ShantanuT01/DACTYL-Pretraining huggingface dataset:
The young open cluster NGC 6611 includes among its candidate members a class of peculiar objects with interesting properties: blue stars with infrared IR excesses. These stars show excesses in IR bands, signature of the presence of a circumstellar disk, but optical colors typical of older field stars. In order to confirm their membership to the cluster, it is therefore important to use new spectroscopic observations, together with previous photometric data. We aim at confirming the membership of these objects and at investigating their physical properties to verify whether the observed colors are intrinsic or altered by the presence of the disk or by the accretion processes. We analyze the intermediate resolution spectroscopic data obtained for a subsample of blue stars in NGC 6611 with FLAMES. In particular, we focus on the study of: 1) the profile of the Ha emission line, to select stars with accretion and outflow activity; 2) the Li absorption line, used as a youth indicator; 3) the radial velocity. Using the spectroscopic analysis, it has been possible to investigate the presence of the Li absorption line as well as to discriminate between stars with inert or active disk. In particular, from the analysis of the Ha emission line we were able to infer the activity due to the accretion and outflow processes and the variability of the emission. We also investigated the binarity of the blue stars and their membership to NGC 6611.
We use new and published near-IR spectra, with synthetic spectra, to derive physical properties of three of the latest-type T dwarfs. A new R~1700 spectrum of the T7.5 dwarf HD 3651B, with existing data, allows a detailed comparison to the well-studied and very similar dwarf, Gl 570D. We find that HD 3651B has both higher gravity and metallicity than Gl 570D, with Teff=820-830K, log g= 5.4-5.5, [m/H]= +0.2 and Kzz=10^4cm^2/s. Its age is 8-12 Gyr and its implied mass is 60-70 M_Jup. We perform a similar analyis of the T8 and T7.5 dwarfs 2MASS J09393548-2448279 and 2MASS J11145133-2618235 using published data, comparing them to the well-studied T8, 2MASS J04151954-0935066. We find that the two dwarfs have the same Teff as the reference dwarf, and similar gravities, but lower metallicities. The parameters are Teff=725-775K and [m/H]= -0.3; log g=5.3-5.45 for 2MASS J09393548-2448279 and log g=5.0-5.3 for 2MASS J11145133- 261823. The age and mass are ~10Gyr and 60M_Jup for 2MASS J09393548-2448279, and ~5 Gyr and 40M_Jup for 2MASS J11145133-261823. A serious limitation is the incompleteness of the line lists of CH4 and NH3 at lambda <1.7um. Spectra of Saturn and Jupiter, and of laboratory CH4 and NH3 gas, suggest that NH3 features in the Y- and J-bands may be useful as indicators of the next cooler spectral type, and not features in the H- and K-bands as previously thought. However large uncertainties remain, as the abundance of NH3 is likely to be significantly below the chemical equilibrium value, and inclusion of laboratory NH3 opacities predicts band shapes that are discrepant with existing data. It is possible that the T spectral class will have to be extended to low temperatures around 400K, when water clouds condense in the atmosphere [abridged].
Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with three simple examples based on the potential-density pairs corresponding to a harmonic oscillator (homogeneous sphere), the well-known Plummer model and a massive spherical dark matter halo model with a logarithmic potential. Moreover, the geodesic circular motion of test particles around such structures is studied. The stability of the orbits against radial perturbations is also analyzed using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models considered satisfy all the energy conditions.
Using hadron dynamics we calculate nuclear transparencies for protons, knocked-out in high-$Q^2$, semi-inclusive reactions. Predicted transparencies are, roughly half a standard deviation above the NE18 data. The latter contain the effects of binned proton missing momenta and mass, and of finite detector acceptances. In order to test sensitivity we compare computed transparencies without restrictions and the same with maximal cuts for missing momenta and the electron energy loss. We find hardly any variation, enabling a meaningful comparison with data and predictions based on hadron dynamics. Should discrepancies persist in high-statistics data, the above may with greater confidence be attributed to exotic components in the description of the outgoing proton.
We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct the most general Chern-Simons theories that can describe these states. We then derive a criterion for when these systems have protected gapless edge modes -- that is, edge modes that cannot be gapped out without breaking time reversal or charge conservation symmetry. The systems with protected edge modes can be regarded as fractionalized analogues of topological insulators. We show that previous examples of 2D fractional topological insulators are special cases of this general construction. As part of our derivation, we define the concept of "local Kramers degeneracy" and prove a local version of Kramers theorem.
