ShantanuT01/DACTYL-Pretraining huggingface dataset:
(Abridged) Dust particles evolve in size and lattice structure in protoplanetary disks, due to coagulation, fragmentation and crystallization, and are radially and vertically mixed in disks. This paper aims at determining the mineralogical composition and size distribution of the dust grains in disks around 58 T Tauri stars observed with Spitzer/IRS. We present a spectral decomposition model that reproduces the IRS spectra over the full spectral range. The model assumes two dust populations: a warm component responsible for the 10\mu m emission arising from the disk inner regions and a colder component responsible for the 20-30\mu m emission, arising from more distant regions. We show evidence for a significant size distribution flattening compared to the typical MRN distribution, providing an explanation for the usual boxy 10\mu m feature profile generally observed. We reexamine the crystallinity paradox, observationally identified by Olofsson et al. (2009), and we find a simultaneous enrichment of the crystallinity in both the warm and cold regions, while grain sizes in both components are uncorrelated. Our modeling results do not show evidence for any correlations between the crystallinity and either the star spectral type, or the X-ray luminosity (for a subset of the sample). The size distribution flattening may suggests that grain coagulation is a slightly more effective process than fragmentation in disk atmospheres, and that this imbalance may last over most of the T Tauri phase. This result may also point toward small grain depletion via strong stellar winds or radiation pressure in the upper layers of disk. The non negligible cold crystallinity fractions suggests efficient radial mixing processes in order to distribute crystalline grains at large distances from the central object, along with possible nebular shocks in outer regions of disks that can thermally anneal amorphous grains.
We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic materials, that is to elastic materials possessing a stored energy function. Under some specific conditions of polyconvexity, coerciveness and growth of the stored energy function, we prove the existence of global minimizers. In addition, we define a general class of polyconvex stored energy functions which satisfies a coerciveness inequality.
The results of joint analyses of available cosmological data have motivated an important debate about a possible detection of a non-zero spatial curvature. If confirmed, such a result would imply a change in our present understanding of cosmic evolution with important theoretical and observational consequences. In this paper we discuss the legitimacy of carrying out joint analyses with the currently available data sets and explore their implications for a non-flat universe and extensions of the standard cosmological model. We use a robust tension estimator to perform a quantitative analysis of the physical consistency between the latest data of Cosmic Microwave Background, type Ia supernovae, Baryonic Acoustic Oscillations and Cosmic Chronometers. We consider the flat and non-flat cases of the $\Lambda$CDM cosmology and of two dark energy models with a constant and varying dark energy EoS parameter. The present study allows us to better understand if possible inconsistencies between these data sets are significant enough to make the results of their joint analyses misleading, as well as the actual dependence of such results with the spatial curvature and dark energy parameterizations.
We test our knowledge of the atomic opacity in the solar UV spectrum. Using the atomic data compiled in Paper I from modern, publicly available, databases, we perform calculations that are confronted with space-based observations of the Sun. At wavelengths longer than about 260 nm, LTE modeling can reproduce quite closely the observed fluxes; uncertainties in the atomic line data account fully for the differences between calculated and observed fluxes. At shorter wavelengths, departures from LTE appear to be important, as our LTE and restricted NLTE calculations differ. Analysis of visible-near infrared Na I and O I lines, two species that produce a negligible absorption in the UV, shows that observed departures from LTE for theses species can be reproduced very accurately with restricted (fixed atmospheric structure) NLTE calculations.
In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we disprove the conjecture and point out the flaws in the arguments leading to the conjectured expressions.
We investigate the effect of modified gravity on the specific angular momentum of galactic halos by analyzing the halo catalogs at z=0 from high-resolution N-body simulations for a f(R) gravity model that meets the solar-system constraint. It is shown that the galactic halos in the f(R) gravity model tend to acquire significantly higher specific angular momentum than those in the standard LCDM model. The largest difference in the specific angular momentum distribution between these two models occurs for the case of the isolated galactic halos with mass less than 10^{11}M_sun/h, which are likely least shielded by the chameleon screening mechanism. As the specific angular momentum of galactic halos is rather insensitive to the other cosmological parameters, it can in principle be an independent discriminator of modified gravity. We speculate a possibility of using the relative abundance of the low surface brightness galaxies (LSBGs) as a test of GR given that the formation of the LSBGs befalls in the fast spinning dark halos.
