ShantanuT01/DACTYL-Pretraining huggingface dataset:
Is the Doppler interpretation of galaxy redshifts in a Friedmann-Lemaitre-Robertson-Walker (FLRW) model valid in the context of the approach to comoving spatial sections pioneered by de Sitter, Friedmann, Lemaitre and Robertson, i.e. according to which the 3-manifold of comoving space is characterised by both its curvature and topology? Holonomy transformations for flat, spherical and hyperbolic FLRW spatial sections are proposed. By quotienting a simply-connected FLRW spatial section by an appropriate group of holonomy transformations, the Doppler interpretation in a non-expanding Minkowski space-time, obtained via four-velocity parallel transport along a photon path, is found to imply that an inertial observer is receding from herself at a speed greater than zero, implying contradictory world-lines. The contradiction in the multiply-connected case occurs for arbitrary redshifts in the flat and spherical cases, and for certain large redshifts in the hyperbolic case. The link between the Doppler interpretation of redshifts and cosmic topology can be understood physically as the link between parallel transport along a photon path and the fact that the comoving spatial geodesic corresponding to a photon's path can be a closed loop in an FLRW model of any curvature. Closed comoving spatial loops are fundamental to cosmic topology.
In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.
For each integer n, an n-folding curve is obtained by folding n times a strip of paper in two, possibly up or down, and unfolding it with right angles. Generalizing the usual notion of infinite folding curve, we define complete folding curves as the curves without endpoint which are unions of increasing sequences of n-folding curves for n integer. We prove that there exists a standard way to extend any complete folding curve into a covering of the plane by disjoint such curves, which satisfies the local isomorphism property introduced to investigate aperiodic tiling systems. This covering contains at most six curves.
We show that there exists no smooth fibration of a smooth complex quasi-projective variety of log-general type over a quasi-abelian variety. The proof uses M. Popa and C. Schnell's construction of Higgs bundle.
It is well known that if the most energetic cosmic rays ($E>10^{20}$ eV) were protons then their acceleration sites should possess some extreme properties, including gigantic luminosity. As no stationary sources with such properties are known in the local ($D<200$ Mpc) neighborhood of the Milky Way, it is highly likely that the UHECR acceleration takes place in some transient events. In this paper we investigate scenario where the UHECRs are produced in strong AGN flares. Using more than 7 years of the Fermi-LAT observations we select candidate flares and, using correlation between jet kinetic luminosity and its bolometric luminosity, estimate local kinetic emissivity of giant AGN flares: $\mathcal{L}\sim3.7\times10^{44}\mathrm{erg~Mpc^{-3}~{yr^{-1}}}$. This value is about an order of magnitude larger than the emissivity in the CRs with $E>10^{20}$ eV, thus making this scenario feasible, if the UHECR escape spectrum is rather hard and/or narrow. This shape of spectrum is predicted in a number of present models of strong relativistic collisionless shocks. Also the scenario of acceleration in AGN flares can accommodate constraints coming from the observed arrival distribution of UHECRs. Finally, we demonstrate that in case of heavier UHECR composition all the constraints are greatly relaxed.
The atomic and electronic structures of a graphene layer on top of the $(2\times2)$ reconstruction of the SiC (000$\bar{1}$) surface are studied from ab initio calculations. At variance with the (0001) face, no C bufferlayer is found here. Si adatoms passivate the substrate surface so that the very first C layer presents a linear dispersion characteristic of graphene. A small graphene-substrate interaction remains in agreement with scanning tunneling experiments (F.Hiebel et al. {\it Phys. Rev. B} {\bf 78} 153412 (2008)). The stacking geometry has little influence on the interaction which explains the rotational disorder observed on this face.
The main point of this paper is a suggestion about the proper treatment of the photon gas in a theory of stellar structure and other plasmas. This problem arises in the study of polytropic gas spheres, where we have already introduced some innovations. The main idea, already advanced in the contextof neutral, homogeneous, polytropic stellar models, is to base the theory firmly on a variational principle. Another essential novelty is to let mass distribution extend to infinity, the boundary between bulk and atmosphere being defined by an abrupt change in the polytropic index, triggered by the density. The logical next step in this program is to include the effect of radiation, which is a very significant complication since a full treatment would have to include an account of ionization, thus fieldsrepresenting electrons, ions, photons, gravitons and neutral atoms as well. In way of preparation, we consider models that are charged but homogeneous, involving only gravity, electromagnetism and a single scalar field that represents both the mass and the electric charge; in short, anon-neutral plasma. While this work only represents a stage in the development of a theory of stars, without direct application to physical systems, it does shed some light on the meaning of the Reissner-Nordstrom solution of the modified Einstein-Maxwell equations., with an application to a simple system.
