ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this small review we present the actual state the knowledge about weighting black holes. Black holes can be found in stellar binary systems in our Galaxy and in other nearby galaxies, in globular clusters, which we can see in our and nearby galaxies, and in centres of all well-developed galaxies. Range of values of their masses is wide and cover about ten orders of magnitude (not taking into account the hypothetic primordial black holes). Establishing the presence of black holes, and in particular the measurement of their mass is one on the key issues for many branches of astronomy, from stellar evolution to cosmology.
In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties of the corresponding Musielak-Orlicz Sobolev spaces (an equivalent norm, uniform convexity, Radon-Riesz property with respect to the modular) and the properties of the new double phase operator (continuity, strict monotonicity, (S$_+$)-property). In contrast to the known constant exponent case we are able to weaken the assumptions on the data. Finally we show the existence and uniqueness of corresponding elliptic equations with right-hand sides that have gradient dependence (so-called convection terms) under very general assumptions on the data. As a result of independent interest, we also show the density of smooth functions in the new Musielak-Orlicz Sobolev space even when the domain is unbounded.
We give a self-contained and elementary proof for boundedness, existence, and uniqueness of solutions to dynamic programming principles (DPP) for biased tug-of-war games with running costs. The domain we work in is very general, and as a special case contains metric spaces. Technically, we introduce game-trees and show that a discretized flow converges uniformly, from which we obtain not only the existence, but also the uniqueness. Our arguments are entirely deterministic, and also do not rely on (semi-)continuity in any way; in particular, we do not need to mollify the DPP at the boundary for well-posedness.
Neutrino oscillation experiments suggest existence of new flavor-violating interactions in high energy scale. It may be possible to probe them by the flavor- and CP-violating processes in leptons and hadrons in the supersymmetric (SUSY) models. In this article the third-generation flavor violation is reviewed in the SUSY seesaw model and SUSY SU(5) GUT with the right-handed neutrinos.
We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components $B_x({\bf x})$, $B_y({\bf x})$, $B_z({\bf x})$, the force-free parameter $\alpha({\bf x})$, the electric current density ${\bf j}({\bf x})$, and are accurate to second-order (of the nonlinear force-free $\alpha$-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.
We study the gravity duals of supercurrent solutions in the AdS black hole background with general phase structure to describe both the first and the second order phase transitions at finite temperature in strongly interacting systems. We argue that the conductivity and the pair susceptibility can be possible phenomenological indications to distinguish the order of phase transitions. We extend our discussion to the AdS soliton configuration. Different from the black hole spacetime, in the probe limit the first order phase transition cannot be brought by introducing the spatial component of the vector potential of the gauge field in the AdS soliton background.
Spin polarization of a topological surface state for GeBi$_2$Te$_4$, the newly discovered three-dimensional topological insulator, has been studied by means of the state of the art spin- and angle-resolved photoemission spectroscopy. It has been revealed that the disorder in the crystal has a minor effect on the surface state spin polarization and it exceeds 75% near the Dirac point in the bulk energy gap region ($\sim$180 meV). This new finding for GeBi$_{2}$Te$_{4}$ promises not only to realize a highly spin polarized surface isolated transport but to add new functionality to its thermoelectric and thermomagnetic properties.
We discuss near-infrared (NIR) slit spectra of six early-type disk galaxies in the Virgo Cluster. While the depth of the CO(2,0) band is consistent with the centers of these galaxies having solar or slightly sub-solar luminosity-weighted metallicities, galaxy-to-galaxy variations in the depth of the NaI 2.21um doublet are found, with NaI2.21um lines in three galaxies (NGC 4491, NGC 4584, and NGC 4620) that are deeper than those predicted for a solar chemical mixture and a solar-neighborhood mass function. Considering the depth of the NaD lines found by Davidge (2018a), the deep NaI2.21um lines are tentatively attributed to a bottom-heavy mass function. This is counter to observed trends between mass function slope and velocity dispersion. Two of the three galaxies with deep NaI2.21um (NGC 4584 and NGC 4620) have Sersic exponents that are consistent with a classical bulge. As for NGC 4491, its central NIR spectrum contains prominent emission lines. The relative strengths of Brgamma and H_2S(1), the presence of [FeII] emission, and the mid-infrared spectral-energy distribution are all consistent with intense recent star formation near the center of that galaxy. Wavelengths that contain the Ballick-Ramsey C_2 band at 1.76um are matched by moderately metal-poor E-MILES model spectra with an age of 2 Gyr. It is concluded that these galaxies have evolved in a cluster environment for at least several Gyr.
