ShantanuT01/DACTYL-Pretraining huggingface dataset:
The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): \[ \sum_{m,n \in \mbox{\bf Z}} (am^2+bmn+cn^2+q)^{-s}, \] is analytically continued in the variable $s$ by using zeta-function techniques. A simple formula is obtained, which extends the Chowla-Selberg formula to inhomogeneous Epstein zeta-functions. The new expression is then applied to solve the problem of computing the determinant of the basic differential operator that appears in an attempt at quantizing gravity by using the Wheeler-De Witt equation in 2+1 dimensional spacetime with the torus topology.
Fast evolution of Internet technologies has led to an explosive growth of video data available in the public domain and created unprecedented challenges in the analysis, organization, management, and control of such content. The problems encountered in video analysis such as identifying a video in a large database (e.g. detecting pirated content in YouTube), putting together video fragments, finding similarities and common ancestry between different versions of a video, have analogous counterpart problems in genetic research and analysis of DNA and protein sequences. In this paper, we exploit the analogy between genetic sequences and videos and propose an approach to video analysis motivated by genomic research. Representing video information as video DNA sequences and applying bioinformatic algorithms allows to search, match, and compare videos in large-scale databases. We show an application for content-based metadata mapping between versions of annotated video.
The Herschel Space Observatory opens the sky for observations in the far infrared at high spectral and spatial resolution. A particular class of molecules will be directly observable; light diatomic hydrides and their ions (CH, OH, SH, NH, CH+, OH+, SH+, NH+). These simple constituents are important both for the chemical evolution of the region and as tracers of high-energy radiation. If outflows of a forming star erode cavities in the envelope, protostellar far UV (FUV; 6 < E_gamma < 13.6 eV) radiation may escape through such low-density regions. Depending on the shape of the cavity, the FUV radiation then irradiates the quiescent envelope in the walls along the outflow. The chemical composition in these outflow walls is altered by photoreactions and heating via FUV photons in a manner similar to photo dominated regions (PDRs).   In this work, we study the effect of cavity shapes, outflow density, and of a disk with the two-dimensional chemical model of a high-mass young stellar object introduced in the second paper in this series.   We find that the shape of the cavity is particularly important in the innermost part of the envelope, where the dust temperatures are high enough (> 100 K) for water ice to evaporate. If the cavity shape allows FUV radiation to penetrate this hot-core region, the abundance of FUV destroyed species (e.g. water) is decreased. In particular, diatomic hydrides and their ions CH$+, OH+ and NH+ are enhanced by many orders of magnitude in the outflow walls due to the combination of high gas temperatures and rapid photodissociation of more saturated species. The enhancement of these diatomic hydrides is sufficient for a detection using the HIFI and PACS instruments onboard Herschel. The effect of X-ray ionization on the chemistry is found to be small, due to the much larger luminosity in FUV bands compared to X-rays.
Phase transition of RN-AdS black hole is investigated from a new perspective. Not only the cosmological constant is treated as pressure, but also the spatial curvature of black hole is treated as topological charge. We obtain the extended thermodynamic first law from which the mass is naturally viewed as enthalpy instead of energy. In canonical ensemble with fixed topological charge and electric charge, interesting van der Waals system's oscillatory behavior in $T-S$, $P-V$ graphes and swallow tail behavior in $G-T$, $G-P$ graphes are observed. By applying the Maxwell equal area law and by analysing the gibbs free energy, we obtain analytical phase transition coexistence curves ($T-P$) which are consistent with each other.
Theoretical description of inclusive tau lepton hadronic decay is performed in the framework of Dispersive approach to QCD. The significance of effects due to hadronization is demonstrated. The approach on hand is capable of describing experimental data on tau lepton decay in vector and axial-vector channels. The vicinity of values of QCD scale parameter obtained in both channels testifies to the self-consistency of developed approach.
The simultaneous detection of electromagnetic and gravitational wave emission from merging neutron star binaries would aid greatly in their discovery and interpretation. By studying turbulent amplification of magnetic fields in local high-resolution simulations of neutron star merger conditions, we demonstrate that magnetar-level (~10^16) G fields are present throughout the merger duration. We find that the small-scale turbulent dynamo converts 60% of the randomized kinetic energy into magnetic fields on a merger time scale. Since turbulent magnetic energy dissipates through reconnection events which accelerate relativistic electrons, turbulence may facilitate the conversion of orbital kinetic energy into radiation. If 10^-4 of the ~ 10^53 erg of orbital kinetic available gets processed through reconnection, and creates radiation in the 15-150 keV band, then the fluence at 200 Mpc would be 10^-7 erg/cm^2, potentially rendering most merging neutron stars in the advanced LIGO and Virgo detection volumes detectable by Swift BAT.