Under mild conditions, it is possible to obtain, from almost purely measure-theoretic considerations and without any specific reference to stochastic processes, a change-of-measures result, resembling the usual Radon-Nikod\'ym change of measures, associated with a variant of stochastic integration for a spectral representation of covariance stationary processes; the ideas are naturally embedded in the Hilbert space theory of $L^{2}$ spaces. The intended main contribution, including a complete proof of change of measures for spectral stochastic integrals, is the refined, self-contained developments of spectral stochastic integration toward change of measures.
The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri's 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.
We investigate the role of stellar mass in shaping the intrinsic thickness of faint systems by determining the probability distribution of apparent axis ratios for two different samples that probe the faint end of the galaxy luminosity function (M_B < -8). We find that the (b/a) distribution is a strong function of M*, and identify a limiting stellar mass M* ~ 2x10^9 Msun below which galaxies start to be systematically thicker. We argue that this is the result of the complex interplay between galaxy mass, specific angular momentum and stellar feedback effects: the increasing importance of turbulent motions in lower mass galaxies leads to the formation of thicker systems. We find a good agreement between our results and the latest numerical simulations of dwarf galaxy formation, and discuss several further implications of this finding --including the formation of bars and spirals in faint galaxies, the deprojection of HI line profiles and simulations of environmental effects on dwarf galaxies.
Super- and highly-deformed rotational bands in the A ~ 60 mass region are studied within cranked relativistic mean field theory and the configuration-dependent shell-correction approach based on the cranked Nilsson potential. Both approaches describe the experimental data well. Low values of the dynamic moments of inertia J^(2) compared with the kinematic moments of inertia J^(1) seen both in experiment and in calculations at high rotational frequencies indicate the high energy cost to build the states at high spin and reflect the limited angular momentum content in these configurations.
A string of recent studies has debated the exact form and physical origin of an evolutionary trend between the peak luminosity of Type Ia supernovae (SNe Ia) and the properties of the galaxies that host them. We shed new light on the discussion by presenting an analysis of ~200 low-redshift SNe Ia in which we measure the separation of Hubble residuals (HR; as probes of luminosity) between two host-galaxy morphological types. We show that this separation can test the predictions made by recently proposed models, using an independently and empirically determined distribution of each morphological type in host-property space. Our results are partially consistent with the new HR--age slope, but we find significant scatter in the predictions from different galaxy catalogues. The inconsistency in age illuminates an issue in the current debate that was not obvious in the long-discussed mass models: HR--host-property models are strongly dependent on the methods employed to determine galaxy properties. While our results demonstrate the difficulty in constructing a universal model for age as a proxy for host environment, our results indeed identify evolutionary trends between mass, age, morphology, and HR values, encouraging (or requiring, if such trends are to be accounted for in cosmological studies) further investigation.
Solar limb observations sometimes reveal the presence of a satellite lobe in the blue wing of the Stokes I profile from pixels belonging to granules. The presence of this satellite lobe has been associated in the past to strong line of sight gradients and, as the line of sight component is almost parallel to the solar surface, to horizontal granular flows. We aim to increase the knowledge about these horizontal flows studying a spectropolarimetric observation of the north solar pole. We will make use of two state of the art techniques, the spatial deconvolution procedure that increases the quality of the data removing the stray light contamination, and spectropolarimetric inversions that will provide the vertical stratification of the atmospheric physical parameters where the observed spectral lines form. We inverted the Stokes profiles using a two component configuration, obtaining that one component is strongly blueshifted and displays a temperature enhancement at upper photospheric layers while the second component has low redshifted velocities and it is cool at upper layers. In addition, we examined a large number of cases located at different heliocentric angles, finding smaller velocities as we move from the centre to the edge of the granule. Moreover, the height location of the enhancement on the temperature stratification of the blueshifted component also evolves with the spatial location on the granule being positioned on lower heights as we move to the periphery of the granular structure.
