ShantanuT01/DACTYL-Pretraining huggingface dataset:
A notion of effective gauge fields which does not involve a background metric is introduced. The role of scale is played by cellular decompositions of the base manifold. Once a cellular decomposition is chosen, the corresponding space of effective gauge fields is the space of flat connections with singularities on its codimension two skeleton, ${\cal A}_{C-flat} \subset \bar{\cal A}_M$. If cellular decomposition $C_2$ is finer than cellular decomposition $C_1$, there is a coarse graining map $\pi_{C_2 \to C_1}: {\cal A}_{C_2-flat} \to {\cal A}_{C_1-flat}$. We prove that the triple $({\cal A}_{C_2-flat}, \pi_{C_2 \to C_1}, {\cal A}_{C_1-flat})$ is a principal fiber bundle with a preferred global section given by the natural inclusion map $i_{C_1 \to C_2}: {\cal A}_{C_1-flat} \to {\cal A}_{C_2-flat}$.   Since the spaces ${\cal A}_{C-flat}$ are partially ordered (by inclusion) and this order is directed in the direction of refinement, we can define a continuum limit, $C \to M$. We prove that, in an appropriate sense, $\lim_{C \to M} {\cal A}_{C-flat} = \bar{\cal A}_M$. We also define a construction of measures in $\bar{\cal A}_M$ as the continuum limit (not a projective limit) of effective measures.
RHESSI observations of a solar flare showing continuous motions of double hard X-ray sources interpreted as footpoints of magnetic loops are presented. The temporal evolution shows many distinct emission peaks of duration of some tens of seconds ('elementary flare bursts'). Elementary flare bursts have been interpreted as instabilities or oscillations of the reconnection process leading to an unsteady release of magnetic energy. These interpretations based on two-dimensional concepts cannot explain these observations, showing that the flare elements are displaced in a third dimension along the arcade. Therefore, the observed flare elements are not a modulation of the reconnection process, but originate as this process progresses along an arcade of magnetic loops. Contrary to previous reports, we find no correlation between footpoint motion and hard X-ray flux. This flare apparently contradicts the predictions of the standard translation invariant 2.5D reconnection models.
We propose a simple model for reaction-diffusion systems with orientational constraints on the reactivity of particles, and map it onto a field theory with upper critical dimension d_c=2. To two-loop level the long-time particle density N(t) is given by the same universal expression as for a nonsteric system, with N(t)~t^{-d/2} for d<=2. For slow rotations of the particles we find an intermediate regime where N(t)~t^{-d/4}, with the crossover to the nonsteric asymptotics determined by the rates of rotations and reactions. Consequences for experiments are discussed.
An efficient algorithm is presented to simulate the O(N) loop model on the square lattice for arbitrary values of $N>0$. The scheme combines the worm algorithm with a new data structure to resolve both the problem of loop crossings and the necessity of counting the number of loops at each Monte Carlo update. With the use of this scheme, the line of critical points (and other properties) of the O($N$) model on the square lattice for $0<N\le 2$ have been determined.
Although van der Waals (vdW) layered MoS2 shows the phase transformation from the semiconducting 2H-phase to the metallic 1T-phase through chemical lithium intercalation, vdW MoTe2 is thermodynamically reversible between the 2H- and 1T'-phases, and can be further transformed by energetics, laser irradiation, strain or pressure, and electrical doping. Here, thickness- and temperature-dependent optical properties of 1T'-MoTe2 thin films grown by chemical vapor depsition are investigated via Fourier-transformed infrared spectroscopy. An optical gap of 28 +/- 2 meV in a 3-layer (or 2 nm) thick 1T'-MoTe2 is clearly observed at a low temperature region below 50K. No discernible optical bandgap is observed in samples thicker than ~4 nm. The observed thickness-dependent bandgap results agree with the measured dc resistivity data; the thickness-dependent 1T'-MoTe2 clearly demonstrates the metal-semiconductor transition at a crossover below the 2 nm-thick sample.
We present Spitzer Space Telescope data of four isolated white dwarfs that were previously known to harbor circumstellar gaseous disks. IRAC photometry shows a significant infrared excess in all of the systems, SDSS0738+1835, SDSS0845+2257, SDSS1043+0855 and SDSS1617+1620, indicative of a dusty extension to those disks. The 4.5-micron excesses seen in SDSS0738, SDSS0845, and SDSS1617 are 7.5, 5.7 and 4.5 times the white dwarf contribution, respectively. In contrast, in SDSS1043, the measured flux density at 4.5 microns is only 1.7 times the white dwarf contribution. We compare the measured IR excesses in the systems to models of geometrically thin, optically thick disks, and find that we are able to match the measured SEDs to within 3 sigma of the uncertainties, although disks with unfeasibly hot inner dust temperatures generally provide a better fit than those below the dust sublimation temperature. Possible explanations for the dearth of dust around SDSS1043+0855 are briefly discussed. Including our previous study of SDSS1228+1040, all five white dwarfs with gaseous debris disks have significant amounts of dust around them. It is evident that gas and dust can coexist around these relatively warm, relatively young white dwarfs.
Quaternary chalcogenide crystal Cu2CdGeS4 was studied both experimentally and theoretically in the present paper. Investigations of polarized fundamental absorption spectra demonstrated a high sensitivity to external light illumination. The photoinduced changes were studied using the cw 532 nm green laser with energy density about 0.4 J/cm2. The spectral maximum of the photoinduced anisotropy was observed at spectral energies equal to about 1.4 eV (energy gap equal to about 1.85 eV) corresponding to maximal density of the intrinsic defect levels. Spectroscopic measurements were performed for polarized and un-polarized photoinducing laser light to separate contribution of the intrinsic defect states from the pure states of the valence and conduction bands. To understand the origin of the observed photoinduced absorption near the fundamental edge, the benchmark first-principles calculations of the structural, electronic, optical and elastic properties of Cu2CdGeS4 were performed in the general gradient approximation (GGA) and local density approximation (LDA) approaches. The calculated dielectric function and optical absorption spectra exhibit some anisotropic behavior within the 0.15...0.20 eV energy range near the absorption edge; the optical anisotropy was also found in the deep inter-band transition spectral range. Peculiar features of chemical bonds in Cu2CdGeS4 were revealed by studying the electron density distribution. Possible intrinsic defects are shown to affect considerably the optical absorption spectra. Pressure effects on the structural and electronic properties were modeled by optimizing the crystal structure and calculating all relevant properties at elevated hydrostatic pressure. The first estimations of the bulk modulus (69 GPa (GGA) or 91 GPa (LDA)) and its pressure derivative for Cu2CdGeS4 are reported.
We present optical interferometric polarimetry measurements of the Mira-like variables R Car and RR Sco, using the Sydney University Stellar Interferometer. By making visibility measurements in two perpendicular polarisations, the relatively low-surface brightness light scattered by atmospheric dust could be spatially separated from the bright Mira photospheric flux. This is the first reported successful use of long-baseline optical interferometric polarimetry. Observations were able to place constraints on the distribution of circumstellar material in R Car and RR Sco. The inner radius of dust formation for both stars was found to be less than 3 stellar radii: much closer than the expected innermost stable location for commonly-assumed astrophysical ``dirty silicate'' dust in these systems (silicate dust with a significant iron content). A model with the dust distributed over a shell which is geometrically thin compared to the stellar radius was preferred over an outflow. We propose dust components whose chemistry and opacity properties enable survival at these extreme inner radii.
We have studied magnetodielectric and spin-lattice coupling in CoNb$_{2}$O$_{6}$ single crystals. Magnetostriction and magnetodielectric experiments are performed at temperatures in and above antifferomagnetic phase of quasi 1D Ising spin chain CoNb$_{2}$O$_{6}$. Field induced magnetic transitions are clearly reflected in magnetodielectric measurement as well as magnetostriction measurement also. Two sharp anomalies are found around the critical fields of antiferromagnetic to ferrimagnetic transition and ferrimagnetic to saturated paramagnetic transition in both magnetodielectric and magnetostriction experiments. High field anomaly is more pronounced for magnetodielectric response and magnetostriction also. So, in CoNb$_{2}$O$_{6}$, spins are strongly coupled with lattice as well as charges also.
An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with arbitrary mass quadrupole moment and is specified by three parameters, the mass $M$, the angular momentum per unit mass $a$ and the quadrupole parameter $q$. It reduces to the Kerr spacetime in the limiting case $q=0$ and to the Erez-Rosen spacetime when the specific angular momentum $a$ vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, turns out to be also a geodesic plane.
We perform the first systematic study on how dynamical stellar tides and general relativistic (GR) effects affect the dynamics and outcomes of binary-single interactions. For this, we have constructed an N-body code that includes tides in the affine approximation, where stars are modeled as self-similar ellipsoidal polytropes, and GR corrections using the commonly-used post-Newtonian formalism. Using this numerical formalism, we are able resolve the leading effect from tides and GR across several orders of magnitude in both stellar radius and initial target binary separation. We find that the main effect from tides is the formation of two-body tidal captures that form during the chaotic and resonant evolution of the triple system. The two stars undergoing the capture spiral in and merge. The inclusion of tides can thus lead to an increase on the stellar coalescence rate. We also develop an analytical framework for calculating the cross section of tidal inspirals between any pair of objects with similar mass. From our analytical and numerical estimates we find that the rate of tidal inspirals relative to collisions increases as the initial semi-major axis of the target binary increases and the radius of the interacting tidal objects decreases. The largest effect is therefore found for triple systems hosting white dwarfs and neutron stars. In this case, we find the rate of highly eccentric white dwarf - neutron star mergers to likely be dominated by tidal inspirals. While tidal inspirals occur rarely, we note that they can give rise to a plethora of thermonuclear transients such as Ca-rich transients.
The WILLI detector, built in IFIN-HH Bucharest, in collaboration with KIT Karlsruhe, is a rotatable modular detector for measuring charge ratio for cosmic muons with energy $<$ 1 GeV. It is under construction a mini-array for measuring the muon charge ratio in Extensive Air Showers. The EAS simulations have been performed with CORSIKA code. The values of the muon flux, calculated with semi-analytical formula, and simulated with CORSIKA code, based on DPMJET and QGSJET models for the hadronic interactions, are compared with the experimental data determined with WILLI detector. No significant differences between the two models and experimental data are observed. The measurements of the muon charge ratio for different angles-of-incidence, (performed with WILLI detector) shows an asymmetry due to the influence of magnetic field on muons trajectory; the values are in agreement with the simulations based on DPMJET hadronic interaction model. The simulations of muon charge ratio in EAS performed with CORSIKA code based on three hadronic interaction models (QGSJET2, EPOS and SYBILL) show relative small difference between models for H and for the Fe showers; the effect is more pronounced at higher inclination of WILLI detector. The future measurements should indicate which model is suitable.
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such solutions near the boundary of the underlying domain.
Volumes of line bundles are known to exist as limits on generically reduced projective schemes. However, it is not known if they always exist as limits on more general projective schemes. We show that they do always exist as a limit on a codimension one subscheme of a nonsingular projective variety.
Given a generically \'etale morphism $f\colon Y\to X$ of quasi-smooth Berkovich curves, we define a different function $\delta_f\colon Y\to[0,1]$ that measures the wildness of the topological ramification locus of $f$. This provides a new invariant for studying $f$, which cannot be obtained by the usual reduction techniques. We prove that $\delta_f$ is a piecewise monomial function satisfying a balancing condition at type 2 points analogous to the classical Riemann-Hurwitz formula, and show that $\delta_f$ can be used to explicitly construct the simultaneous skeletons of $X$ and $Y$. As an application, we use our results to completely describe the topological ramification locus of $f$ when its degree equals to the residue characteristic $p$.