This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, Matsumura and Nishihara showed in [A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas. Comm. Math. Phys. 222 (2001), 449-474] that there exists boundary layer solution to the inflow problem and both the boundary layer solution, the rarefaction wave, and the superposition of boundary layer solution and rarefaction wave are nonlinear stable under small initial perturbation. The main purpose of this paper is to show that similar stability results for the boundary layer solution and the supersonic rarefaction wave still hold for a class of large initial perturbation which can allow the initial density to have large oscillation. The proofs are given by an elementary energy method and the key point is to deduce the desired lower and upper bounds on the density function.
We consider stochastic rules of mass transport which lead to steady states that factorize over the links of a one-dimensional ring. Based on the knowledge of the steady states, we derive the onset of a phase transition from a liquid to a condensed phase that is characterized by the existence of a condensate. For various types of weight functions which enter the hopping rates, we determine the shape of the condensate, its scaling with the system size, and the single-site mass distribution as characteristic static properties. As it turns out, the condensate's shape and its scaling are not universal, but depend on the competition between local and ultralocal interactions. So we can tune the shape from a delta-like envelope to a parabolic-like or a rectangular one. While we treat the liquid phase in the grand-canonical formalism, we develop a different analytical approach for the condensed phase. Its predictions are well confirmed by numerical simulations. Possible extensions to higher dimensions are indicated.
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction, giving a prescribed two-electron density, has also been solved. The two-electron densities are found to lie in a convex set in a vector space. We show that density matrices are more complicated objects than densities, and density matrices do not seem to lie in a convex set. An algorithm to compute the ground-state energy of a few-particle system is proposed, based on the obtained results, where the correlation is treated exactly.
We extend the classical coupon collector's problem to one in which two collectors are simultaneously and independently seeking collections of $d$ coupons. We find, in finite terms, the probability that the two collectors finish at the same trial, and we find, using the methods of Gessel-Viennot, the probability that the game has the following ``ballot-like'' character: the two collectors are tied with each other for some initial number of steps, and after that the player who first gains the lead remains ahead throughout the game. As a by-product we obtain the evaluation in finite terms of certain infinite series whose coefficients are powers and products of Stirling numbers of the second kind.   We study the variant of the original coupon collector's problem in which a single collector wants to obtain at least $h$ copies of each coupon. Here we give a simpler derivation of results of Newman and Shepp, and extend those results. Finally we obtain the distribution of the number of coupons that have been obtained exactly once (``singletons'') at the conclusion of a successful coupon collecting sequence.
We use QCD sum-rules to study the decays $\phi \to \eta \gamma$ and $\phi \to \eta^\prime \gamma$, obtaining ${\cal B}(\phi \to \eta \gamma)=(1.15 \pm 0.2) 10^{-2}$ and ${\cal B}(\phi \to \eta^\prime \gamma)=(1.18 \pm 0.4) 10^{-4}$, in very good agreement with existing experimental data. We also discuss the issue of $\eta-\eta^\prime$ mixing, predicting the $\eta$ and $\eta^\prime$ decay constants in a mixing scheme in the quark-flavour basis.
A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.
In this paper, we present a multi-color photometric study of the nearby spiral galaxy M81, using images obtained with the Beijing Astronomical Observatory 60/90 cm Schmidt Telescope in 13 intermediate-band filters from 3800 to 10000{\AA}. The observations cover the whole area of M81 with a total integration of 51 hours from February 1995 to February 1997. This provides a multi-color map of M81 in pixels of $1\arcsec.7 \times 1\arcsec.7$. Using theoretical stellar population synthesis models, we demonstrate that some BATC colors and color indices can be used to disentangle the age and metallicity effect. We compare in detail the observed properties of M81 with the predictions from population synthesis models and quantify the relative chemical abundance, age and reddening distributions for different components of M81. We find that the metallicity of M81 is about $Z=0.03$ with no significant difference over the whole galaxy. In contrast, an age gradient is found between stellar populations of the central regions and of the bulge and disk regions of M81: the stellar population in its central regions is older than 8 Gyr while the disk stars are considerably younger, $\sim 2$ Gyr. We also give the reddening distribution in M81. Some dust lanes are found in the galaxy bulge region and the reddening in the outer disk is higher than that in the central regions.