Let $(M,g)$ be an $n$-dimensional compact boudaryless Riemannian manifold with nonpositive sectional curvature, then our conclusion is that we can give improved estimates for the $L^p$ norms of the restrictions of eigenfunctions to smooth submanifolds of dimension $k$, for $p>\dfrac{2n}{n-1}$ when $k=n-1$ and $p>2$ when $k\leq n-2$, compared to the general results of Burq, G\'erard and Tzvetkov \cite{burq}. Earlier, B\'erard \cite{Berard} gave the same improvement for the case when $p=\infty$, for compact Riemannian manifolds without conjugate points for $n=2$, or with nonpositive sectional curvature for $n\geq3$ and $k=n-1$. In this paper, we give the improved estimates for $n=2$, the $L^p$ norms of the restrictions of eigenfunctions to geodesics. Our proof uses the fact that, the exponential map from any point in $x\in M$ is a universal covering map from $\mathbb{R}^2\backsimeq T_{x}M$ to $M$, which allows us to lift the calculations up to the universal cover $(\mathbb{R}^2,\tilde{g})$, where $\tilde{g}$ is the pullback of $g$ via the exponential map. Then we prove the main estimates by using the Hadamard parametrix for the wave equation on $(\mathbb{R}^2,\tilde{g})$, the stationary phase estimates, and the fact that the principal coefficient of the Hadamard parametrix is bounded, by observations of Sogge and Zelditch in \cite{SZ}. The improved estimates also work for $n\geq 3$, with $p>\frac{4k}{n-1}$. We can then get the full result by interpolation.
The Five-hundred-meter Aperture Spherical radio Telescope(FAST) is expected to complete its commissioning in 2019. FAST will soon begin the Commensal Radio Astronomy FasT Survey(CRAFTS), a novel and unprecedented commensal drift scan survey of the entire sky visible from FAST. The goal of CRAFTS is to cover more than 20000 $deg^{2}$ and reach redshift up to about 0.35. We provide empirical measurements of the beam size and sensitivity of FAST across the 1.05 to 1.45 GHz frequency range of the FAST L-band Array of 19-beams(FLAN). Using a simulated HI-galaxy catalogue based on the HI Mass Function(HIMF), we estimate the number of galaxies that CRAFTS may detect. At redshifts below 0.35, over $6\, \times \, 10^{5}$ HI galaxies may be detected. Below the redshift of 0.07, the CRAFTS HIMF will be complete above a mass threshold of $10^{9.5}\,M_{\odot}$. FAST will be able to investigate the environmental and redshift dependence of the HIMF to an unprecedented depth, shedding light onto the missing baryon and missing satellite problems.
In the present paper, we generalize some of the results on Kloosterman sums proven in \cite{BG} for prime moduli to general moduli. This requires to establish the corresponding additive properties of the reciprocal set $$ I^{-1}=\{x^{-1}:\quad x\in I\}, $$ where $I$ is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun-Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of general modulus.
Globular clusters are an important test bed for Newtonian gravity in the weak-acceleration regime, which is vital to our understanding of the nature of the gravitational interaction. Recent claims have been made that the velocity dispersion profiles of globular clusters flatten out at large radii, despite an apparent paucity of dark matter in such objects, indicating the need for a modification of gravitational theories. We continue our investigation of this claim, with the largest spectral samples ever obtained of 47 Tucanae and M55. Furthermore, this large sample allows for an accurate metallicity calibration based on the equivalent widths of the calcium triplet lines and K band magnitude of the Tip of the Red Giant Branch. Assuming an isothermal distribution, the rotations of each cluster are also measured with both clusters exhibiting clear rotation signatures. The global velocity dispersions of NGC 121 and Kron 3, two globular clusters in the Small Magellanic Cloud, are also calculated. By applying a simple dynamical model to the velocity dispersion profiles of 47 Tuc and M55, we calculate their mass-to-light profiles, total masses and central velocity dispersions. We find no statistically significant flattening of the velocity dispersion at large radii for M55, and a marked increase in the profile of 47 Tuc for radii greater than approximately half the tidal radius. We interpret this increase as an evaporation signature, indicating that 47 Tuc is undergoing, or has undergone, core-collapse, but find no requirement for dark matter or a modification of gravitational theories in either cluster.
We prove an A'Campo type formula for the tame monodromy zeta function of a smooth and proper variety over a discretely valued field $K$. As a first application, we relate the orders of the tame monodromy eigenvalues on the $\ell$-adic cohomology of a $K$-curve to the geometry of a relatively minimal $sncd$-model, and we show that the semi-stable reduction theorem and Saito's criterion for cohomological tameness are immediate consequences of this result. As a second application, we compute the error term in the trace formula for smooth and proper $K$-varieties. We see that the validity of the trace formula would imply a partial generalization of Saito's criterion to arbitrary dimension.
