m$, the so-called generalized Cardassian models. We mainly focus our attention on the constraints from statistical properties of gravitationally lensed quasars on the parameters $n$ and $q$ that fully characterize the models. We show that these models are in agreement with the current gravitationally lensed quasar data for a large interval of the $q - n$ parametric space. The dependence of the acceleration redshift (the redshift at which the universe begins to accelerate) on these parameters is also briefly discussed.
We rigorously investigate the quantum non-Markovian dissipative dynamics of a system coupled to a harmonic oscillator bath by deriving hierarchical Schrodinger equations of motion (HSEOM) and studying their dynamics. The HSEOM are the equations for wave functions derived on the basis of the Feynman-Vernon influence functional formalism for the density operator, $\langle q|\rho(t)|q' \rangle$, where $\langle q|$ and $|q' \rangle$ are the left- and right-hand elements. The time evolution of $\langle q|$ is computed from time $0$ to $t$, and subsequently, the time evolution of $|q' \rangle$ is computed from time $t$ to $0$ along a contour in the complex time plane. By appropriately choosing functions for the bath correlation function and the spectral density, we can take advantage of an HSEOM method to carry out simulations without the need for a great amount of computational memory. As a demonstration, quantum annealing simulation for a ferromagnetic $p$-spin model is studied.
IGR J16195-4945 is a hard X-ray source discovered by INTEGRAL during the Core Program observations performed in 2003. We analyzed the X-ray emission of this source exploiting the Swift-BAT survey data from December 2004 to March 2015, and all the available Swift-XRT pointed observations. The source is detected at a high significance level in the 123-month BAT survey data, with an average 15-150 keV flux of the source of ~1.6 mCrab. The timing analysis on the BAT data reveals with a significance higher than 6 standard deviations the presence of a modulated signal with a period of 3.945 d, that we interpret as the orbital period of the binary system. The folded light curve shows a flat profile with a narrow full eclipse lasting ~3.5% of the orbital period. We requested phase-constrained XRT observations to obtain a more detailed characterization of the eclipse in the soft X-ray range. Adopting resonable guess values for the mass and radius of the companion star, we derive a semi-major orbital axis of ~31 R_sun, equivalent to ~1.8 times the radius of the companion star. From these estimates and from the duration of the eclipse we derive an orbital inclination between 55 and 60 degrees. The broad band time-averaged XRT+BAT spectrum is well modeled with a strongly absorbed flat power law, with absorbing column N_H=7x 10^22 cm^(-2) and photon index Gamma=0.5, modified by a high energy exponential cutoff at E_cut=14 keV.
The sources responsible for the emission of high-energy ($\gtrsim$ 100 TeV) neutrinos detected by IceCube are still unknown. Among the possible candidates, active galactic nuclei with relativistic jets are often examined, since the outflowing plasma seems to offer the ideal environment to accelerate the required parent high-energy cosmic rays. The non-detection of single point sources or -- almost equivalently -- the absence, in the IceCube events, of multiplets originating from the same sky position, constrains the cosmic density and the neutrino output of these sources, pointing to a numerous population of faint sources. Here we explore the possibility that FR0 radiogalaxies, the population of compact sources recently identified in large radio and optical surveys and representing the bulk of radio-loud AGN population, can represent suitable candidates for neutrino emission. Modeling the spectral energy distribution of a FR0 radiogalaxy recently associated to a $\gamma$-ray source detected by the Large Area Telescope onboard Fermi, we derive the physical parameters of its jet, in particular the power carried by it. We consider the possible mechanisms of neutrino production, concluding that $p\gamma$ reactions in the jet between protons and ambient radiation is too inefficient to sustain the required output. We propose an alternative scenario, in which protons, accelerated in the jet, escape from it and diffuse in the host galaxy, producing neutrinos as a result of $pp$ scattering with the interstellar gas, in strict analogy with the processes taking place in star-forming galaxies.
To any pair of coverings $f_i: X \ra X_i, i = 1,2$ of smooth projective curves one can associate an abelian subvariety of the Jacobian $J_X$, the Prym variety $P(f_1,f_2)$ of the pair $(f_1,f_2)$. In some cases we can compute the type of the restriction of the canonical principal polarization of $JX$. We obtain 2 families of Prym-Tyurin varieties of exponent 6.