We study quantum systems with broken symmetry that can be modelled as cyclic three-level atoms with coexisting one- and two-photon transitions. They can be selectively optically excited to any state. As an example, we show that left- and right-handed chiral molecules starting in the same initial states can evolve into different final states by a purely dynamic transfer process. That means, left- and right-handed molecules can be distinguished purely dynamically.
We consider the effects of advection and radial gradients of pressure and radial drift velocity on the structure of optically thick accretion disks. We concentrate our efforts on highly viscous disks, $\alpha=1.0$, with large accretion rates. Contrary to disk models neglecting advection, we find that continuous solutions extending from the outer disk regions to the inner edge exist for all accretion rates we have considered. We show that the sonic point moves outward with increasing accretion rate, and that in the innermost disk region advection acts as a heating process that may even dominate over dissipative heating. Despite the importance of advection on it's structure, the disk remains geometrically thin.
Recent advances in many-body physics have made it possible to study correlated electron systems at the two-particle level. In Dynamical Mean-Field theory, it has been shown that the metal-insulator phase diagram is closely related to the eigenstructure of the susceptibility. So far, this situation has been studied using accurate but numerically expensive solvers. Here, the Iterated Perturbation Theory (IPT) approximation is used instead. Its simplicity makes it possible to obtain analytical results for the two-particle vertex and the DMFT Jacobian. The limited computational cost also enables a detailed comparison of analytical expressions for the response functions to results obtained using finite differences. At the same time, the approximate nature of IPT precludes an interpretation of the metal-insulator transition in terms of a Landau free energy functional.
We show that the generating function for the higher Weil-Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten's free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a ``very large phase space'', correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande. From this formula we derive an asymptotical expression for the Weil-Petersson volume as conjectured by C. Itzykson. We also discuss a topological interpretation of the genus expansion formula of Itzykson-Zuber, as well as a related bialgebra acting upon quantum cohomology as a complex version of the classical path groupoid.
The main purpose of this work is to study self-similar branching Markov chains. First we will construct such a process. Then we will establish certain Limit Theorems using the theory of self-similar Markov processes.
The discovery of novae as sources of ~GeV gamma-rays highlights the key role of shocks and relativistic particle acceleration in these transient systems. Although there is evidence for a spectral cut-off above energies ~1-100 GeV at particular epochs in some novae, the maximum particle energy achieved in these accelerators has remained an open question. The high densities of the nova ejecta (~10 orders of magnitude larger than in supernova remnants) render the gas far upstream of the shock neutral and shielded from ionizing radiation. The amplification of the magnetic field needed for diffusive shock acceleration requires ionized gas, thus confining the acceleration process to a narrow photo-ionized layer immediately ahead of the shock. Based on the growth rate in this layer of the hybrid non-resonant cosmic ray current-driven instability (considering also ion-neutral damping), we quantify the maximum particle energy, Emax, across the range of shock velocities and upstream densities of interest. We find values of Emax ~ 10 GeV - 10 TeV, which are broadly consistent with the inferred spectral cut-offs, but which could also in principle lead to emission extending to higher energies >100 GeV accessible to atmosphere Cherenkov telescopes, such as the planned Cherenkov Telescope Array (CTA). Detecting TeV neutrinos with IceCube in hadronic scenarios appears to be more challenging, although the prospects are improved if the shock power during the earliest, densest phases of the nova outburst is higher than is implied by the observed GeV light curves, due to downscattering of the gamma-rays by electrons within the ejecta. Novae provide ideal nearby laboratories to study magnetic field amplification and the onset of cosmic ray acceleration, because other time-dependent sources (e.g. radio supernovae) typically occur too distant to detect as gamma-ray sources.
