ShantanuT01/DACTYL-Pretraining huggingface dataset:
We write down explicit expressions for the $x$-evolution (equivalent to energy or rapidity evolution) of $2 n$ ($n = 1, 2, ...$) Wilson lines using the JIMWLK equation and the Color Glass Condensate formalism. We investigate the equation in the weak gluon field limit (linear regime) by expanding the Wilson lines in powers of the gluon field and show that it reduces to the BJKP equation describing the evolution of a state of $2 n$ Reggeized gluons with energy. We also make available for download a {\it Mathematica} program which provides this expression for any value of $n$.
We investigate the dichotomy between jetted and non-jetted Active Galactic Nuclei (AGNs), focusing on the fundamental differences of these two classes in the accretion physics onto the central supermassive black hole (SMBH). Our aim is to study and constrain the structure, kinematics and physical state of the nuclear environment in the Broad Line Radio Galaxy (BLRG) PKS 2251+11. The high X-ray luminosity and the relative proximity make such AGN an ideal candidate for a detailed analysis of the accretion regions in radio galaxies. We performed a spectral and timing analysis of a $\sim$64 ks observation of PKS 2251+11 in the X-ray band with XMM-Newton. We modeled the spectrum considering an absorbed power law superimposed to a reflection component. We performed a time-resolved spectral analysis to search for variability of the X-ray flux and of the individual spectral components. We found that the power law has a photon index $\Gamma=1.8\pm 0.1$, absorbed by an ionized partial covering medium with a column density $N_H=(10.1\pm 0.8) \times 10^{23}$ cm$^{-2}$, a ionization parameter $\log{\xi}=1.3\pm 0.1$ erg s$^{-1}$ cm and a covering factor $f\simeq90\%$. Considering a density of the absorber typical of the Broad Line Region (BLR), its distance from the central SMBH is of the order of $r\sim 0.1$ pc. An Fe K$\alpha$ emission line is found at 6.4 keV, whose intensity shows variability on time scales of hours. We derived that the reflecting material is located at a distance $r\gtrsim600r_s$, where $r_s$ is the Schwarzschild radius. Concerning the X-ray properties, we found that PKS 2251+11 does not differ significantly from the non-jetted AGNs, confirming the validity of the unified model in describing the inner regions around the central SMBH, but the lack of information regarding the state of the very innermost disk and SMBH spin still leave unconstrained the origin of the jet.
A two-cluster microscopic model is applied to study elastic alpha-alpha scattering and resonance structure of $^{8}$Be. The model is an algebraic version of the Resonating Group Method, which makes use complete set of oscillator functions to expand wave function of two-cluster system. Interaction between clusters is determined by well-known semi-realistic nucleon-nucleon potentials of Hasegawa-Nagata, Minnesota and Volkov. Detail analysis of resonance wave functions is carried out in oscillator, coordinate and momentum spaces. Effects of the Pauli principle on wave functions of the $^{8}$Be continuous spectrum states are thoroughly studied.
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4$\times$4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic 5-dimensional GR, derive some of their properties using ADecM and construct the \textit{most general unique power series solutions}. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.
I review recent progress on exclusive hadronic B meson decays in the perturbative QCD approach, with focus on puzzles in the branching ratios and the CP asymmetries of the B -> pi K and B -> pi pi modes, and polarization fractions in B -> VV modes.
Coronal mass ejections (CMEs) are often associated with coronal dimmings, i.e. transient dark regions that are most distinctly observed in Extreme Ultra-violet (EUV) wavelengths. Using Atmospheric Imaging Assembly (AIA) data, we apply Differential Emission Measure (DEM) diagnostics to study the plasma characteristics of six coronal dimming events. In the core dimming region, we find a steep and impulsive decrease of density with values up to 50-70%. Five of the events also reveal an associated drop in temperature of 5-25%. The secondary dimming regions also show a distinct decrease in density, but less strong, decreasing by 10-45%. In both the core and the secondary dimming the density changes are much larger than the temperature changes, confirming that the dimming regions are mainly caused by plasma evacuation. In the core dimming, the plasma density reduces rapidly within the first 20-30 min after the flare start, and does not recover for at least 10 hrs later, whereas the secondary dimming tends to be more gradual and starts to replenish after 1-2 hrs. The pre-event temperatures are higher in the core dimming (1.7-2.6 MK) than in the secondary dimming regions (1.6-2.0 MK). Both core and secondary dimmings are best observed in the AIA 211 \AA\ and 193 \AA\ filters. These findings suggest that the core dimming corresponds to the footpoints of the erupting flux rope rooted in the AR, while the secondary dimming represents plasma from overlying coronal structures that expand during the CME eruption.