Asteroseismology of white dwarf (WD) stars is a powerful tool that allows to reveal the hidden chemical structure of WD and infer details about their evolution by comparing the observed periods with those obtained from stellar models. A recent asteroseismological study has reproduced the period spectrum of the helium rich pulsating WD KIC 08626021 with an unprecedented precision. The chemical structure derived from that analysis is notably different from that expected for a WD according to currently accepted formation channels, thus posing a challenge to the theory of stellar evolution. We explore the relevant micro- and macro-physics processes acting during the formation and evolution of KIC 08626021 that could lead to a chemical structure similar to that found through asteroseismology. We quantify to which extent is necessary to modify the physical processes that shapes the chemical structure, in order to reproduce the most important features of the asteroseismic model. We model the previous evolution of KIC 08626021 by exploring specific changes in the 12C+alpha reaction rate, screening processes, microscopic diffusion, as well as convective boundary mixing during core-He burning. We find that, in order to reproduce the core chemical profile derived for KIC 0862602, the 12C+alpha nuclear reaction rate has to be increased by a factor of $\sim$ 10 during the helium-core burning, and reduced by a factor of $\sim$ 1000 during the following helium-shell burning, as compared with the standard predictions for this rate. In addition, the main chemical structures derived for KIC 0862602 cannot be reconciled with our present knowledge of white dwarf formation. We find that within our current understanding of white dwarf formation and evolution, it is difficult to reproduce the most important asteroseismologically-derived features of the chemical structure of KIC 08626021.
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle number $N$, volume $V$, and temperature $T$, the pair distribution function contains as many information about the system as a full Gibbs distribution. The latter is represented as a series expansion in the pair distribution function. A recurrence relation system is constructed, which allows all terms of this expansion to be calculated successively.
This paper aims to contribute to validate, for numerical semigroups of reasonably large genus, the so-called Conjecture of Wilf. There is no counter-example for the conjecture among the over 3*10^{10} numerical semigroups of genus up to 60, as it has been computationally verified by Fromentin and Hivert. The computations use the idea of parsing a semigroups tree, making tests in each node. As a mean to combine parsing of the semigroups tree with known theoretical results, we introduce the concept of cutting semigroup. Assume that there exists a property on numerical semigroups that implies that a semigroup satisfying it necessarily satisfies Wilf's conjecture. Assume also that, besides, this property is hereditary, that is, if a semigroup satisfies it, then all its descendants in the semigroups tree also have the same property. Such properties exist. Interesting ones can be easily deduced from some deep results of Eliahou. A semigroup satisfying such a property is called a cutting semigroup (for that property). When looking for counter-examples to Wilf's conjecture, if a cutting semigroup is found, then it can be cut off, since no counter example lies among its descendants. One can therefore consider the trimmed tree obtained by cutting off all the cutting semigroups. Depending on the properties, these ideas allow in some cases to avoid parsing a very significant part of the tree and can be applied to other related problems. For instance, they can be used to find all numerical semigroups with negative Eliahou number up to a genus bigger than 60, which is the current record. Computations by Fromentin had shown that there are exactly 5 numerical semigroups in these circumstances.
We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting implication of the result is that the asymptotic value for each secretary problem with multiple stoppings is in fact a typical lower bound in a much more general class of multiple stopping problems as modifications of odds problem.
When an optimal measurement is made on a qubit and what we call an Unbiased Mixture of the resulting ensembles is taken, then the post measurement density matrix is shown to be related to the pre-measurement density matrix through a simple and linear relation. It is shown that such a relation holds only when the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is also shown explicitly that non-orthogonal measurements fail to give such a linear relation no matter how the ensembles are mixed. The result has been proved to be true for arbitrary quantum mechanical systems of finite dimensional Hilbert spaces. The result is true irrespective of whether the initial state is pure or mixed.
We present calculated, electronic and related properties of wurtzite cadmium sulfide (w-CdS). Our ab-initio, non-relativistic calculations employed a local density functional approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). Following the Bagayoko, Zhao, and Williams (BZW) method, we solved self-consistently both the Kohn-Sham equation and the equation giving the ground state density in terms of the wave functions of the occupied states. Our calculated, direct band gap of 2.47 eV, at the point, is in excellent agreement with experiment. So are the calculated density of states and the electron effective mass. In particular, our results reproduce the peaks in the conduction band density of states, within the experimental uncertainties.
We consider vertex decompositions of (di)graphs which appear in Automata Theory, and establish some their properties. Then we apply them to the problem of forbidden subgraphs.
