ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use the image sum method to reproduce Sushkov's result that for a massless automorphic field on the initial globally hyperbolic region $IGH$ of Misner space, one can always find a special value of the automorphic parameter $\alpha$ such that the renormalized expectation value $\langle\alpha|T_{ab}|\alpha\rangle$ in the {\it Sushkov state} ``$\langle\alpha|\cdot|\alpha\rangle$'' (i.e. the automorphic generalization of the Hiscock-Konkowski state) vanishes. However, we shall prove by elementary methods that the conclusions of a recent general theorem of Kay-Radzikowski-Wald apply in this case. I.e. for any value of $\alpha$ and any neighbourhood $N$ of any point $b$ on the chronology horizon there exists at least one pair of non-null related points $(x,x') \in (N\cap IGH)\times (N\cap IGH)$ such that the renormalized two-point function of an automorphic field $G^\alpha_{\rm ren}(x,x')$ in the Sushkov state is singular. In consequence $\langle\alpha|T_{ab}|\alpha\rangle$ (as well as other renormalized expectation values such as $\langle\alpha|\phi^2|\alpha\rangle$) is necessarily singular {\it on} the chronology horizon. We point out that a similar situation (i.e. singularity {\it on} the chronology horizon) holds for states on Gott space and Grant space.
Graphene is only one atom thick and becomes the ultimate thin film to explore membrane physics and mechanics. Here we study hierarchy of graphene wrinkles induced by thermal strain engineering and demonstrate that the wrinkling hierarchy can be accounted for by the wrinklon theory. We derive an equation {\lambda} = (ky)0.5 explaining evolution of wrinkling wavelength {\lambda} with the distance to the edge y observed in our experiment by considering both bending energy and stretching energy of the graphene flakes. The prefactor k in the equation is determined to be about 55 nm, which is independent of the size of the graphene flakes. Our experimental result indicates that the classical membrane behavior of graphene persists down to about 100 nm of the wrinkling wavelength.
In this paper, we study the initial-boundary value problem of compressible Euler equations with friction and heating that model the combined Fanno-Rayleigh flows through symmetric variable area nozzles, in particular, the case of contracting nozzles is considered. A new version of a generalized Glimm scheme (GGS) is presented for establishing the global existence of transonic entropy solutions. Modified Riemann and boundary Riemann solutions are applied to design this GGS which obtained by the contraction matrices acting on the homogeneous Riemann (or boundary-Riemann) solutions. The extended Glimm-Goodman wave interaction estimates are investigated for ensuring the stability of the scheme and the positivity of gas velocity that leads to the existence of the weak solution. The limit of approximation solutions serves as an entropy solution. Moreover, a quantitative relation between the shape of the nozzle, the friction, and the heat is proposed. Under this relation, the global existence of weak solution for contracting nozzle is achieved. Simulations of contraction-expansion and expansion-contraction nozzles are presented to illustrate the relevant theoretical results.
The energy spectrum of ultra-high energy cosmic rays (UHECRs) provides essential information on the most energetic phenomena in the Universe. Beyond EeV energies, the Telescope Array and Pierre Auger Observatory have the largest exposures to UHECRs ever accumulated in the Northern and Southern hemispheres, respectively. The results show independently a steepening of the energy spectrum above a few tens of EeV. However, the comparison of the spectra shows differences that are not explainable in terms of an overall uncertainty on the energy scale used to reconstruct the extensive air showers. The differences are also observed in the region of the sky covered by both instruments, where the spectra should be in agreement within uncertainties when directional-exposure effects are accounted for. For this contribution, a working group from both collaborations examined these differences considering the energy-dependent systematic uncertainties. A special focus is given to the characterization of the spectral features, which provide an accurate tool to enhance our understanding of the comparisons.