In this paper, we study representations of real numbers in the positional numeration system with negative basis, as introduced by Ito and Sadahiro. We focus on the set $\Z_{-\beta}$ of numbers whose representation uses only non-negative powers of $-\beta$, the so-called $(-\beta)$-integers. We describe the distances between consecutive elements of $\Z_{-\beta}$. In case that this set is non-trivial we associate to $\beta$ an infinite word $\boldsymbol{v}_{-\beta}$ over an (in general infinite) alphabet. The self-similarity of $\Z_{-\beta}$, i.e., the property $-\beta \Z_{-\beta}\subset \Z_{-\beta}$, allows us to find a morphism under which $\boldsymbol{v}_{-\beta}$ is invariant. On the example of two cubic irrational bases $\beta$ we demonstrate the difference between Rauzy fractals generated by $(-\beta)$-integers and by $\beta$-integers.
Let $(u_n)_{n \ge 0}$ be a nondegenerate Lucas sequence and $g_u(n)$ be the arithmetic function defined by $\gcd(n, u_n).$ Recent studies have investigated the distributional characteristics of $g_u$. Numerous results have been proven based on the two extreme values $1$ and $n$ of $g_{u}(n)$. Sanna investigated the average behaviour of $g_{u}$ and found asymptotic formulas for the moments of $\log g_{u}$. In a related direction, Jha and Sanna investigated properties of $g_{u}$ at shifted primes. In light of these results, we prove that for each positive integer $\lambda,$ we have $$\sum_{\substack{p\le x\\p\text{ prime}}} (\log g_{u}(p-1))^{\lambda} \sim P_{u,\lambda}\pi(x),$$ where $P_{u, \lambda}$ is a constant depending on $u$ and $\lambda$ which is expressible as an infinite series. Additionally, we provide estimates for $P_{u,\lambda}$ and $M_{u,\lambda},$ where $M_{u, \lambda}$ is the constant for an analogous sum obtained by Sanna [J. Number Theory 191 (2018), 305-315]. As an application of our results, we prove upper bounds on the count $\#\{p\le x : g_{u}(p-1)>y\}$ and also establish the existence of infinitely many runs of $m$ consecutive primes $p$ in bounded intervals such that $g_{u}(p-1)>y$ based on a breakthrough of Zhang, Maynard, Tao, et al. on small gaps between primes. Exploring further in this direction, it turns out that for Lucas sequences with nonunit discriminant, we have $\max\{g_{u}(n) : n \le x\} \gg x$. As an analogue, we obtain that that $\max\{g_u(p-1) : p \le x\} \gg x^{0.4736}$ unconditionally, while $\max\{g_u(p-1): p \le x\} \gg x^{1 - o(1)}$ under the hypothesis of Montgomery's or Chowla's conjecture.
Raman measurements in carbon allotropes are generally associated with the exploration of the vibrational modes. Here, we present a theory of the non-resonant inelastic light scattering accompanied by the excitations of intersubband electron-hole pairs in carbon nanotubes and predict the selection rules and polarization properties of the dominant intersubband Raman active modes.
It is shown that any defect gives an Ohmic contribution to the damping of any normal mode of the crystal lattice with nonzero wavevector which does not vanish at zero temperature. This explains the large phason damping observed at low temperatures in incommensurate phases, and might be a key factor to understand the linear-in-$T$ specific heat observed in a number of real dielectrics at low enough temperatures.
Owing to the development of research on local aggregation operators, dramatic breakthrough has been made in point cloud analysis models. However, existing local aggregation operators in the current literature fail to attach decent importance to the local information of the point cloud, which limits the power of the models. To fit this gap, we propose an efficient Vector Attention Convolution module (VAConv), which utilizes K-Nearest Neighbor (KNN) to extract the neighbor points of each input point, and then uses the elevation and azimuth relationship of the vectors between the center point and its neighbors to construct an attention weight matrix for edge features. Afterwards, the VAConv adopts a dual-channel structure to fuse weighted edge features and global features. To verify the efficiency of the VAConv, we connect the VAConvs with different receptive fields in parallel to obtain a Multi-scale graph convolutional network, VA-GCN. The proposed VA-GCN achieves state-of-the-art performance on standard benchmarks including ModelNet40, S3DIS and ShapeNet. Remarkably, on the ModelNet40 dataset for 3D classification, VA-GCN increased by 2.4% compared to the baseline.
We give a survey on some recent results concerning the Landau-Lifshitz equation, a fundamental nonlinear PDE with a strong geometric content, describing the dynamics of the magnetization in ferromagnetic materials. We revisit the Cauchy problem for the anisotropic Landau-Lifshitz equation, without dissipation, for smooth solutions, and also in the energy space in dimension one. We also examine two approximations of the Landau-Lifshitz equation given by of the Sine-Gordon equation and cubic Schr\"odinger equations, arising in certain singular limits of strong easy-plane and easy-axis anisotropy, respectively.   Concerning localized solutions, we review the orbital and asymptotic stability problems for a sum of solitons in dimension one, exploiting the variational nature of the solitons in the hydrodynamical framework.   Finally, we survey results concerning the existence, uniqueness and stability of self-similar solutions (expanders and shrinkers) for the isotropic Landau-Lifshitz equation with Gilbert term. Since expanders are associated with a singular initial condition with a jump discontinuity, we also review their well-posedness in spaces linked to the BMO space.
Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $\Lambda$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, $Q$, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant; and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or Wheeler-DeWitt equation as an affine algebra requires a non-vanishing cosmological constant; and a fundamental uncertainty relation of the form $\frac{\Delta{V}}{<{V}>}\Delta {Q}\geq 2\pi \Lambda L^2_{Planck}$ (wherein $V$ is the total volume) may apply to all physical states of quantum gravity.
The full complex phase structure of the meson-baryon reaction amplitude in coupled channels approach is investigated, including also the photon-baryon channel. The result may be viewed as a generalization of the well-known Watson's theorem. Furthermore, the complex phase structure is exhibited for the pole and nonpole parts of the reaction amplitude in such a way that it will serve as a convenient common starting point for constructing models with different levels of approximation, in particular, for building isobar models where the basic properties of the $S$-matrix can be maintained. Such models should be useful, especially, in coupled multichannel calculations, where a large amount of experimental data are considered in resonance analyses, a situation encountered in modern baryon spectroscopy. In particular, it is shown that the unitarity of the pole part of the $T$-matrix arises automatically from the dressing mechanism inherent in the basic scattering equation. This implies that no separate conditions are required for making this part of the resonance amplitude unitary as it has been done in some of the existing isobar models.
Ford circles are parameterized by the rational numbers but are also the result of an iterative geometric procedure. We review this and introduce an apparently new parameterization by solutions of a certain quadratic Diophantine equation. We then generalize to Eisenstein and Gaussian rationals where the resulting "Ford spheres" are also the result of iterative geometric procedures and are also parameterized by solutions of certain quadratic Diophantine equations. We generalize still further to imaginary quadratic fields.
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.
We consider a complete nonsingular variety $X$ over $\bC$, having a normal crossing divisor $D$ such that the associated logarithmic tangent bundle is generated by its global sections. We show that $H^i\big(X, L^{-1} \otimes \Omega_X^j(\log D)\big) = 0$ for any nef line bundle $L$ on $X$ and all $i < j - c$, where $c$ is an explicit function of $(X,D,L)$. This implies e.g. the vanishing of $H^i(X, L \otimes \Omega_X^j)$ for $L$ ample and $i > j$, and gives back a vanishing theorem of Broer when $X$ is a flag variety.
This paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks. Optically thin lines from Keplerian planar disks are considered. Model line profiles are calculated for simple field topologies of axial fields (i.e., vertical to the disk plane) and toroidal fields (i.e., purely azimuthal). A scheme for discerning field strengths and geometries in disks is developed based on Stokes Q-U diagrams for the run of polarization across line profiles that are Doppler broadened by the disk rotation. A discussion of the Hanle effect for magnetized disks in which the magnetorotational instability (MRI) is operating is also presented. Given that the MRI has a tendency to mix the vector field orientation, it may be difficult to detect the disk fields with the longitudinal Zeeman effect, since the amplitude of the circularly polarized signal scales with the net magnetic flux in the direction of the observer. The Hanle effect does not suffer from this impediment, and so a multi-line analysis could be used to constrain field strengths in disks dominated by the MRI.
A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly- and doubly-closed-shell nuclei are compared with available experimental data.
We have determined the physical ground state properties of the compounds CeRuPO and CeOsPO by means of magnetic susceptibility chi(T), specific heat C(T), electrical resistivity rho(T), and thermopower S(T) measurements. chi(T) reveals a trivalent 4f1 cerium state in both compounds. For CeRuPO a pronounced decrease of rho(T) below 50K indicates the onset of coherent Kondo scattering which is confirmed by enhanced S(T). The temperature and magnetic field dependence of chi(T) and C(T) evidence ferromagnetic (FM) order at TC=15K. Thus, CeRuPO seems to be one of the rare example of a FM Kondo lattice. In contrast, CeOsPO shows antiferromagnetic order at TN=4.4K despite only minor changes in lattice parameters and electronic configuration. Additional 31P NMR results support these scenarios. LSDA+U calculations evidence a quasi two dimensional electronic band structure, reflecting a strong covalent bonding within the CeO and RuP layers and a weak ionic like bonding between the layers.