We study possible quantum states of two correlated electrons in a two-dimensional crystal and find a metastable energy band of the electron pair between the two lowest single-electron bands. These metastable states result from the interplay of electron correlations and the strength of the crystal potential. The two paired electrons are bound in the same unit cell in relative coordinates with an average distance between them about one third of the crystal period. Furthermore, we show how such electron-pairs can be stabilized in a many-electron system.
We assume that the individual stars which are located at the peripheral parts of the spiral galaxies are experiencing a drag force acting upon them radially. Such a force might be produced by some sort of a dynamically generated viscous medium, and as the stars are in the state of free fall toward the center of the galaxy, then it would balance the centripetal force acting on the star, thus resulting in a terminal velocity. We make no attempt to explain the origin of the assumed drag force or show how it could be generated, but we have tried to test such an assumption by fitting the calculated velocity curves of 18 spiral galaxies with rotation curves obtained from actual observations. Results show remarkable agreements.
We present a detailed study of a linear sigma model containing one chiral nonet transforming under U(1)$_A$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-anti diquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an "excited" pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.
A series of stellar models of spectral type G is computed to study the rotation laws resulting from mean-field equations. The rotation laws of the slowly rotating Sun, the fast rotating MOST stars epsilon Eri and kappa1 Cet and the rapid rotators R58 and LQ Lup can easily be reproduced. We also find that differences in the depth of the convection zone cause large differences in the surface rotation law and that the extreme surface shear of HD 171488 can only be explained with a artificially shallow convection layer. We also check the thermal wind equilibrium in fast-rotating G dwarfs and find that the polar subrotation (dOmega/dz<0) is due to the barocline effect and that the equatorial superrotation (dOmega/dr>0) is due to the Lambda effect as part of the Reynolds stresses. In the bulk of the convection zones where the meridional flow is slow and smooth the thermal wind equilibrium actually holds between the centrifugal and the pressure forces. It does not hold, however, in the bounding shear layers including the equatorial region where the Reynolds stresses dominate.
We prove Fujita's freeness conjecture for Gorenstein complexity-one $T$-varieties with rational singularities.
We present a systematic investigation of the electronic properties of bulk and few layer ReS$_2$ van der Waals crystals using low temperature optical spectroscopy. Weak photoluminescence emission is observed from two non-degenerate band edge excitonic transitions separated by $\sim$ 20 meV. The comparable emission intensity of both excitonic transitions is incompatible with a fully thermalized (Boltzmann) distribution of excitons, indicating the hot nature of the emission. While DFT calculations predict bilayer ReS$_2$ to have a direct fundamental band gap, our optical data suggests that the fundamental gap is indirect in all cases.
We have investigated the detailed torque-reversal behavior of 4U 1626--67 in the framework of the recently developed comprehensive model of the inner disk radius and torque calculations for neutron stars accreting from geometrically thin disks. The model can reproduce the torque -- X-ray luminosity relation across the torque reversals of 4U 1626--67. Our results imply that: (1) rotational equilibrium is reached when the inner disk radius equals the co-rotation radius, $r_\mathrm{co}$, while the conventional Alfven radius is greater than and close to $r_\mathrm{co}$, (2) both spin-up and spin-down torques are operating on either side of torque reversal, (3) with increasing accretion rate the spin-up torque associated with accretion onto the star gradually dominates the spin-down torque exerted by the disk. The torque reversals are the natural outcome of transitions between the well-defined weak-propeller and spin-up phases of the star with a stable geometrically thin accretion disk.
This paper proposes a novel model fitting algorithm for 3D facial expression reconstruction from a single image. Face expression reconstruction from a single image is a challenging task in computer vision. Most state-of-the-art methods fit the input image to a 3D Morphable Model (3DMM). These methods need to solve a stochastic problem and cannot deal with expression and pose variations. To solve this problem, we adopt a 3D face expression model and use a combined feature which is robust to scale, rotation and different lighting conditions. The proposed method applies a cascaded regression framework to estimate parameters for the 3DMM. 2D landmarks are detected and used to initialize the 3D shape and mapping matrices. In each iteration, residues between the current 3DMM parameters and the ground truth are estimated and then used to update the 3D shapes. The mapping matrices are also calculated based on the updated shapes and 2D landmarks. HOG features of the local patches and displacements between 3D landmark projections and 2D landmarks are exploited. Compared with existing methods, the proposed method is robust to expression and pose changes and can reconstruct higher fidelity 3D face shape.