We present extensive radio observations of the nearby Type Ibc supernovae 2004cc, 2004dk, and 2004gq spanning 8-1900 days after explosion. Using a dynamical model developed for synchrotron emission from a slightly decelerated shockwave, we estimate the velocity and energy of the fastest ejecta and the density profile of the circumstellar medium. The shockwaves of all three supernovae are characterized by non-relativistic velocities of v ~ (0.1-25)c and associated energies of E ~ (2-10) * 1e47 erg, in line with the expectations for a typical homologous explosion. Smooth circumstellar density profiles are indicated by the early radio data and we estimate the progenitor mass loss rates to be ~ (0.6-13) * 1e-5 M_sun/yr (wind velocity 10^3 km/s). These estimates approach the saturation limit (~1e-4 M_sun/yr) for line-driven winds from Wolf-Rayet stars, the favored progenitors of SNe Ibc including those associated with long-duration GRBs. Intriguingly, at later epochs all three supernovae show evidence for abrupt radio variability that we attribute to large density modulations (factor of ~3-6) at circumstellar radii of r ~ (1-50) * 1e16 cm. If due to variable mass loss, these modulations are associated with progenitor activity on a timescale of ~ 10-100 years before explosion. We consider these results in the context of variable mass loss mechanisms including wind clumping, metallicity-independent continuum-driven ejections, and binary-induced modulations. It may also be possible that the SN shockwaves are dynamically interacting with wind termination shocks, however, this requires the environment to be highly pressurized and/or the progenitor to be rapidly rotating prior to explosion. The proximity of the density modulations to the explosion sites may suggest a synchronization between unusual progenitor mass loss and the SN explosion, reminiscent of Type IIn supernovae. [ABRIDGED]
Due to the COVID-19 pandemic, wearing face masks has become a mandate in public places worldwide. Face masks occlude a significant portion of the facial region. Additionally, people wear different types of masks, from simple ones to ones with graphics and prints. These pose new challenges to face recognition algorithms. Researchers have recently proposed a few masked face datasets for designing algorithms to overcome the challenges of masked face recognition. However, existing datasets lack the cultural diversity and collection in the unrestricted settings. Country like India with attire diversity, people are not limited to wearing traditional masks but also clothing like a thin cotton printed towel (locally called as ``gamcha''), ``stoles'', and ``handkerchiefs'' to cover their faces. In this paper, we present a novel \textbf{Indian Masked Faces in the Wild (IMFW)} dataset which contains images with variations in pose, illumination, resolution, and the variety of masks worn by the subjects. We have also benchmarked the performance of existing face recognition models on the proposed IMFW dataset. Experimental results demonstrate the limitations of existing algorithms in presence of diverse conditions.
We consider a Cauchy problem of energy-critical fractional Schr\"odinger equation with Hartree nonlinearity below the energy space. Using a method of randomization of functions on $\mathbb{R}^d$ associated with the Wiener decomposition, introduced by \'{A}. B\'{e}nyi, T. Oh, and O. Pocovnicu \cite{beohpo1,beohpo2}, we prove that the Cauchy problem is almost surely locally well-posed. Our result includes Hartree Schr\"odinger equation ($\alpha = 2$).
The raise and peel model (RPM) is a nonlocal stochastic model describing the space and time fluctuations of an evolving one dimensional interface. Its relevant parameter $u$ is the ratio between the rates of local adsorption and nonlocal desorption processes (avalanches) processes. The model at $u=1$ give us the first example of a conformally invariant stochastic model. For small values $u<u_0$ the model is known to be noncritical, while for $u>u_0$ it is critical.   By calculating the structure function of the height profiles in the reciprocal space we confirm with good precision that indeed $u_0=1$. We establish that at the conformal invariant point $u=1$ the RPM has a roughness transition with dynamical and roughness critical exponents $z=1$ and $\alpha=0$, respectively. For $u>1$ the model is critical with an $u$-dependent dynamical critical exponent $z(u)$ that tends towards zero as $u\to \infty$. However at $1/u=0$ the RPM is exactly mapped into the totally asymmetric exclusion problem (TASEP). This last model is known to be noncritical (critical) for open (periodic) boundary conditions. Our studies indicate that the RPM as $u \to \infty$, due to its nonlocal dynamics processes, has the same large-distance physics no matter what boundary condition we chose. For $u>1$, our analysis show that differently from previous predictions, the region is composed by two distinct critical phases. For $u\leq u < u_c\approx 40$ the height profiles are rough ($\alpha = \alpha(u) >0$), and for $u>u_c$ the height profiles are flat at large distances ($\alpha = \alpha(u) <0$). We also observed that in both critical phases ($u>1$) the RPM at short length scales, has an effective behavior in the Kardar-Parisi-Zhang (KPZ) critical universality class, that is not the true behavior of the system at large length scales.