Following Rankin's method, D. Zagier computed the $n$-th Rankin-Cohen bracket of a modular form $g$ of weight $k_1$ with the Eisenstein series of weight $k_2$ and then computed the inner product of this Rankin-Cohen bracket with a cusp form $f$ of weight $k = k_1+k_2+2n$ and showed that this inner product gives, upto a constant, the special value of the Rankin-Selberg convolution of $f$ and $g$. This result was generalized to Jacobi forms of degree 1 by Y. Choie and W. Kohnen. In this paper, we generalize this result to Jacobi forms defined over ${\mathcal H} \times {\mathbb C}^{(g, 1)}$.
Even though ideas of extracting future-related, or Faster-Than-Light (FTL) information from hyperspace using quantum entanglement have generally been refuted in the last ten years, in this paper we show that the original 'Delayed Choice Quantum Eraser Experiment', 1st performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, designed by Marlan O. Scully & Druhl in 1982-1999, still features hidden topological properties that may have been overlooked by previous analysis, and which prohibit, by principle, the extraction of future-related or real-time information from the detection of the signal particle on the delayed choice of its entangled idler twin(s). We show that such properties can be removed, and quantum-level information from certain hypersurfaces of past, present or future spacetime may be collected real-time, without resulting in any paradox or violation of causality.
This thesis research focusses on the study of the young and energetic isolated ordinary pulsar population detected by the Fermi gamma-ray space telescope. We compared the model expectations of four emission models and the LAT data. We found that all the models fail to reproduce the LAT detections, in particular the large number of high spin-down power objects observed. This inconsistency is not model dependent. A discrepancy between the radio-loud/radio-quiet objects ratio was also found between the observed and predicted samples. The gamma-ray luminosity proportional to the 0.5 power of the spin-down power relation is robustly confirmed by all the assumed models with particular agreement in the slot gap (SG) case. On luminosity bases, the intermediate altitude emission of the two pole caustic SG model is favoured. The beaming factor shows an spin-down power dependency that is slightly visible in theSG case. Estimates of the pulsar orientations have been obtained to explain the simultaneous gamma and radio light-curves. By analysing the solutions we found a relation between the observed energy cutoff and the width of the emission slot gap. This relation has been theoretically predicted. A possible magnetic obliquity alignment with time is rejected -for all the models- on timescale of the order of a million years. The light-curve morphology study shows that the outer magnetosphere gap emission are favoured to explain the observed radio-gamma lag. The light curve moment studies (symmetry and sharpness) on the contrary favour a two pole caustic slot gap emission. All the model predictions suggest a different magnetic field layout with an hybrid two pole caustic and intermediate altitude emission to explain both the pulsar luminosity and light curve morphology . The low magnetosphere emission mechanism of the polar cap model, is systematically rejected by all the tests done.
We analyse multi-wavelength Hubble Space Telescope (HST) observations of a large number of star clusters in the nearby (post-) starburst dwarf galaxy NGC 1569. Their spectral energy distributions (SEDs) cover at least the wavelength range from U to I in equivalent HST filters, in most cases supplemented by near-infrared data. Using our most up-to-date evolutionary synthesis models of the Goettingen GALEV code we determine ages, metallicities, extinction values and masses for each individual cluster robustly and independently. We confirm the youth of most of these objects. The majority were formed in a very intense starburst starting around 25 Myr ago. While there are two prominent ``super star clusters'' present in this galaxy, with masses of (5-16) * 10^5 Msun, almost all remaining clusters are significantly less massive than an average Milky Way globular cluster, and are generally consistent with open cluster-type objects. We determine the cluster mass function from individual cluster masses derived by scaling the model SEDs of known mass to the observed cluster SEDs for each individual cluster. We find signs of a change in the cluster mass function as the burst proceeds, which we attribute to the special conditions of star cluster formation in this starburst dwarf galaxy environment.
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society.
We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov-Kimball (EFKM) model with the tunable Coulomb interaction $U$ between both species. By lowering the temperature, the electron-hole system may become unstable with respect to the formation of the excitons, i.e, electron-hole pairs at temperature $T=T_{\Delta}$, exhibiting a gap $\Delta$ in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formula for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.