ShantanuT01/DACTYL-Pretraining huggingface dataset:
We revisited the sunspot observations published by Johannes Hevelius in his book Machina Coelestis (1679) corresponding to the period 1653-1675 (just in the middle of the Maunder Minimum). We show detailed translations of the original Latin texts describing the sunspot records and provide the general context of these sunspot observations. From this source only, we present an estimate of the annual values of the Group Sunspot Number based only on the records that explicitly inform about the presence or absence of sunspots. Although we obtain very low values of the Group Sunspot Number, in accordance with a grand minimum of solar activity, these values are significantly higher in general than the values provided by Hoyt and Schatten (1998) for the same period.
We present results of the first extensive and deep CCD photometric survey carried out in the field of the open cluster Trumpler 27, an object in the constellation of Sagittarius not far from the Galaxy center.   We look for young stars clumps that might plausibly be associated with spiral structure. Wide-field UBVI photometry combined with infrared information allows us to reconstruct the distribution in reddening and distance of young stars in the field using the Color-Color and Color-Magnitude diagrams.   The analysis of our data, combined too with extensive spectroscopy taken from literature shows that the real entity of Trumpler 27 as an open cluster is far from being firmly stated. In fact, instead of finding a relatively compact group of stars confined to a small distance range, we found that stars associated to Trumpler 27 are, indeed, a superposition of early type stars seen along the line of sight extending over several kiloparsecs beyond even the center of the galaxy. We demonstrate that at each distance range it becomes possible to generate a color-magnitude diagram resembling that of an open cluster. This way, our analysis indicates that what was considered an open cluster characterized by a significant age spread is a stellar continuum that reaches its maximum number of stars at approximately 3.5 kpc from the Sun, the distance of the Scutum-Crux arm approximately. At the same time, and after analyzing the way early type stars distribute with distance, we found some of these stellar groups may be linked, within the distance errors, with other inner spiral arms of our galaxy, including the Near 3 kpc arm at approximately 5 kpc from the Sun. However, very young stars by themselves do not seem to trace strongly the inner spiral arms since they are distributed evenly across several kiloparsecs toward the center of the Galaxy.
Recently, the author defined multiple Dedekind zeta values \cite{MDZF} associated to a number $K$ field and a cone $C$. In this paper we construct explicitly non-trivial examples of mixed Tate motives over the ring of integers in $K$, for a real quadratic number field $K$ and a particular cone C. The period of such a motive is a multiple Dedekind zeta values at $(s_1,s_2)=(1,2)$, associated to the pair $(K;C)$, times a nonzero element of $K$.
The formation and evolution of an X--ray cluster is studied using a 3--D N-body + hydrodynamical simulation which includes feedback of energy and iron from cluster galaxies. The differences in evolution and final state between the simulation and a similar run without feedback are highlighted. We address the energetics of cluster gas; the distribution of dark matter, gas, and galaxies; the thermodynamic state of cluster gas, the beta model, and the beta discrepancy; x-ray evolution; the validity of estimates of the binding mass and of the baryon fraction of the cluster; dynamics of the galaxy population and velocity bias; and of the evolution of the iron abundance distribution in the cluster. We find that preheating by galactic winds results in a lower core density for the ICM, which in turn makes the simulated cluster fainter at high redshift and undergo rapid luminosity evolution to the present. A strong iron abundance gradient is present, even at high redshift. Velocity bias is present in the galaxy population; this bias combined with the preheating from winds drives the value of $\beta_{spec}\,=\,\sigma^{2}/\left(kT/\mu m_{p}\right)$ to values less than one. The two fluid simulation, modelling infall only, predicts $\beta_{spec}\,\geq\,1$, less in line with observation.
The stochastic model that describes radiative heat transfer in dielectric medium is built. The model is based on the representation that heat transfer is realized both by heat conductivity mechanism in it and due to the electromagnetic radiation that is generated by thermal fluctuations of atoms in the medium. Using the fluctuation-dissipative theorem, on the basis of such physical suppositions, the stochastic model is formulated in the form of the infinite dimensional Ornstein-Uhlenbeck process that describes medium fluctuations. In the model frameworks, the energy flux density of fluctuating electromagnetic field is calculated in the form of the functional of temperature distribution in three-dimensional medium sample.
By generalizing the usual current density to a matrix with respect to spin variables, a general equation of continuity satisfied by the density matrix and current density matrix has been derived. This equation holds in arbitrary spin-orbit coupling systems as long as its Hamiltonian can be expressed in terms of a power series in momentum. Thereby, the expressions of the current density matrix and a torque density matrix are obtained. The current density matrix completely describes both the usual current and spin current as well; while the torque density matrix describes the spin precession caused by a total effective magnetic field, which may include a realistic and an effective one due to the spin-orbit coupling. In contrast to the conventional definition of spin current, this expression contains an additional term if the Hamiltonian includes nonlinear spin-orbit couplings. Moreover, if the degree of the full Hamiltonian $\geq3$, then the particle current must also be modified in order to satisfy the local conservation law of number.