Given a smooth R^d-valued diffusion, we study how fast the Euler scheme with time step 1/n converges in law. To be precise, we look for which class of test functions f the approximate expectation E[f(X^{n,x}_1)] converges with speed 1/n to E[f(X^x_1)]. If X is uniformly elliptic, we show that this class contains all tempered distributions, and all measurable functions with exponential growth. We give applications to option pricing and hedging, proving numerical convergence rates for prices, deltas and gammas.
The nebular-epoch spectrum of the rapidly declining, "transitional" type Ia supernova (SN) 2007on showed double emission peaks, which have been interpreted as indicating that the SN was the result of the direct collision of two white dwarfs. The spectrum can be reproduced using two distinct emission components, one red-shifted and one blue shifted. These components are similar in mass but have slightly different degrees of ionization. They recede from one another at a line-of-sight speed larger than the sum of the combined expansion velocities of their emitting cores, thereby acting as two independent nebulae. While this configuration appears to be consistent with the scenario of two white dwarfs colliding, it may also indicate an off-centre delayed detonation explosion of a near Chandrasekhar-mass white dwarf. In either case, broad emission line widths and a rapidly evolving light curve can be expected for the bolometric luminosity of the SN. This is the case for both SNe 2007on and 2011iv, also a transitional SN Ia which exploded in the same elliptical galaxy, NGC 1404. Although SN 2011iv does not show double-peaked emission line profiles, the width of its emission lines is such that a two-component model yields somewhat better results than a single-component model. Most of the mass ejected is in one component, however, which suggests that SN 2011iv was the result of the off-centre ignition of a Chandrasekhar-mass white dwarf.
We show the Kontsevich space of rational curves of degree at most roughly $\frac{2-\sqrt{2}}{2}n$ on a general hypersurface $X\subset \mathbb{P}^n$ of degree $n-1$ is equidimensional of expected dimension and has two components: one consisting generically of smooth, embedded rational curves and the other consisting of multiple covers of a line. This proves more cases of a conjecture of Coskun, Harris, and Starr and shows the Gromov-Witten invariants in these cases are enumerative.
The superposition principle is at the heart of quantum mechanics and at the root of many paradoxes arising when trying to extend its predictions to our everyday world. Schroedinger's cat is the prototype of such paradoxes and here, in contrast to many others, we choose to investigate it from the operational point of view. We experimentally demonstrate a universal strategy for producing an unambiguously distinguishable type of superposition, that of an arbitrary pure state and its orthogonal. It relies on only a limited amount of information about the input state to first generate its orthogonal one. Then, a simple change in the experimental parameters is used to produce arbitrary superpositions of the mutually orthogonal states. Constituting a sort of Schroedinger's black box, able to turn a whole zoo of input states into coherent superpositions, our scheme can produce arbitrary continuous-variable optical qubits, which may prove practical for implementing quantum technologies and measurement tasks.
A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 66601 (2018)] is applied to nodal line and Weyl semimetals (including graphene), and to spin-orbit split semiconductor bands in two and three dimensions. The calculation reduces to a ratio of two equilibrium susceptibilities, where corrections are negligible at weak disorder. Deviations from Drude's inverse carrier density are associated with band degeneracies, Fermi surface topology, and interband scattering. Experiments which can measure these deviations are proposed.
We attempt to generalize a congruence property of elliptic modular forms proved by Sturm to that of Haupttypus of Siegel modular forms of degree 2 with level. Namely, we give an explicit bound of Fourier coefficients required to determine the congruence of modular forms. We give the analog of Sturm's theorem for Jacobi forms, which is required in the proof. In the case that Nebentypus of Siegel modular forms with prime level, in order to prove the congruence between two modular forms, we show that it suffices to check the congruence of the finitely many Fourier coefficients. Finally, we give two examples of our main theorem.