Starting from the linearized fluctuating Boussinesq equations we derive an expression for the structure factor of fluids in stationary convection-free thermal nonequilibrium states, taking into account both gravity and finite-size effects. It is demonstrated how the combined effects of gravity and finite size causes the structure factor to go through a maximum value as a function of the wave number $q$. The appearance of this maximum is associated with a crossover from a $q^{-4}$ dependence for larger $q$ to a $q^2$ dependence for very small $q$. The relevance of this theoretical result for the interpretation of light scattering and shadowgraph experiments is elucidated. The relationship with studies on various aspects of the problem by other investigators is discussed. The paper thus provides a unified treatment for dealing with fluctuations in fluid layers subjected to a stationary temperature gradient regardless of the sign of the Rayleigh number $R$, provided that $R$ is smaller than the critical value $R_\mathrm{c}$ associated with the appearance of Rayleigh-B\'{e}nard convection.
We elaborate on the Ashtekar's formalism for spherically symmetric midisuperspaces and, for loop quantization, propound a new quantization scheme which yields a graph-preserving Hamiltonian constraint operator and by which one can impose the fundamental discreteness of loop quantum gravity a la the strategy of "improved" dynamics in loop quantum cosmology (LQC). Remarkable consequences are inferred at the heuristic level of effective dynamics: first, consistency of the constraint algebra regarding the Hamiltonian and diffeomorphism constraints fixes the improved quantization scheme to be of the form reminiscent of the improved scheme in LQC which preserves scaling invariance; second, consistency regarding two Hamiltonian constraints further demands the inclusion of higher order holonomy corrections and fixes a ratio factor of 2 for the improved scheme. It is suggested that the classical singularity is resolved and replaced by a quantum bounce which bridges a classical solution to another classical phase. However, the constraints violate briefly during the bouncing period, indicating that one cannot make sense of symmetry reduction by separating the degrees of freedom of the full theory into spherical and non-spherical ones in the vicinity of the quantum bounce, although the heuristic effective dynamics can still give a reliable semiclassical description of large-scale physics. Particularly, for the Schwarzschild solution in accordance with the Kruskal coordinates, revealing insights lead us to conjecture the complete quantum extension of the Schwarzschild spacetime: the black hole is evaporated via the Hawking radiation and meanwhile the quantum spacetime is largely extended from the classical one via the quantum bounce, suggesting that the information paradox might be resolved.
In this paper we show how to explicitly write down equations of hyperelliptic curves over Q such that for all odd primes l the image of the mod l Galois representation is the general symplectic group. The proof relies on understanding the action of inertia groups on the l-torsion of the Jacobian, including at primes where the Jacobian has non-semistable reduction. We also give a framework for systematically dealing with primitivity of symplectic mod l Galois representations.   The main result of the paper is the following. Suppose n=2g+2 is an even integer that can be written as a sum of two primes in two different ways, with none of the primes being the largest primes less than n (this hypothesis appears to hold for all g different from 0,1,2,3,4,5,7 and 13). Then there is an explicit integer N and an explicit monic polynomial $f_0(x)\in \mathbb{Z}[x]$ of degree n, such that the Jacobian $J$ of every curve of the form $y^2=f(x)$ has $Gal(\mathbb{Q}(J[l])/\mathbb{Q})\cong GSp_{2g}(\mathbb{F}_l)$ for all odd primes l and $Gal(\mathbb{Q}(J[2])/\mathbb{Q})\cong S_{2g+2}$, whenever $f(x)\in\mathbb{Z}[x]$ is monic with $f(x)\equiv f_0(x) \bmod{N}$ and with no roots of multiplicity greater than $2$ in $\overline{\mathbb{F}}_p$ for any p not dividing N.