It has been shown in experiments that self-climb of prismatic dislocation loops by pipe diffusion plays important roles in their dynamical behaviors, e.g., coarsening of prismatic loops upon annealing, as well as the physical and mechanical properties of materials with irradiation. In this paper, we show that this dislocation dynamics self-climb formulation that we derived in Ref. [1] is able to quantitatively describe the properties of self-climb of prismatic loops that were observed in experiments and atomistic simulations. This dislocation dynamics formulation applies to self-climb by pipe diffusion for any configurations of dislocations. For small circular prismatic loops, our formulation recovers the available models in the literature based on linearly mobility relation driven by the interaction force between the loops and an external stress gradient. We also present DDD implementation method of this self-climb formulation. Simulations performed show evolution, translation and coalescence of prismatic loops as well as prismatic loops driven by an edge dislocation by self-climb motion and the elastic interaction between them. These results are in excellent agreement with available experimental and atomistic results. We have also performed systematic analyses of the behaviors of a prismatic loop under the elastic interaction with an infinite, straight edge dislocation by motions of self-climb and glide.
We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber dynamics for the Ising model may get trapped in sets of partially ordered metastable states even for finite system size, and this becomes more probable as the size increases. Voter dynamics instead always converges to full order on finite networks, even if this does not occur via coherent growth of domains. The time needed for order to be reached diverges with the system size. In both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale-free.
We prove the weak positivity of the kernels of Kodaira-Spencer- type maps for pure Hodge module extensions of generically defined variations of Hodge structure.
The nonlinear electron and heat currents of quantum dot molecules (QDMs) under a temperature bias are theoretically investigated, including all correlation functions arising from electron Coulomb interactions in QDMs. Unlike the case of double QDs, the maximum efficiency of serially coupled triple QDs (SCTQD) occurs in the orbital depletion regime owing to the interdot Coulomb blockade. The electron current in SCTQD shows a bipolar oscillatory behavior with respect to the variation of QD energy levels, whereas the heat current does not show such a behavior. This is mainly attributed to thermal-induced bias. In addition, we illustrate how the efficiency of SCTQD is influenced by the external load resistance, and phonon heat flow. Finally, a direction-dependent electron current driven by a temperature bias has been demonstrated for a SCTQD with staircase-like energy levels.
{\it Chandra} spectroscopy of transient stellar-mass black holes in outburst has clearly revealed accretion disk winds in soft, disk--dominated states, in apparent anti-correlation with relativistic jets in low/hard states. These disk winds are observed to be highly ionized, dense, and to have typical velocities of $\sim$1000 km/s or less projected along our line of sight. Here, we present an analysis of two {\it Chandra} High Energy Transmission Grating spectra of the Galactic black hole candidate IGR J17091$-$3624 and contemporaneous EVLA radio observations, obtained in 2011. The second {\it Chandra} observation reveals an absorption line at 6.91$\pm$0.01 keV; associating this line with He-like Fe XXV requires a blue-shift of $9300^{+500}_{-400}$ km/s (0.03$c$, or the escape velocity at 1000 R$_{Schw}$). This projected outflow velocity is an order of magnitude higher than has previously been observed in stellar-mass black holes, and is broadly consistent with some of the fastest winds detected in active galactic nuclei. A potential feature at 7.32 keV, if due to Fe XXVI, would imply a velocity of $\sim 14600$ km/s (0.05$c$), but this putative feature is marginal. Photoionization modeling suggests that the accretion disk wind in IGR J17091$-$3624 may originate within 43,300 Schwarzschild radii of the black hole, and may be expelling more gas than accretes. The contemporaneous EVLA observations strongly indicate that jet activity was indeed quenched at the time of our {\it Chandra} observations. We discuss the results in the context of disk winds, jets, and basic accretion disk physics in accreting black hole systems.
For every simplicial complex K there exists a vertex-transitive simplicial complex homotopy equivalent to a wedge of copies of K with some copies of the circle. It follows that every simplicial complex can occur as a homotopy wedge summand in some vertex-transitive complex. One can even demand that the vertex-transitive complex is the clique complex of a Cayley graph or that it is facet-transitive.
We calculate holographically one and two-point functions of scalar operators at finite density and/or finite temperature. In the case of finite density and zero temperature we argue that only scalar operators can have non-zero VEVs. In the case in which both the chemical potential and the temperature are finite, we present a systematic expansion of the two-point correlators in powers of the temperature T and the chemical potential $\Omega$.   The holographic result is in agreement with the general form of the OPE which dictates that the two-point function may be written as a linear combination of the Gegenbauer polynomials $C_J^{(1)}(\xi)$ but with the coefficients depending now on both the temperature and the chemical potential, as well as on the CFT data. The leading terms in this expansion originate from the expectation values of the scalar operator $\phi^2$, the R-current ${\cal J}^\mu_{\phi_3}$ and the energy-momentum tensor $T^{\mu\nu}$.   By employing the Ward identity for the R-current and by comparing the appropriate term of the holographic result for the two-point correlator to the corresponding term in the OPE, we derive the value of the R-charge density of the background. Compelling agreement with the analysis of the thermodynamics of the black hole is found. Finally, we determine the behaviour of the two-point correlators, in the case of finite temperature, and in the limit of large temporal or spatial distance of the operators.
This paper has been withdrawn by the first author due to disagreement with experiments.
Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Gr\"uneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rate of in-plane and flexural phonons as function of temperature, wave vector and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There we find that the transition temperature from negative to positive thermal expansion is lowered with smaller system size and by renormalization of the flexural mode frequency. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of Normal and Umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.
Let $g$ be an even positive integer, and $p$ be a prime number. We compute the cohomological invariants with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of the stacks of hyperelliptic curves $\mathscr{H}_g$ over an algebraically closed field $k_0$.
The galaxy cluster SPT-CL J0205-5829 currently has the highest spectroscopically-confirmed redshift, z=1.322, in the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) survey. XMM-Newton observations measure a core-excluded temperature of Tx=8.7keV producing a mass estimate that is consistent with the Sunyaev-Zel'dovich derived mass. The combined SZ and X-ray mass estimate of M500=(4.9+/-0.8)e14 h_{70}^{-1} Msun makes it the most massive known SZ-selected galaxy cluster at z>1.2 and the second most massive at z>1. Using optical and infrared observations, we find that the brightest galaxies in SPT-CL J0205-5829 are already well evolved by the time the universe was <5 Gyr old, with stellar population ages >3 Gyr, and low rates of star formation (<0.5Msun/yr). We find that, despite the high redshift and mass, the existence of SPT-CL J0205-5829 is not surprising given a flat LambdaCDM cosmology with Gaussian initial perturbations. The a priori chance of finding a cluster of similar rarity (or rarer) in a survey the size of the 2500 deg^2 SPT-SZ survey is 69%.
A new formula for the gravitational potential of flattened systems is proposed. It is a modification of the Miyamoto-Nagai potential and should be applied to very flattened systems, exponential discs as a typical example. The resulting rotation curve agrees sufficiently well with that obtained by using special functions and the total masses remain the same. The functions contained in the new term can improve the agreement for the rotation curve and also reduce the effect of negative density values which appear off the midplane.
Numerical models of atomic diffusion in magnetic atmospheres of ApBp stars predict abundance structures that differ from the empirical abundance maps derived with (Zeeman) Doppler mapping (ZDM). Whereas both equilibrium abundance stratification calculations and stationary solutions to the time-dependent diffusion equations predict (warped) rings about the magnetic equator in dipole-like magnetic geometries, spot-like structures dominate published maps. An in-depth analysis of this apparent disagreement investigates the detectability by means of ZDM of a variety of abundance structures, including (warped) rings predicted by theory, but also some complex spot-like structures. As it turns out, a number of published maps have to be considered spurious either because strong magnetic fields have been neglected or because they are based on spectra where photon noise dominates over the signal of the alleged abundance structures. Even when spectra of high signal to noise ratio are available, it can prove altogether impossible to correctly recover shapes, positions and abundances of a mere handful of spots, even using all 4 Stokes parameters and knowing the field geometry, the recovery of (warped) rings can be equally challenging. Inversions -- based on just one or two spectral lines -- of complex abundance maps usually admit of multiple solutions. It turns out that there is no guarantee that a properly chosen regularisation function will lead to the true abundance map. Attention is drawn to the need for a study that would elucidate the relation between the stratified, field-dependent abundance structures predicted by diffusion theory and empirical maps obtained by means of "canonical" ZDM, i.e. with mean atmospheres and unstratified abundances. Finally we point out difficulties arising from the 3D nature of the atomic diffusion process in magnetic ApBp star atmospheres.
Unfortunately, some proofs in the first version of this paper were incorrect. In this revised version, some minor gaps are fixed, one serious mistake found. The main theorem is now claimed only under a restrictive technical assumption. This invalidates the application to quotient singularities by the Weyl group of type $G_2$. Everything else still stands (in particular, the claim that every symplectic resolution is semismall).
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which minimize some forms of graph cut. Previous research already gave some results about the cut bounds for unweighted regular graph. In this paper, we prove a result about the lower bound for weighted graphs that have some regular properties and show similar results for more general case.
We construct cosmological models based on a complex scalar field with a power-law potential $V=\frac{K}{\gamma-1}(\frac{m}{\hbar})^{2\gamma}|\varphi|^{2\gamma}$ associated with a polytropic equation of state $P=K\rho^{\gamma}$ (the potential associated with an isothermal equation of state $P=\rho k_B T/m$ is $V=\frac{m k_B T}{\hbar^2}|\varphi|^2 [\ln(m^2|\varphi|^2/\rho_*\hbar^2)-1]$ and the potential associated with a logotropic equation of state $P=A\ln(\rho/\rho_P)$ is $V=-A[\ln(m^2|\varphi|^2/\hbar^2\rho_P)+1]$). We consider a fast oscillation regime of ``spintessence'' where the equations of the problem can be simplified. We study all possible cases with arbitrary (positive and negative) values of the polytropic constant and polytropic index. The $\Lambda$CDM model, the Chaplygin gas model and the Bose-Einstein condensate model are recovered as particular cases of our study corresponding to a constant potential ($\gamma=0$), an inverse square-law potential ($\gamma=-1$), and a quartic potential ($\gamma=2$). We also derive the two-fluid representation of the Chaplygin gas model.
We present X-ray light curves of Cygnus X-3 as measured by the recently launched AstroSat satellite. The light curve folded over the binary period of 4.8 hours shows a remarkable stability over the past 45 years and we find that we can use this information to measure the zero point to better than 100 s. We revisit the historical binary phase measurements and examine the stability of the binary period over 45 years. We present a new binary ephemeris with the period and period derivative determined to an accuracy much better than previously reported. We do not find any evidence for a second derivative in the period variation. The precise binary period measurements, however, indicate a hint of short term episodic variations in periods. Interestingly, these short term period variations coincide with the period of enhanced jet activity exhibited by the source. We discuss the implications of these observations on the nature of the binary system.
We study the stationary Stokes system in divergence form. The coefficients are assumed to be merely measurable in one direction and have Dini mean oscillations in the other directions. We prove that if $(u,p)$ is a weak solution of the system, then $(Du,p)$ is bounded and its certain linear combinations are continuous. We also prove a weak type-$(1,1)$ estimate for $(Du,p)$ under a stronger assumption on the $L^1$-mean oscillation of the coefficients. The corresponding results up to the boundary on a half ball are also established. These results are new even for elliptic equations and systems.
The quasi-thermal components found in many Fermi gamma-ray bursts (GRBs) imply that the photosphere emission indeed contributes to the prompt emission of many GRBs. But whether the observed spectra empirically fitted by the Band function or cutoff power law, especially the spectral and peak energy ($E_{p}$) evolutions can be explained by the photosphere emission model alone needs further discussion. In this work, we investigate in detail the time-resolved spectra and $E_{p}$ evolutions of photospheric emission from a structured jet, with an inner-constant and outer-decreasing angular Lorentz factor profile. Also, a continuous wind with a time-dependent wind luminosity has been considered. We show that the photosphere spectrum near the peak luminosity is similar to the cutoff power-law spectrum. The spectrum can have the observed average low-energy spectral index $\alpha $ $ \sim -1$, and the distribution of the low-energy spectral index in our photosphere model is similar to that observed ($-2\lesssim $ $\alpha \lesssim 0$). Furthermore, the two kinds of spectral evolutions during the decay phase, separated by the width of the core ($\theta _{c}$), are consistent with the time-resolved spectral analysis results of several Fermi multi-pulse GRBs and single-pulse GRBs, respectively. Also, for this photosphere model we can reproduce the two kinds of observed $E_{p}$ evolution patterns rather well. Thus, by considering the photospheric emission from a structured jet, we reproduce the observations well for the GRBs best fitted by the cutoff power-law model for the peak-flux spectrum or the time-integrated spectrum.
The probability for quantum creation of an inflationary universe with a pair of black holes in 1/R - gravitational theory has been studied. Considering a gravitational action which includes a cosmological constant ($\Lambda$) in addition to $ \delta R^{- 1} $ term, the probability has been evaluated in a semiclassical approximation with Hartle-Hawking boundary condition. We obtain instanton solutions determined by the parameters $\delta$ and $\Lambda$ satisfying the constraint $ \delta \leq \frac{4 \Lambda^{2}}{3}$. However, we note that two different classes of instanton solutions exists in the region $0 < \delta < \frac{4 \Lambda^{2}}{3}$. The probabilities of creation of such configurations are evaluated. It is found that the probability of creation of a universe with a pair of black holes is strongly suppressed with a positive cosmological constant except in one case when $0 < \delta < \Lambda^{2}$. It is also found that gravitational instanton solution is permitted even with $\Lambda = 0$ but one has to consider $\delta < 0$. However, in the later case a universe with a pair of black holes is less probable.