A three degrees of freedom (3-dof) barred galaxy model composed of a spherically symmetric nucleus, a bar, a flat disc and a spherically symmetric dark matter halo is used for investigating the dynamics of the system. We use colour-coded plots to demonstrate how the value of the semi-major axis of the bar influences the regular or chaotic dynamics of the 3-dof system. For distinguishing between ordered and chaotic motion we use the Smaller ALingment Index (SALI) method, a fast yet very accurate tool. Undoubtedly, the most important elements of the dynamics are the normally hyperbolic invariant manifolds (NHIMs) located in the vicinity of the index 1 Lagrange points $L_2$ and $L_3$. These manifolds direct the flow of stars over the saddle points, while they also trigger the formation of rings and spirals. The dynamics in the neighbourhood of the saddle points is visualized by bifurcation diagrams of the Lyapunov orbits as well as by the restriction of the Poincar\'e map to the NHIMs. In addition, we reveal how the semi-major axis of the bar influences the structure of these manifolds which determine the final stellar structure (rings or spirals). Our numerical simulations suggest that in galaxies with weak bars the formation of $R_1$ rings or $R_1'$ pseudo-rings is favoured. In the case of galaxies with intermediate and strong bars the invariant manifolds seem to give rise to $R_1R_2$ rings and twin spiral formations, respectively. We also compare our numerical outcomes with earlier related work and with observational data.
In this paper we consider a class of critical concave convex Ambrosetti-Prodi type problems for the fractional $p$-Laplacian operator. By applying the Linking Theorem and the Mountain Pass Theorem as well, the interaction of the nonlinearities with the first eigenvalue of fractional $p$-Laplacian will be used to prove existence and multiplicity of solutions.
The recently proposed Einstein molecule approach is extended to compute the free energy of molecular solids. This method is a variant of the Einstein crystal method of Frenkel and Ladd[J. Chem. Phys. 81,3188 (1984)]. In order to show its applicability, we have computed the free energy of a hard-dumbbells solid, of two recently discovered solid phases of water, namely, ice XIII and ice XIV, where the interactions between water molecules are described by the rigid non-polarizable TIP4P/2005 model potential, and of several solid phases that are thermodynamically stable for an anisotropic patchy model with octahedral symmetry which mimics proteins.Our calculations show that both the Einstein crystal method and the Einstein molecule approach yield the same results within statistical uncertainty.In addition, we have studied in detail some subtle issues concerning the calculation of the free energy of molecular solids. First, for solids with non-cubic symmetry, we have studied the effect of the shape of the simulation box on the free energy. Our results show that the equilibrium shape of the simulation box must be used to compute the free energy in order to avoid the appearance of artificial stress in the system that will result in an increase of the free energy. In complex solids, such as the solid phases of water, another difficulty is related to the choice of the reference structure. As in some cases there is not an obvious orientation of the molecules, it is not clear how to generate the reference structure. Our results will show that,as long as the structure is not too far from the equilibrium structure,the calculated free energy is invariant to the reference structure used in the free energy calculations. Finally, the strong size dependence of the free energy of solids is also studied.
We study the flow structure in 3D magnetohydrodynamic (MHD) simulations of accretion onto Sagittarius A* via the magnetized winds of the orbiting Wolf-Rayet stars. These simulations cover over 3 orders of magnitude in radius to reach $\approx$ 300 gravitational radii, with only one poorly constrained parameter (the magnetic field in the stellar winds). Even for winds with relatively weak magnetic fields (e.g., plasma $\beta$ $\sim$ $10^6$), flux freezing/compression in the inflowing gas amplifies the field to $\beta$ $\sim$ few well before it reaches the event horizon. Overall, the dynamics, accretion rate, and spherically averaged flow profiles (e.g., density, velocity) in our MHD simulations are remarkably similar to analogous hydrodynamic simulations. We attribute this to the broad distribution of angular momentum provided by the stellar winds, which sources accretion even absent much angular momentum transport. We find that the magneto-rotational instability is not important because of i) strong magnetic fields that are amplified by flux freezing/compression, and ii) the rapid inflow/outflow times of the gas and inefficient radiative cooling preclude circularization. The primary effect of magnetic fields is that they drive a polar outflow that is absent in hydrodynamics. The dynamical state of the accretion flow found in our simulations is unlike the rotationally supported tori used as initial conditions in horizon scale simulations, which could have implications for models being used to interpret Event Horizon Telescope and GRAVITY observations of Sgr A*.