We study the effects of final state interactions in two-proton emission by nuclei. Our approach is based on the solution the time-dependent Schr\"odinger equation. We show that the final relative energy between the protons is substantially influenced by the final state interactions. We also show that alternative correlation functions can be constructed showing large sensitivity to the spin of the diproton system.
We study the single production of charged Higgs bosons in e+e- collisions, chiefly in the Minimal Supersymmetric Standard Model. Our analysis complements foregoing studies of the pair production channel especially in regions where the kinematic constraint suppresses pair production. We present cross sections relevant to experiments at the next generation linear colliders and some brief discussions of their phenomenology. Our analysis shows that the single production is a useful alternative channel for studying the phenomenology of charged Higgs bosons, and there are regions of parameter space where it is accessible beyond the kinematic limit for pair production.
Radiation pressure dominated accretion discs may have turbulent velocities that exceed the electron thermal velocities. Bulk Comptonization by the turbulence may therefore dominate over thermal Comptonization in determining the emergent spectrum. We discuss how to self-consistently resolve and interpret this effect in calculations of spectra of radiation MHD simulations. In particular, we show that this effect is dominated by radiation viscous dissipation and can be treated as thermal Comptonization with an equivalent temperature. We investigate whether bulk Comptonization may provide a physical basis for warm Comptonization models of the soft X-ray excess in AGN. We characterize our results with temperatures and optical depths to make contact with other models of this component. We show that bulk Comptonization shifts the Wien tail to higher energy and lowers the gas temperature, broadening the spectrum. More generally, we model the dependence of this effect on a wide range of fundamental accretion disc parameters, such as mass, luminosity, radius, spin, inner boundary condition, and alpha. Because our model connects bulk Comptonization to one dimensional vertical structure temperature profiles in a physically intuitive way, it will be useful for understanding this effect in future simulations run in new regimes. We also develop a global Monte Carlo code to study this effect in global radiation MHD simulations. This code can be used more broadly to compare global simulations with observed systems, and in particular to investigate whether magnetically dominated discs can explain why observed high Eddington accretion discs appear to be thermally stable.
In the context of Differential Renormalization, using Constrained Differential Renormalization rules at one loop, we show how to obtain concrete results in two loop calculations without making use of Ward identities. In order to do that, we obtain a list of integrals with overlapping divergences compatible with CDR that can be applied to various two loop background field calculations. As an example, we obtain the two loop coefficient of the beta function of QED, SuperQED and Yang-Mills theory.
We propose a second version of the van der Waals density functional (vdW-DF2) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy, equilibrium separation, and potential-energy curve shape are close to those of accurate quantum chemical calculations on 22 duplexes. We anticipate the enabling of chemically accurate calculations in sparse materials of importance for condensed-matter, surface, chemical, and biological physics.
We discuss the nonfactorization effects in $B\to J/\Psi+X_{s}$, which is similar to the nonperturbative effect found by Voloshin in the decay $B\to \gamma +X_{s}$. The QCD sum rule has been used to estimate the hadron matrix elements. We find that the correction from this effect is very large and the large discrepancy between the theory and the experimental data can be reduced considerably.
Preliminary results are presented from the CLEF hydrodynamics simulation, a large (N=2(428)^3 particles within a 200 Mpc/h comoving box) simulation of the LCDM cosmology that includes both radiative cooling and a simple model for galactic feedback. Specifically, we focus on the X-ray properties of the simulated clusters at z=0 and demonstrate a reasonable level of agreement between simulated and observed cluster scaling relations.
In the framework of the modified FRITIOF model, the inclusive spectra of the cumulative $\pi ^0$-, $\pi ^- $-mesons and protons produced in the nucleus-nucleus interactions at 4.5 GeV/c/nucleon and 4.2 GeV/c/nucleon are calculated. It is shown that the model reproduces qualitatively, and in some cases quantitatively the main experimental regularities of $\pi$-mesons production, and "soft" part of the proton spectra. According to the model the production of the cumulative particles is connected with the mechanism of the "soft" nucleon-nucleon interaction.