We report the detection of a curved magnetic field in the ring-like shell of the bubble N4, derived from near-infrared polarization of reddened diskless stars located behind this bubble. The magnetic field in the shell is curved and parallel to the ring-like shell, and its strength is estimated to be $\sim120\,\mu$G in the plane of the sky. The magnetic field strength in the shell is significantly enhanced compared to the local field strength. We calculate the mass-to-flux ratio for the submillimeter clumps in the shell and find that they are all magnetically subcritical. Our results demonstrate that the magnetic field strengthens as the interstellar medium is compressed into a shell, and suggest that the magnetic field has the potential to hinder star formation triggered by \ion{H}{2} region expansion.
We derive dispersion relations for the electroweak oblique observables measured at LEP in the context of $SO(5)/SO(4)$ composite Higgs models. It is shown how these relations can be used and must be modified when modeling the spectral functions through a low-energy effective description of the strong dynamics. The dispersion relation for the parameter $\epsilon_3$ is then used to estimate the contribution from spin-1 resonances at the 1-loop level. Finally, it is shown that the sign of the contribution to the $\hat S$ parameter from the lowest-lying spin-1 states is not necessarily positive definite, but depends on the energy scale at which the asymptotic behavior of current correlators is attained.
First results of near-IR adaptive optics (AO)-assisted imaging, interferometry, and spectroscopy of this Luminous Blue Variable (LBV) are presented. They suggest that the Pistol Star is at least double. If the association is physical, it would reinforce questions concerning the importance of multiplicity for the formation and evolution of extremely massive stars.
We consider the behaviour of minimax recursions defined on random trees. Such recursions give the value of a general class of two-player combinatorial games. We examine in particular the case where the tree is given by a Galton-Watson branching process, truncated at some depth $2n$, and the terminal values of the level-$2n$ nodes are drawn independently from some common distribution. The case of a regular tree was previously considered by Pearl, who showed that as $n\to\infty$ the value of the game converges to a constant, and by Ali Khan, Devroye and Neininger, who obtained a distributional limit under a suitable rescaling.   For a general offspring distribution, there is a surprisingly rich variety of behaviour: the (unrescaled) value of the game may converge to a constant, or to a discrete limit with several atoms, or to a continuous distribution. We also give distributional limits under suitable rescalings in various cases.   We also address questions of endogeny. Suppose the game is played on a tree with many levels, so that the terminal values are far from the root. To be confident of playing a good first move, do we need to see the whole tree and its terminal values, or can we play close to optimally by inspecting just the first few levels of the tree? The answers again depend in an interesting way on the offspring distribution.   We also mention several open questions.
We consider a one-dimensional chain of coupled oscillators in contact at both ends with heat baths at different temperatures, and subject to an external force at one end. The Hamiltonian dynamics in the bulk is perturbed by random exchanges of the neighbouring momenta such that the energy is locally conserved. We prove that in the stationary state the energy and the volume stretch profiles, in large scale limit, converge to the solutions of a diffusive system with Dirichlet boundary conditions. As a consequence the macroscopic temperature stationary profile presents a maximum inside the chain higher than the thermostats temperatures, as well as the possibility of uphill diffusion (energy current against the temperature gradient). Finally, we are also able to derive the non-stationary macroscopic coupled diffusive equations followed by the energy and volume stretch profiles.
Recent approaches on trajectory forecasting use tracklets to predict the future positions of pedestrians exploiting Long Short Term Memory (LSTM) architectures. This paper shows that adding vislets, that is, short sequences of head pose estimations, allows to increase significantly the trajectory forecasting performance. We then propose to use vislets in a novel framework called MX-LSTM, capturing the interplay between tracklets and vislets thanks to a joint unconstrained optimization of full covariance matrices during the LSTM backpropagation. At the same time, MX-LSTM predicts the future head poses, increasing the standard capabilities of the long-term trajectory forecasting approaches. With standard head pose estimators and an attentional-based social pooling, MX-LSTM scores the new trajectory forecasting state-of-the-art in all the considered datasets (Zara01, Zara02, UCY, and TownCentre) with a dramatic margin when the pedestrians slow down, a case where most of the forecasting approaches struggle to provide an accurate solution.
We address the decoherence of a localized electron spin in an external magnetic field due to the hyperfine interaction with a lattice of nuclear spins. Using a completely non-perturbative method, rigorous bounds on the T_1 and T_2 coherence times for the electron spin are provided. It is shown that for magnetic fields B greater than some critical field B_c (B_c ~ .001 - 2 Tesla for the systems studied here), the z-polarization of the electron spin cannot relax, and hence T_1 is infinite. However, even at high fields dephasing can still occur. We provide a lower bound on the T_2 coherence time that explicitly takes into account the effects of a spin echo pulse sequence.