Grover's algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r unmarked states. These equations are solved exactly. An expression for the optimal measurement time T \sim O(\sqrt{N/r}) is derived which is shown to depend only on the initial average amplitudes of the marked and unmarked states. A bound on the probability of measuring a marked state is derived, which depends only on the standard deviation of the initial amplitude distributions of the marked or unmarked states.
We investigate the general properties of a class of scalar-field dark energy models (i.e., $\phi$CDM models) which behave like cosmological trackers at early times. Particularly, we choose three $\phi$CDM models with typical potentials, i.e., $V(\phi)\propto \phi^{-\alpha}$ (inverse power-law (IPL) model), $V(\phi)\propto \coth^{\alpha}{\phi}$ (L-model) and $V(\phi)\propto \cosh(\alpha\phi)$ (Oscillatory tracker model), where the latter two models are based on the $\alpha$-attractors originated from the study of inflation. These models, which reduce to the $\Lambda$CDM model with $\alpha \to 0$, are studied and compared with the recent observations, including the Pantheon sample of type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO) measurements extracted from 6dFGS, BOSS and eBOSS, as well as the temperature and polarization anisotropy power spectra data of cosmic microwave background radiation (CMB) from Planck 2018 results. The observational constraints from the combining sample (SNe Ia + BAO + CMB) indicate that none of the three $\phi$CDM models exclude the $\Lambda$CDM model at $68.3\%$ confidence level. We find that the CMB anisotropy data have obvious advantages in constraining the dark energy models compared with other cosmological probes, which is particularly evident in the L-model. Furthermore, we apply the Bayesian evidence to compare the $\phi$CDM models and the $\Lambda$CDM model with the analysis of the combining sample. The concordance $\Lambda$CDM model is still the most supported one. In addition, among the three $\phi$CDM models, the IPL model is the most competitive one, while the L-model/Oscillatory tacker model is moderately/strongly disfavored.
We measure the redshift-space correlation function from a spectroscopic sample of 2783 emission line galaxies from the FastSound survey. The survey, which uses the Subaru Telescope and covers the redshift ranges of $1.19<z<1.55$, is the first cosmological study at such high redshifts. We detect clear anisotropy due to redshift-space distortions (RSD) both in the correlation function as a function of separations parallel and perpendicular to the line of sight and its quadrupole moment. RSD has been extensively used to test general relativity on cosmological scales at $z<1$. Adopting a LCDM cosmology with the fixed expansion history and no velocity dispersion $\sigma_{\rm v}=0$, and using the RSD measurements on scales above 8Mpc/h, we obtain the first constraint on the growth rate at the redshift, $f(z)\sigma_8(z)=0.482\pm 0.116$ at $z\sim 1.4$ after marginalizing over the galaxy bias parameter $b(z)\sigma_8(z)$. This corresponds to $4.2\sigma$ detection of RSD. Our constraint is consistent with the prediction of general relativity $f\sigma_8\sim 0.392$ within the $1-\sigma$ confidence level. When we allow $\sigma_{\rm v}$ to vary and marginalize it over, the growth rate constraint becomes $f\sigma_8=0.494^{+0.126}_{-0.120}$. We also demonstrate that by combining with the low-z constraints on $f\sigma_8$, high-z galaxy surveys like the FastSound can be useful to distinguish modified gravity models without relying on CMB anisotropy experiments.
A permutomino of size n is a polyomino determined by particular pairs (P1, P2) of permutations of size n, such that P1(i) is different from P2(i), for all i. Here we determine the combinatorial properties and, in particular, the characterization for the permutations defining convex permutominoes.   Using such a characterization, these permutations can be uniquely represented in terms of the so called square permutations, introduced by Mansour and Severini. Then, we provide a closed formula for the number of these permutations with size n.
We study three dimensional insulators with inversion symmetry, in which other point group symmetries, such as time reversal, are generically absent. Their band topology is found to be classified by the parities of occupied states at time reversal invariant momenta (TRIM parities), and by three Chern numbers. The TRIM parities of any insulator must satisfy a constraint: their product must be +1. The TRIM parities also constrain the Chern numbers modulo two. When the Chern numbers vanish, a magneto-electric response parameterized by "theta" is defined and is quantized to theta= 0, 2pi. Its value is entirely determined by the TRIM parities. These results may be useful in the search for magnetic topological insulators with large theta. A classification of inversion symmetric insulators is also given for general dimensions. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground state wave-function.