We study behaviour of dynamical critical exponents of the two-dimensional Ising model with a line of defects. Simulations done at an early time (first 100 Monte Carlo steps) reveal that the critical exponent of Janssen et al (Z. Phys. B 73 539) depends on the strength of the exchange coupling constant (J') of the altered line. On the other hand, our simulations permit us to conclude that the dynamical critical exponent z is not sensitive to changes in J'. In adition, we investigate the possible invariance of the anomalous dimension of the magnetization at the beginning of the process.
Semiclassical Hamiltonian field theory is investigated from the axiomatic point of view. A notion of a semiclassical state is introduced. An "elementary" semiclassical state is specified by a set of classical field configuration and quantum state in this external field. "Composed" semiclassical states viewed as formal superpositions of "elementary" states are nontrivial only if the Maslov isotropic condition is satisfied; the inner product of "composed" semiclassical states is degenerate. The mathematical proof of Poincare invariance of semiclassical field theory is obtained for "elementary" and "composed" semiclassical states. The notion of semiclassical field is introduced; its Poincare invariance is also mathematically proved.
A new method is described for recognising internal non-randomness in deep galaxy surveys.
We present axisymmetric two-temperature general relativistic radiation magnetohydrodynamic (GRRMHD) simulations of the inner region of the accretion flow onto the supermassive black hole M87. We address uncertainties from previous modeling efforts through inclusion of models for (1) self-consistent dissipative and Coulomb electron heating (2) radiation transport (3) frequency-dependent synchrotron emission, self-absorption, and Compton scattering. We adopt a distance $D=16.7$ Mpc, an observer angle $\theta = 20^{\circ}$, and consider black hole masses $M/M_{\odot} = (3.3\times10^{9}, 6.2\times10^{9})$ and spins $a_{\star} = (0.5, 0.9375)$ in a four-simulation suite. For each $(M, a_{\star})$, we identify the accretion rate that recovers the 230 GHz flux from VLBI measurements. We report on disk thermodynamics at these accretion rates ($\dot{M}/\dot{M}_{\mathrm{Edd}} \sim 10^{-5}$). The disk remains geometrically thick; cooling does not lead to a thin disk component. While electron heating is dominated by Coulomb rather than dissipation for $r \gtrsim 10 GM/c^2$, the accretion disk remains two-temperature. Radiative cooling of electrons is not negligible, especially for $r \lesssim 10 GM/c^2$. The Compton $y$ parameter is of order unity. We then compare derived and observed or inferred spectra, mm images, and jet powers. Simulations with $M/M_{\odot} = 3.3\times10^{9}$ are in conflict with observations. These simulations produce mm images that are too small, while the low-spin simulation also overproduces X-rays. For $M/M_{\odot} = 6.2\times10^{9}$, both simulations agree with constraints on radio/IR/X-ray fluxes and mm image sizes. Simulation jet power is a factor $10^2-10^3$ below inferred values, a possible consequence of the modest net magnetic flux in our models.
The origin and chemical composition of ultra high energy cosmic rays is still an open question in astroparticle physics. The observed large-scale isotropy and also direct composition measurements can be interpreted as an extragalactic proton dominance above the ankle at about 10^10 GeV. Photopion production of extragalactic protons in the cosmic microwave background predicts a cutoff at about 5x10^10 GeV in conflict with excesses reported by some experiments. In this report we will outline a recent statistical analysis (astro-ph/0506698) of cosmic ray data using strongly interacting neutrinos as primaries for these excesses.
We construct a novel preorder on the set of nodes of a simple undirected graph. We prove that the preorder (induced by the topology of the graph) is preserved, e.g., by the logistic dynamical system (both in discrete and continuous time). Moreover, the underlying equivalence relation of the preorder corresponds to the coarsest equitable partition (CEP). This will further imply that the logistic dynamical system on a graph preserves its coarsest equitable partition. The results provide a nontrivial invariant set for the logistic and the like dynamical systems, as we show. We note that our construct provides a functional characterization for the CEP as an alternative to the pure set theoretical iterated degree sequences characterization. The construct and results presented might have independent interest for analysis on graphs or qualitative analysis of dynamical systems over networks.