It is shown that nonzero orbital momentum in the vertex of secondary interaction in the triangle graph leads to a more clear picture corresponding to the moving complex singularity compared with the case of constant vertex. The peak in the distribution of the final particles invariant mass becomes narrower and its shift with momentum transfer more distinct. It opens the possibility to observe this picture experimentally.
The radius-luminosity (R-L) relationship of active galactic nuclei (AGNs) established by the reverberation mapping (RM) observations has been widely used as a single-epoch black hole mass estimator in the research of large AGN samples. However, the recent RM campaigns discovered that the AGNs with high accretion rates show shorter time lags by factors of a few comparing with the predictions from the R-L relationship. The explanation of the shortened time lags has not been finalized yet. We collect 8 different single-epoch spectral properties to investigate how the shortening of the time lags correlate with those properties and to understand what is the origin of the shortened lags. We find that the flux ratio between Fe II and H$\beta$ emission lines shows the most prominent correlation, thus confirm that accretion rate is the main driver for the shortened lags. In addition, we establish a new scaling relation including the relative strength of Fe II emission. This new scaling relation can provide less biased estimates of the black hole mass and accretion rate from the single-epoch spectra of AGNs.
This paper reviews some aspects of one of the major unsolved problems in understanding astrophysical (in particular, accretion) disks: whether the disk interiors may be effectively viscous in spite of the absence of marnetorotational instability? In this case a rotational homogeneous inviscid flow with a Keplerian angular velocity profile is spectrally stable, making the transient growth of perturbations a candidate mechanism for energy transfer from the regular motion to perturbations. Transient perturbations differ qualitatively from perturbation modes and can grow substantially in shear flows due to the nonnormality of their dynamical evolution operator. Since the eigenvectors of this operator, alias perturbation modes, are mutually nonorthogonal, they can mutually interfere, resulting in the transient growth of their linear combinations. Physically, a growing transient perturbation is a leading spiral whose branches are shrunk as a result of the differential rotation of the flow. This paper discusses in detail the transient growth of vortex shear harmonics in the spatially local limit as well as methods for identifying the optimal (fastest growth) perturbations. Special attention is given to obtaining such solutions variationally, by integrating the direct and adjoint equations forward and backward in time, respectively. The material is presented in a newcomer-friendly style.
It is generally believed that the shadows of either a black hole or naked singularity arise due to photon spheres developing in these spacetimes. Here we propose a new spherically symmetric naked singularity spacetime solution of Einstein equations which has no photon sphere, and we show that the singularity casts a shadow in the absence of the photon sphere. We discuss some novel features of this shadow and the lightlike geodesics in this spacetime. We compare the shadow of the naked singularity here with shadows cast by Schwarzschild black hole and the first type of Joshi-Malafarina-Narayan (JMN1) naked singularity, where for the last two spacetimes the shadow is formed due to the presence of a photon sphere. It is seen, in particular, that the size of shadow of the singularity is considerably smaller than that of a black hole. Our analysis shows that the shadow of this naked singularity is distinguishable from the shadow of a Schwarzschild black hole and the JMN1 naked singularity. These results are useful and important in the context of recent observations of shadow of the M87 galactic center.
Density probability distribution functions (PDFs) for turbulent self-gravitating clouds should be convolutions of the local log-normal PDF, which depends on the local average density rho-ave and Mach number M, and the probability distribution functions for rho-ave and M, which depend on the overall cloud structure. When self-gravity drives a cloud to increased central density, the total PDF develops an extended tail. If there is a critical density or column density for star formation, then the fraction of the local mass exceeding this threshold becomes higher near the cloud center. These elements of cloud structure should be in place before significant star formation begins. Then the efficiency is high so that bound clusters form rapidly, and the stellar initial mass function (IMF) has an imprint in the gas before destructive radiation from young stars can erase it. The IMF could arise from a power-law distribution of mass for cloud structure. These structures should form stars down to the thermal Jeans mass MJ at each density in excess of a threshold. The high-density tail of the PDF, combined with additional fragmentation in each star-forming core, extends the IMF into the Brown Dwarf regime. The core fragmentation process is distinct from the cloud structuring process and introduces an independen core fragmentation mass function (CFMF). The CFMF would show up primarily below the IMF peak.
We consider elliptic fibrations with arbitrary base dimensions, and generalise previous work by the second author. In particular, we check universal closedness for the moduli of semistable objects with respect to a polynomial stability that reduces to PT-stability on threefolds. We also show openness of this polynomial stability. On the other hand, we write down criteria under which certain 2-term polynomial semistable complexes are mapped to torsion-free semistable sheaves under a Fourier-Mukai transform. As an application, we construct an open immersion from a moduli of complexes to a moduli of Gieseker stable sheaves on higher dimensional elliptic fibrations.
Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional electron systems and, ultimately, create materials with tailored electronic properties. Previously, it proved difficult to realize superlattices with sufficiently short periodicity and weak disorder, and most of the observed features could be explained in terms of commensurate cyclotron orbits. Evidence for the formation of superlattice minibands (so called Hofstadter's butterfly) has been limited to the observation of new low-field oscillations and an internal structure within Landau levels. Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moire potential leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity accompanied by reversal of the Hall effect. The latter indicates that the sign of the effective mass changes within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning of the third generation of Dirac points that are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices open a venue to study the rich physics expected for incommensurable quantum systems and illustrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostuctures.
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. The associated microscopic dynamics satisfies the detailed balance condition and is equivalent to a lattice gas model on the edge-dual graph of a fully connected network. In our studies -- based on an exact enumeration method, Monte-Carlo simulations, and theoretical considerations -- we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure of the network. Depending on the energy function chosen, the observed transitions can be best monitored using the order parameters Phi_s=s_{max}/M, i.e., the size of the largest connected component divided by the number of edges, or Phi_k=k_{max}/M, the largest degree in the network divided by the number of edges. If, for example the energy is chosen to be E=-s_{max}, the observed transition is analogous to the percolation phase transition of random graphs. For this choice of the energy, the phase-diagram in the [<k>,T] plane is constructed. Single vertex energies of the form   E=sum_i f(k_i), where k_i is the degree of vertex i, are also studied. Depending on the form of f(k_i), first order and continuous phase transitions can be observed. In case of f(k_i)=-(k_i+c)ln(k_i), the transition is continuous, and at the critical temperature scale-free graphs can be recovered.
In this paper, we analyze 91 coronal mass ejection (CME) events studied by Manoharan et al. (2004) and Gopalswamy and Xie (2008). These earth-directed CMEs are large (width $>$160$^\circ$) and cover a wide range of speeds ($\sim$120--2400 {\kmps}) in the LASCO field of view. This set of events also includes interacting CMEs and some of them take longer time to reach 1 AU than the travel time inferred from their speeds at 1 AU. We study the link between the travel time of the CME to 1 AU (combined with its final speed at the Earth) and the effective acceleration in the Sun-Earth distance. Results indicate that (1) for almost all the events (85 out of 91 events), the speed of the CME at 1 AU is always less than or equal to its initial speed measured at the near-Sun region, (2) the distributions of initial speeds, CME-driven shock and CME speeds at 1 AU clearly show the effects of aero-dynamical drag between the CME and the solar wind and in consequence, the speed of the CME tends to equalize to that of the background solar wind, (3) for a large fraction of CMEs (for $\sim$50% of the events), the inferred effective acceleration along the Sun-Earth line dominates the above drag force. The net acceleration suggests an average dissipation of energy $\sim$10$^{31-32}$ ergs, which is likely provided by the Lorentz force associated with the internal magnetic energy carried by the CME.
The galaxy Luminosity Function (LF) is a key observable for galaxy formation, evolution studies and for cosmology. In this work, we propose a novel technique to forward model wide-field broad-band galaxy surveys using the fast image simulator UFig and measure the LF of galaxies in the B-band. We use Approximate Bayesian Computation (ABC) to constrain the galaxy population model parameters of the simulations and match data from CFHTLS. We define a number of distance metrics between the simulated and the survey data. By exploring the parameter space of the galaxy population model through ABC to find the set of parameters that minimize these distance metrics, we obtain constraints on the LFs of blue and red galaxies as a function of redshift. We find that $\mathrm{M^*}$ fades by $\Delta \mathrm{M}^*_{\mathrm{0.1-1.0,b}} = 0.68 \pm 0.52$ and $\Delta \mathrm{M}^*_{\mathrm{0.1-1.0,r}} = 0.54 \pm 0.48$ magnitudes between redshift $\mathrm{z = 1}$ and $\mathrm{z = 0.1}$ for blue and red galaxies, respectively. We also find that $\phi^*$ for blue galaxies stays roughly constant between redshift $\mathrm{z = 0.1}$ and $\mathrm{z=1}$, while for red galaxies it decreases by $\sim 35\%$. We compare our results to other measurements, finding good agreement at all redshifts, for both blue and red galaxies. To further test our results, we compare the redshift distributions for survey and simulated data. We use the spectroscopic redshift distribution from the VIMOS Public Extragalactic Redshift Survey (VIPERS) and we apply the same selection in colours and magnitudes on our simulations. We find a good agreement between the survey and the simulated redshift distributions. We provide best-fit values and uncertainties for the parameters of the LF. This work offers excellent prospects for measuring other galaxy population properties as a function of redshift using ABC.