Using a Rayleigh-Schr\"odinger perturbation expansion of multi-band Hubbard models, we present analytic expressions for the super-exchange coupling constants between magnetic transition metal ions of arbitrary separation in Mott-Hubbard insulators. The only restrictions are i) all ligand ions are closed shell anions and ii) all contributing interaction paths are of equal length. For short paths, our results essentially confirm the Goodenough-Kanamori-Anderson rules, yet in general there does not exist any simple rule to predict the sign of the magnetic coupling constants. The most favorable situation for ferromagnetic coupling is found for ions with less than half filled d shells, the (relative) tendency to ferromagnetic coupling increases with increasing path length. As an application, the magnetic interactions of the Cr compounds Rb$_2$CrCl$_4$, CrCl$_3$, CrBr$_3$ and CrI$_3$ are investigated, all of which except CrCl$_3$ are ferromagnets.
Big Bang Nucleosynthesis (BBN), along with the cosmic background radiation and the Hubble expansion, is one of the pillars ofthe standard, hot, big bang cosmology since the primordial synthesis of the light nuclides (D, $^3$He, $^4$He, $^7$Li) must have occurred during the early evolution of a universe described by this model. The overall consistency between the predicted and observed abundances of the light nuclides, each of which spans a range of some nine orders of magnitude, provides impressive support for the standard models of cosmology and particle physics. Here, the results of recent, statistically consistent tests of BBN are described. This new confrontation between theory and data challenges the standard model. The crises confronting BBN are identified and several possible resolutions are outlined.
In this paper, we provide a physical model for the origin of variations in the shapes and bump strengths of dust attenuation laws in galaxies by combining a large suite of cosmological "zoom-in" galaxy formation simulations with 3D Monte Carlo dust radiative transfer calculations. We model galaxies over 3 orders of magnitude in stellar mass, ranging from Milky Way like systems through massive galaxies at high-redshift. Critically, for these calculations we employ a constant underlying dust extinction law in all cases, and examine how the role of geometry and radiative transfer effects impact the resultant attenuation curves. Our main results follow. Despite our usage of a constant dust extinction curve, we find dramatic variations in the derived attenuation laws. The slopes of normalized attenuation laws depend primarily on the complexities of star-dust geometry. Increasing fractions of unobscured young stars flatten normalized curves, while increasing fractions of unobscured old stars steepen curves. Similar to the slopes of our model attenuation laws, we find dramatic variation in the 2175 Angstrom ultraviolet (UV) bump strength, including a subset of curves with little to no bump. These bump strengths are primarily influenced by the fraction of unobscured O and B stars in our model, with the impact of scattered light having only a secondary effect. Taken together, these results lead to a natural relationship between the attenuation curve slope and 2175 Angstrom bump strength. Finally, we apply these results to a 25 Mpc/h box cosmological hydrodynamic simulation in order to model the expected dispersion in attenuation laws at integer redshifts from z=0-6. A significant dispersion is expected at low redshifts, and decreases toward z=6. We provide tabulated results for the best fit median attenuation curve at all redshifts.
We study the nodal set of solutions to equations of the form $$ (-\Delta)^s u = \lambda_+ (u_+)^{q-1} - \lambda_- (u_-)^{q-1}\quad\text{in $B_1$}, $$ where $\lambda_+,\lambda_->0, q \in [1,2)$, and $u_+$ and $u_-$ are respectively the positive and negative part of $u$. This collection of nonlinearities includes the unstable two-phase membrane problem $q=1$ as well as sublinear equations for $1<q<2$. We initially prove the validity of the strong unique continuation property and the finiteness of the vanishing order, in order to implement a blow-up analysis of the nodal set. As in the local case $s=1$, we prove that the admissible vanishing orders can not exceed the critical value $k_q= 2s/(2- q)$. Moreover, we study the regularity of the nodal set and we prove a stratification result. Ultimately, for those parameters such that $k_q< 1$, we prove a remarkable difference with the local case: solutions can only vanish with order $k_q$ and the problem admits one dimensional solutions. Our approach is based on the validity of either a family of Almgren-type or a 2-parameter family of Weiss-type monotonicity formulas, according to the vanishing order of the solution.