In this paper we find the generating function for the number of vertices that have k elements in their subtree and use this generating function to calculate the probability that a vertex has a size k subtree. We also show how this same technique can be applied to calculate the probabilities for other trees and specifically apply it to 4 different types of trees.
Dimethylammonium magnesium formate, [(CH$_3$)$_2$NH$_2$][Mg(HCOO)$_3$] or DMAMgF, is a model to study high temperature hybrid perovskite-like dielectrics. This compound displays a phase transition from para to ferroelectric at about 260~K. Using multifrequency electron spin resonance in continuous wave and pulsed modes, we herein present the quantum dynamic of Mn$^{2+}$ ion probe in DMAMgF. In the high temperature paraelectric phase, we observe a large distribution of the zero field splitting that is attributed to high local disorder and further supported by DFT computations. In the low temperature ferroelectric phase, a single structure phase is detected and shown to contain two magnetic structures. The complex EPR signals were identifed by the means of Rabi oscillation method combined to crystal fields kernel density estimation.
Current simulations indicate that the first stars were formed predominantly in binary systems. The study of the contribution of the first accreting binary systems to the reionization and heating of the intergalactic medium requires the formulation of a concrete model for microquasars of Population III. We aim at constructing a complete model for microquasars where the donor star is of Population III. We consider that the mas-loss of the star is caused exclusively by the spill of matter through the Roche lobe towards the black hole. We calculate the spectral energy distribution of the radiation produced by the accretion disk, the radiation-pressure driven wind, and the relativistic particles in the jets, within the framework of a lepto-hadronic model. In addition, we estimate the impact on the reionization by the first microquasars. We determine that Population III microquasars are powerful sources of ultraviolet radiation produced by the winds of their super-critical disks, and generate a broadband non-thermal emission in jets. Our results indicate that microquasars in the early Universe could have been important for the reionization and heating of the intergalactic medium.
Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterize their quantum structure. In particular we calculate the Renyi entropy $S_2$, on model wavefunctions obtained by Gutzwiller projection of a Fermi sea. Although the wavefunctions are not sign positive, $S_2$ can be calculated on relatively large systems (>324 spins), using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi-sea state violates the boundary law, with $S_2$ enhanced by a logarithmic factor. This is an unusual result for a bosonic wave-function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.
We present a detailed, realistic analysis of the implementation of a proposal for a quantum phase gate based on atomic vibrational states, specializing it to neutral rubidium atoms on atom chips. We show how to create a double--well potential with static currents on the atom chips, using for all relevant parameters values that are achieved with present technology. The potential barrier between the two wells can be modified by varying the currents in order to realize a quantum phase gate for qubit states encoded in the atomic external degree of freedom. The gate performance is analyzed through numerical simulations; the operation time is ~10 ms with a performance fidelity above 99.9%. For storage of the state between the operations the qubit state can be transferred efficiently via Raman transitions to two hyperfine states, where its decoherence is strongly inhibited. In addition we discuss the limits imposed by the proximity of the surface to the gate fidelity.
We consider a new family of $\R^d$-valued L\'{e}vy processes that we call Lamperti stable. One of the advantages of this class is that the law of many related functionals can be computed explicitely (see for instance \cite{cc}, \cite{ckp}, \cite{kp} and \cite{pp}). This family of processes shares many properties with the tempered stable and the layered stable processes, defined in Rosi\'nski \cite{ro} and Houdr\'e and Kawai \cite{hok} respectively, for instance their short and long time behaviour. Additionally, in the real valued case we find a series representation which is used for sample paths simulation. In this work we find general properties of this class and we also provide many examples, some of which appear in recent literature.
The exceptional group $G_2$, when constructed over $Q_p$, may at the same time be considered as the group of automorphisms of an octonion algebra over $Q_p$, or alternatively it may be constructed as a Chevalley group from the root diagram of the appropriate Lie algebra, $g_2$. Each construction has its benefits and drawbacks, and the first part of this work focuses on drawing parallels between the two and describing certain group structures in terms of both. In particular, we explicitly identify the Chevalley generators of $G_2$ as automorphisms of octonions.   In the second part of this work we describe the standard (affine) apartment of the Bruhat-Tits building of $G_2$, constructing it from the coroot diagram of the Lie algebra $g_2$. Previous work of W.T. Gan and J.K. Yu (2003) describes this Bruhat-Tits building, alternatively, in terms of certain "maximinorante norms" and lattices in the octonion algebra. Using our work from Part One, we describe these norms and lattices in detail, which allows us to act on our lattices using explicit octonion automorphisms and draw a very complete picture of the standard apartment.
We report that the number of > 500 MeV protons (Ng) inferred from sustained gamma ray emission (SGRE) from the Sun is significantly correlated with that of protons propagating into space (NSEP) as solar energetic particles (SEPs). Under the shock paradigm for SGRE, shocks driven by coronal mass ejections (CMEs) accelerate high-energy protons sending them toward the Sun to produce SGRE by interacting with the atmospheric particles. Particles also escape into the space away from the Sun to be detected as SEP events. Therefore, the significant NSEP vs. Ng correlation (correlation coefficient 0.77) is consistent with the common shock origin for the two proton populations. Furthermore, the underlying CMEs have properties akin to those involved in ground level enhancement (GLE) events indicating the presence of high-energy (up to GeV) particles required for SGRE. We show that the observed gamma-ray flux is an underestimate in limb events (central meridian distance > 60 degrees) because SGRE sources are partially occulted when the emission is spatially extended. With the assumption that the SEP spectrum at the shock nose is hard and that the 100 MeV particles are accelerated throughout the shock surface (half width in the range 60 to 120 degrees) we find that the latitudinal widths of SEP distributions are energy dependent with the smallest width at the highest energies. Not using the energy-dependent width results in an underestimate of NSEP in SGRE events occurring at relatively higher latitudes. Taking these two effects into account removes the apparent lack of NSEP - Ng correlation reported in previous studies.
In this paper we study the possibility of probing the low-energy part of the spectrum of non-thermal electrons in galaxy clusters by detecting their non-thermal bremsstrahlung (NTB) emission in the soft gamma ray band, using instruments like e-ASTROGAM. Using the Coma cluster as a reference case, we find that, for very low values of the minimum energy of the electrons, in principle the NTB is detectable, but this situation is possible only for conditions that can be maintained only for a short time compared to the cluster lifetime. The possibility of constraining the low energy spectrum of non-thermal electrons through NTB is therefore hard to achieve in next years.
We explain in this letter how using a recent Modularity Lifting Theorem proved by Lue Pan the proofs of Serre's Modularity Conjecture over $\mathbb{Q}$ given by Khare-Wintenberger and the author can be greatly simplified. The main difference with the previous proofs is that neither the process of "weight reduction" developed by Khare in his proof of the level 1 case nor the alternative method of "weight reduction via Galois conjugation" developed by the author are required: weight reduction can now be obtained just with two applications of Pan's result, together with a Lemma that guarantees that the residual representations in the last two steps are not in the bad-dihedral case.
We report on the single-molecule electronic and thermoelectric properties of strategically chosen anthracene-based molecules with anchor groups capable of binding to noble metal substrates, such as gold and platinum. Specifically, we study the effect of different anchor groups, as well as quantum interference, on the electric conductance and the thermopower of gold/single-molecule/gold junctions and generally find good agreement between theory and experiment. All molecular junctions display transport characteristics consistent with coherent transport and a Fermi alignment approximately in the middle of the HOMO/LUMO gap. Single-molecule results are in agreement with previously reported thin-film data, further supporting the notion that molecular design considerations may be translated from the single- to the many-molecule devices. For combinations of anchor groups where one binds significantly more strongly to the electrodes than the other, the stronger anchor group appears to dominate the thermoelectric behaviour of the molecular junction. For other combinations, the choice of electrode material can determine the sign and magnitude of the thermopower. This finding has important implications for the design of thermoelectric generator devices, where both n- and p-type conductor are required for thermoelectric current generation.
Optical and X-ray observations of the quadruply imaged quasar 1RXS J1131-1231 show flux ratio anomalies among the images factors of ~2 in the optical and \~3-9 in X-rays. Temporal variability of the quasar seems an unlikely explanation for the discrepancies between the X-ray and optical flux ratio anomalies. The negative parity of the most affected image and the decreasing trend of the anomalies with wavelength suggest microlensing as a possible explanation; this would imply that the source of optical radiation in RXS J1131 is ~10^4 R_g in size for a black hole mass of ~10^8 M_sun. We also present evidence for different X-ray spectral hardness ratios among the four images.
The temperature-induced shift of the Raman G line in epitaxial graphene on SiC and Ni surfaces, as well as in graphene supported on SiO2, is investigated with Raman spectroscopy. The thermal shift rate of epitaxial graphene on 6H-SiC(0001) is found to be about three times that of freestanding graphene. This result is explained quantitatively as a consequence of pinning by the substrate. In contrast, graphene grown on polycrystalline Ni films is shown to be unpinned, i.e., to behave elastically as freestanding, despite the relatively strong interaction with the metal substrate. Moreover, it is shown that the transfer of exfoliated graphene layers onto a supporting substrate can result in pinned or unpinned layers, depending on the transfer protocol.