It seems to be a widely accepted opinion that the types of accretion disks (or flows) generally realized in the nuclei of radio galaxies and in further lower mass-accretion rate nuclei are inner, hot, optically thin, radiatively inefficient accretion flows (RIAFs) surrounded by outer, cool, optically thick, standard type accretion disks. However, observational evidence for the existence of such outer cool disks in these nuclei is rather poor. Instead, recent observations sometimes suggest the existence of inner cool disks of non-standard type, which develop in the region very close to their central black holes. Taking NGC 4261 as a typical example of such light eating nuclei, for which both flux data ranging from radio to X-ray and data for the counterjet occultation are available, we examine the plausibility of such a picture for the accretion states as mentioned above, based on model predictions. It is shown that the explanation of the gap seen in the counterjet emission in terms of the free-free absorption by an outer standard disk is unrealistic, and moreover, the existence itself of such an outer standard disk seems very implausible. Instead, the model of RIAF in an ordered magnetic field (so called resistive RIAF model) can well serve to explain the emission gap in terms of the synchrotron absorption, as well as to reproduce the observed features of the overall spectral energy distribution (SED). This model also predicts that the RIAF state starts directly from an interstellar hot gas phase at around the Bondi radius and terminates at the inner edge whose radius is about 100 times the Schwartzschild radii. Therefore, there is a good possibility for a cool disk to develop within this innermost region.
We have measured an annual parallax of the Mira variable R~Ursae~Majoris (R~UMa) with the VLBI exploration for Radio Astronomy (VERA). From the monitoring VLBI observations spanning about two years, we detected H$_2$O maser spots in the LSR velocities ranges from 37 to 42 km\,s$^{-1}$. We derived an annual parallax of 1.97$\pm$0.05\,mas, and it gives a corresponding distance of 508$\pm$13\,pc. The VLBI maps revealed 72 maser spots distributed in $\sim$110 au area around an expected stellar position. Circumstellar kinematics of the maser spots were also revealed by subtracting a systemic motion in the Hipparcos catalog from proper motions of each maser spots derived from our VLBI observations. Infrared photometry is also conducted to measure a $K$ band apparent magnitude, and we obtained a mean magnitude of $m_K$ = 1.19$\pm$0.02\,mag. Using the trigonometric distance, the $m_K$ is converted to a $K$ band absolute magnitude of $M_K = -$7.34$\pm$0.06\,mag. This result gives a much more accurate absolute magnitude of R~UMa than previously provided. We solved a zero-point of $M_K - \log P$ relation for the Galactic Mira variables and obtained a relation of $M_K = -$3.52 $\log P$ + (1.09 $\pm$ 0.14). Other long period variables including red supergiants, whose distances were determined from astrometric VLBI, were also compiled to explore the different sequences of $M_K - \log P$ relation.
The physics of active super massive black holes (BHs) is governed by their mass (M_BH), spin (a*) and accretion rate ($\dot{M}$). This work is the first in a series of papers with the aim of testing how these parameters determine the observable attributes of active galactic nuclei (AGN). We have selected a sample in a narrow redshift range, centered on z~1.55, that covers a wide range in M_BH and $\dot{M}$, and are observing them with X-shooter, covering rest wavelengths ~1200-9800 \AA. The current work covers 30 such objects and focuses on the origin of the AGN spectral energy distribution (SED). After estimating M_BH and $\dot{M}$ based on each observed SED, we use thin AD models and a Bayesian analysis to fit the observed SEDs in our sample. We are able to fit 22/30 of the SEDs. Out of the remaining 8 SEDs, 3 can be fit by the thin AD model by correcting the observed SED for reddening within the host galaxy and 4 can be fit by adding a disc wind to the model. In four of these 8 sources, Milky Way-type extinction, with the strong 2175\AA\ feature, provides the best reddening correction. The distribution in spin parameter covers the entire range, from -1 to 0.998, and the most massive BHs have spin parameters greater than 0.7. This is consistent with the "spin-up" model of BH evolution. Altogether, these results indicate that thin ADs are indeed the main power houses of AGN, and earlier claims to the contrary are likely affected by variability and a limited observed wavelength range.