Primordial black holes (PBHs) are a fascinating candidate for being the dark matter, albeit one which has been heavily constrained. This review presents an in depth look at those observational constraints, particularly at their nuances and uncertainties. Despite their varied origins, the standard PBH formation path is assumed to be collapse of perturbations after inflation, which should leave signals visible in the CMB at certain scales. Other constraints come from microlensing surveys, which severely limit PBHs as dark matter in the solar to satellite range, but there are diminishing results in regards to lower mass ranges. Gravitational waves signals and PBH evaporation from Hawking radiation also make for useful probes, but the former requires the next generation of experiments before making constraints beyond the solar mass range, and the later is severely limited above $10^{-16} \rm M_{\odot}$. Other dynamical and accretion constraints exist for PBH of large masses. Care also has to be given, as all these constraints can carry different implications coming from differences between monochromatic and extended mass distributions, and their degree of clustering. Beyond all these issues, a window still exists for primordial black holes to be all of the dark matter between $10^{-16}$ and $10^{-11} \rm M_{\odot}$
Consider a centred random walk in dimension one with a positive finite variance $\sigma^2$, and let $\tau_B$ be the hitting time for a bounded Borel set $B$ with a non-empty interior. We prove the asymptotic $P_x(\tau_B > n) \sim \sqrt{2 / \pi} \sigma^{-1} V_B(x) n^{-1/2}$ and provide an explicit formula for the limit $V_B$ as a function of the initial position $x$ of the walk. We also give a functional limit theorem for the walk conditioned to avoid $B$ by the time $n$. As a main application, consider the case that $B$ is an interval and study the size of the largest gap $G_n$ (maximal spacing) within the range of the walk by the time $n$. We prove a limit theorem for $G_n$, which is shown to be of the constant order, and describe its limit distribution. In addition, we prove an analogous result for the number of non-visited sites within the range of an integer-valued random walk.
Numerical calculations of orbit evolutions of 1694 numbered asteroids included in the IRAS catalogue, from 13.11.1996 to 06.03.2006 were carried out. The values da - differences between the catalogue semimajor axes at 06.03.2006 and the calculated ones were computed. The average dependence da on albido p shows decrease of da at increase of p, and it is significant. In other words, semimajor axes of low-albedo asteroids are, on average, increasing as compared with high-albedo ones. Speed of such possible spatial separation for very dim and very bright asteroids of from 10 to 50km in order of magnitude is about 1 AU per 100 My. To explain this fact it may suppose an existence possibility of a non-gravitational effect. Such supposition is confirmed by distributions p(a) for asteroid families, above all, Flora family. An analysis of errors and residuals in the used asteroid catalogues is evidence of such supposition.
Despite having been introduced in 1962 by C.L. Mallows, the combinatorial algorithm Patience Sorting is only now beginning to receive significant attention due to such recent deep results as the Baik-Deift-Johansson Theorem that connect it to fields including Probabilistic Combinatorics and Random Matrix Theory.   The aim of this work is to develop some of the more basic combinatorics of the Patience Sorting Algorithm. In particular, we exploit the similarities between Patience Sorting and the Schensted Insertion Algorithm in order to do things that include defining an analog of the Knuth relations and extending Patience Sorting to a bijection between permutations and certain pairs of set partitions. As an application of these constructions we characterize and enumerate the set S_n(3-\bar{1}-42) of permutations that avoid the generalized permutation pattern 2-31 unless it is part of the generalized pattern 3-1-42.
In this paper we propose a very special relativity (VSR)-inspired description of the axion electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(2)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects give a health departure from the usual axion field theory. The axionic classical dynamics is analysed in full detail, first by a discussion of its solution in the presence of an external magnetic field. Next, we compute photon-axion transition in VSR scenario by means of Primakoff interaction, showing the change of a linearly polarized light to a circular one. Afterwards, duality symmetry is discussed in the VSR framework.
The scattering length density profile for a thin film structure can be determined uniquely if both modulus and phase of the reflection coefficient is known. Here, we describe a method for recovering the phase information which utilize a magnetic substrate and based on polarization analysis of the reflected beam. The method is derived in the formalism of transfer matrix so it is applicable for any unknown real scattering length density of nonmagnetic films (i.e. in the case where there is no effective absorption).
We show that Sine$_\beta$, the bulk limit of the Gaussian $\beta$-ensembles is the spectrum of a self-adjoint random differential operator \[ f\to 2 {R_t^{-1}} \left[ \begin{array}{cc} 0 &-\tfrac{d}{dt} \tfrac{d}{dt} &0 \end{array} \right] f, \qquad f:[0,1)\to \mathbb R^2, \] where $R_t$ is the positive definite matrix representation of hyperbolic Brownian motion with variance $4/\beta$ in logarithmic time. The result connects the Montgomery-Dyson conjecture about the Sine$_2$ process and the non-trivial zeros of the Riemann zeta function, the Hilbert-P\'olya conjecture and de Brange's attempt to prove the Riemann hypothesis. We identify the Brownian carousel as the Sturm-Liouville phase function of this operator.   We provide similar operator representations for several other finite dimensional random ensembles and their limits: finite unitary or orthogonal ensembles, Hua-Pickrell ensembles and their limits, hard-edge $\beta$-ensembles, as well as the Schr\"odinger point process. In this more general setting, hyperbolic Brownian motion is replaced by a random walk or Brownian motion on the affine group.   Our approach provides a unified framework to study $\beta$-ensembles that has so far been missing in the literature. In particular, we connect It\^o's classification of affine Brownian motions with the classification of limits of random matrix ensembles.