It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.
The prospect of combining the dissipationless nature of superconducting currents with the spin-polarization of magnetic materials is interesting with respect to exploring superconducting analogues of topics in spintronics. In order to accomplish this aim, it is pivotal to understand how spin-supercurrents interact dynamically with magnetization textures. We investigate the appearance of a spin-supercurrent and the resulting magnetization dynamics in a textured magnetic Josephson current by using three experimentally relevant models: i) a S/F/S junction with spin-active interfaces, ii) a S/F1/F2/F3/S Josephson junction with a ferromagnetic trilayer, and iii) a Josephson junction containing a domain wall. In all of these cases, the supercurrent is spin-polarized and exerts a spin-transfer torque on the ferromagnetic interlayers which causes magnetization dynamics. Using a scattering matrix formalism in the clean limit, we compute the Andreev-bound states and free energy of the system which is used to solve the Landau-Lifshiftz-Gilbert equation. We compute both how the inhomogeneous magnetism influences the phase-dependence of the charge supercurrent as well as the magnetization dynamics caused by the spin-supercurrent. Using a realistic experimental parameter set, we find that the supercurrent can induce magnetization switching that is controlled by the superconducting phase difference. Moreover, we demonstrate that the combined effect of chiral spin symmetry breaking and interface scattering causes the system to act as a phase battery that may supply any superconducting phase difference phi in the ground state. Such a phi junction is accompanied by an anomalous supercurrent appearing even at zero phase difference, and we demonstrate that the flow direction of this current is controlled by the chirality of the magnetization configuration.
Although crystallized neutron star crust is responsible for many fascinating observational phenomena, its actual microscopic structure in tremendous gravitational and magnetic fields is not understood. Here we show that in a non-uniform magnetic field, three-dimensional ionic Coulomb crystals comprising the crust may stretch or shrink while their electrostatic pressure becomes anisotropic. The pressure depends non-linearly on the magnitude of the stretch, so that a continuous magnetic field evolution may result in an abrupt crystal elongation or contraction. This may provide a trigger for magnetar activity. A phonon mode instability is revealed, which sets the limits of magnetic field variation beyond which the crystal is destroyed. These limits sometimes correspond to surprisingly large deformations. It is not known what happens to crust matter subject to a pressure anisotropy exceeding these limits. We hypothesize that the ion system then possesses a long-range order only in one or two dimensions, that is becomes a liquid crystal.
The azimuthal asymmetry of heavy quarks production on double polarized proton-proton and proton-antiproton colliders are studied in this work at next-to-leading order in $\alpha_s$, with some details included. The purpose is to see whether the effect of extracted transversity distribution functions can be seen on present and near future colliders. All analytic one-loop hard coefficients are given. Numerical results for the asymmetry on proton-(anti)proton colliders are presented.
We show, by using a correlated Jastrow wave function and a mapping onto a classical model, that the two-dimensional Mott transition in a simple half-filled one-band model can be unconventional and very similar to the binding-unbinding Kosterlitz-Thouless transition of vortices and anti-vortices, here identified by empty and doubly occupied sites. Within this framework, electrons strongly interact with collective plasmon excitations that induce anomalous critical properties on both sides of the transition. In particular, the insulating phase is characterized by a singular power law behavior in the photoemission spectrum, that can be continuously connected to the fully-projected insulating state, relevant to strongly correlated low-energy models.
We consider the class of complete discretely valued fields such that the residue field is of prime characteristic p and the cardinality of a $p$-base is 1. This class includes two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It appears that a Hasse-Herbrand type functions can be defined with all the usual properties. Therefore, a theory of upper ramification groups, as well as the ramification theory of infinite extensions, can be developed. Next, we consider an equal characteristic two-dimensional local field $K$. We introduce some filtration on the second K-group of a given field. This filtration is other than the filtration induced by the valuation. We prove that the reciprocity map of two-dimensional local class field theory identifies this filtration with the ramification filtration.
A 2-level atom with degenerate ground state interacting with a quantum field is investigated. We show, that the field drives the state of the atom to a stationary state, which is non-unique, but depends on the initial state of the system through some conserved quantities. This non-uniqueness follows from the degeneracy of the ground state of the atom, and when the ground subspace is two-dimensional, the family of stationary states will depend on a one-dimensional parameter. Only one of the stationary states in this family is a pure state, and this state coincides with the known non-coupled population trapped state (zero population in the excited level. Another one stationary state corresponds to an equal weight mixture of the excited level and of the coupled state.
We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs.