ShantanuT01/DACTYL-Pretraining huggingface dataset:
In order to investigate the interaction between single vacancies in a graphene sheet, we have used spin-polarized density functional theory (DFT). Two distinct configurations were considered, either with the two vacancies located in the same sublattice or in different sublattices, and the effect of changing the separation between the vacancies was also studied. Our results show that the ground state of the system is indeed magnetic, but the presence of the vacancies in the same sublattice or in different sublattices and the possible topological configurations can lead to different contributions from the $\pi$ and $\sigma$ orbitals to magnetism. On the other hand, our findings reveal that the net magnetic moment of the system with the two vacancies in the same sublattice move towards the value of the magnetic moment per isolated vacancy with the increase of the distance between the vacancies, which is ascribed to the different contributions due to $\pi$ electrons. Moreover, it is also found that the local magnetic moments for vacancies in the same sublattice are in parallel configuration, while they have different orientations when the vacancies are created in different sublattices. So, our findings have clearly evidenced how difficult it would be to observe experimentally the emergence of magnetic order in graphene-based systems containing randomly created atomic vacancies, since the energy difference between cases of antiferromagnetic and ferromagnetic order decreases quickly with the increase in the distance separating each vacancy pair.
We calculate the chiral anomaly in the neighbourhood of the fixed point space M_h which is constructed by the group action of a discrete symmetry h on a compact manifold M. The Feynman diagrams approach for the corresponding supersymmetric quantum mechanical system with twisted boundary conditions is used. The result we derive in this way agrees with the generalization of the ordinary index theorem (the G-index theorem) on the spin complex.
One of the methods for deriving disk masses relies on direct observations of the gas, whose bulk mass is in the outer cold ($T\lesssim30$K) regions. This zone can be well traced by rotational lines of less abundant CO isotopologues, that probe the gas down to the midplane. The total CO gas mass is then obtained with the isotopologue ratios taken to be constant at the elemental isotope values found in the local ISM. This approach is however imprecise, because isotope selective processes are ignored. The aim of this work is an isotopologue selective treatment of CO isotopologues, in order to obtain a more accurate determination of disk masses. The isotope-selective photodissociation, the main process controlling the abundances of CO isotopologues in the CO-emissive layer, is properly treated for the first time in a full disk model (DALI, Bruderer et al. 2012; Bruderer 2013). The chemistry, thermal balance, line and continuum radiative transfer are all considered together with a chemical network that treats $^{13}$CO, C$^{18}$O, C$^{17}$O, isotopes of all included atoms, and molecules, as independent species. Isotope selective processes lead to regions in the disk where the isotopologues abundance ratios are considerably different from the elemental ratio. The results of this work show that considering CO isotopologue ratios as constants can lead to an underestimate of disk masses by up to almost two orders of magnitude if grains have grown to larger sizes. This may explain observed discrepancies in mass determinations from different tracers. The dependence of the various isotopologues emission on stellar and disk parameters is investigated. Including CO isotope selective processes is crucial to determine the gas mass of the disk accurately (through ALMA observations) and thus to provide the amount of gas which may eventually form planets or change the dynamics of forming planetary systems.
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic oscillator by the replacement of {\omega} to i{\omega}, this leads to unbounded eigenvectors. This explicitly demonstrates that there are some unclear points involved in redefining the variables in the harmonic oscillator inversion. To remedy this situation, we introduce a scaling operator (Dyson transformation) by connecting the inverted harmonic oscillator to an anti-PT-symmetric harmonic oscillator, we obtain the standard quasi-Hermiticity relation which would ensure the time invariance of the eigenfunction's norm. We give a complete description for the eigenproblem. We show that the wavefunctions for this system are normalized in the sense of the pseudo-scalar product. A Gaussian wave packet of the inverted oscillator is investigated by using the ladder operators method. This wave packet is found to be associated with the generalized coherent state that can be crucially utilized for investigating the mean values of the space and momentum operators. We find that these mean values reproduce the classical motion.
In a previous contribution, Phys. Rev. Lett 107, 230601 (2011), we have proposed a method to treat first order phase transitions at low temperatures. It describes arbitrary order parameter through an analytical expression $W$, which depends on few coefficients. Such coefficients can be calculated by simulating relatively small systems, hence with a low computational cost. The method determines the precise location of coexistence lines and arbitrary response functions (from proper derivatives of $W$). Here we exploit and extend the approach, discussing a more general condition for its validity. We show that in fact it works beyond the low $T$ limit, provided the first order phase transition is strong enough. Thus, $W$ can be used even to study athermal problems, as exemplified for a hard-core lattice gas. We furthermore demonstrate that other relevant thermodynamic quantities, as entropy and energy, are also obtained from $W$. To clarify some important mathematical features of the method, we analyze in details an analytically solvable problem. Finally, we discuss different representative models, namely, Potts, Bell-Lavis, and associating gas-lattice, illustrating the procedure broad applicability.
Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension $c$ is at most ${{c+1} \choose {2}}$ and the equality is attained if and only if the variety is of minimal degree. Also G. Fano's generalization of Castelnuovo Lemma implies that the next case occurs if and only if the variety is a del Pezzo variety. Recently, these results are extended to the next case. This paper is intended to complete the classification of varieties satisfying at least ${{c+1} \choose {2}}-3$ linearly independent quadratic equations. Also we investigate the zero set of those quadratic equations and apply our results to projective varieties of degree $\geq 2c+1$.
We study various aspects of the scattering of generalized compact oscillons in the signum-Gordon model in (1+1) dimensions. Using covariance of the model we construct traveling oscillons and study their interactions and the dependence of these interactions on the oscillons initial velocities and their relative phases. The scattering processes transform the two incoming oscillons into two outgoing ones and lead to the generation of extra oscillons which appear in the form of jet-like cascades. Such cascades vanish for some values of free parameters and the scattering processes, even though our model is non-integrable, resemble typical scattering processes normally observed for integrable or quase-integrable models. Occasionally, in the intermediate stage of the process, we have seen the emission of shock waves and we have noticed that, in general, outgoing oscillons have been more involved in their emission than the initial ones i.e. they have a border in form of curved world-lines. The results of our studies of the scattering of oscillons suggest that the radiation of the signum-Gordon model has a fractal-like nature.
Single image dehazing, which aims to recover the clear image solely from an input hazy or foggy image, is a challenging ill-posed problem. Analysing existing approaches, the common key step is to estimate the haze density of each pixel. To this end, various approaches often heuristically designed haze-relevant features. Several recent works also automatically learn the features via directly exploiting Convolutional Neural Networks (CNN). However, it may be insufficient to fully capture the intrinsic attributes of hazy images. To obtain effective features for single image dehazing, this paper presents a novel Ranking Convolutional Neural Network (Ranking-CNN). In Ranking-CNN, a novel ranking layer is proposed to extend the structure of CNN so that the statistical and structural attributes of hazy images can be simultaneously captured. By training Ranking-CNN in a well-designed manner, powerful haze-relevant features can be automatically learned from massive hazy image patches. Based on these features, haze can be effectively removed by using a haze density prediction model trained through the random forest regression. Experimental results show that our approach outperforms several previous dehazing approaches on synthetic and real-world benchmark images. Comprehensive analyses are also conducted to interpret the proposed Ranking-CNN from both the theoretical and experimental aspects.
The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims at finding hot subdwarf stars with massive compact companions like massive white dwarfs (M>1.0 M$_\odot$), neutron stars, or stellar-mass black holes. We present orbital and atmospheric parameters and put constraints on the nature of the companions of 12 close hot subdwarf B star (sdB) binaries found in the course of the MUCHFUSS project. The systems show periods between 0.14 and 7.4 days. Three systems most likely have white dwarf companions. SDSS J083006.17+475150.3 is likely to be a rare example of a low-mass helium-core white dwarf. SDSS J095101.28+034757.0 shows an excess in the infrared that probably originates from a third companion in a wide orbit. SDSS J113241.58-063652.8 is the first helium deficient sdO star with a confirmed close companion. This study brings to 142 the number of sdB binaries with orbital periods of less than 30 days and with measured mass functions. We present an analysis of the minimum companion mass distribution and show that it is bimodal. One peak around 0.1 M$_\odot$ corresponds to the low-mass main sequence and substellar companions. The other peak around 0.4 M$_\odot$ corresponds to the white dwarf companions. The derived masses for the white dwarf companions are significantly lower than the average mass for single carbon-oxygen white dwarfs. In a T$_{\rm eff}$-log(g) diagram of sdB+dM companions, we find signs that the sdB components are more massive than the rest of the sample. The full sample was compared to the known population of extremely low-mass white dwarf binaries as well as short-period white dwarfs with main sequence companions. Both samples show a significantly different companion mass distribution. We calculate merger timescales and timescales when the companion will fill its Roche Lobe and the system evolves into a cataclysmic variable.
Ab inito calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the nuclear equation-of-state (EOS) far away from the saturation point of nuclear matter. I compare predictions from microscopic and phenomenological approaches. Constraints on the EOS derived from heavy ion reactions, in particular from subthreshold kaon production, as well as constraints from neutron stars are discussed.
We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically that conformal invariance and signatures of critical percolation appear in the stationary KPZ state. In terms of the two-component Coulomb gas description of the Edwards-Wilkinson stationary state, our finding is understood as the invariance of one component under the effect of the non-linear KPZ term. On the other hand, we show a breaking of conformal invariance when the level lines of the other component are considered.
We compare the results of the SuSAv2 model including meson-exchange currents (MEC) with the recent measurement of the quasielastic-like double differential antineutrino cross section on hydrocarbon (CH) performed by the MINERvA Collaboration. The relativistic nature of the model makes it suitable to describe these data, which correspond to a mean beam energy of 3.5 GeV. The standard SuSAv2 model predictions agree well with the data without needing any additional or tuned parameter. The role of longitudinal MEC is non-negligible and improves the agreement with the data. We also consider the impact of different treatments of the $\Delta$-resonance propagator in the two-body currents on the data comparison.
We consider the problem of determining whether a given prime p is a congruent number. We present an easily computed criterion that allows us to conclude that certain primes for which congruency was previously undecided, are in fact not congruent. As a result, we get additional information on the possible sizes of Tate-Shafarevich groups of the associated elliptic curves.   We also present a related criterion for primes p such that 16 divides the class number of the imaginary quadratic field Q(sqrt(-p)). Both results are based on descent methods.   While we cannot show for either criterion individually that there are infinitely many primes that satisfy it nor that there are infinitely many that do not, we do exploit a slight difference between the two to conclude that at least one of the criteria is satisfied by infinitely many primes.
By modelling H$^0$ column densities in eclipsing S-type symbiotic stars EG And and SY Mus, we derived the wind velocity profile and the corresponding mass-loss rate from their giants. Our analysis revealed a strong enhancement of the wind at the orbital plane.
We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map - a cantor set given by a region of exactly zero reflectivity - prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for step like functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case.
Upcoming Weak Lensing (WL) surveys can be used to constrain Dark Energy (DE) properties, namely if tomographic techniques are used to improve their sensitivity. In this work, we use a Fisher matrix technique to compare the power of CMB anisotropy and polarization data with tomographic WL data, in constraining DE parameters. Adding WL data to available CMB data improves the detection of all cosmological parameters, but the impact is really strong when DE--DM coupling is considered, as WL tomography can then succeed to reduce the errors on some parameters by factors >10.
We measure the gas-phase oxygen abundances of ~3000 star-forming galaxies at z=0.05-0.75 using optical spectrophotometry from the AGN and Galaxy Evolution Survey (AGES), a spectroscopic survey of I_AB<20.45 galaxies over 7.9 deg^2 in the NOAO Deep Wide Field Survey (NDWFS) Bootes field. We use state-of-the-art techniques to measure the nebular emission lines and stellar masses, and explore and quantify several potential sources of systematic error, including the choice of metallicity diagnostic, aperture bias, and contamination from unidentified active galactic nuclei (AGN). Combining volume-limited AGES samples in six independent redshift bins and ~75,000 star-forming galaxies with r_AB<17.6 at z=0.05-0.2 selected from the Sloan Digital Sky Survey (SDSS) that we analyze in the identical manner, we measure the evolution of the stellar mass-metallicity (M-Z) between z=0.05 and z=0.75. We find that at fixed stellar mass galaxies at z~0.7 have just 30%-60% the metal content of galaxies at the present epoch, where the uncertainty is dominated by the strong-line method used to measure the metallicity. Moreover, we find no statistically significant evidence that the M-Z relation evolves in a mass-dependent way for M=10^9.8-10^11 Msun star-forming galaxies. Thus, for this range of redshifts and stellar masses the M-Z relation simply shifts toward lower metallicity with increasing redshift without changing its shape.
We report $^{153}$Eu and $^{69,71}$Ga NMR under a zero magnetic field on the antiferromagnetic state of EuGa$_{4}$ with $T_{\rm{N}}\approx 16$ K. We have successfully observed a $^{153}$Eu zero-field NMR signal with well-resolved nuclear quadrupole splitting in the antiferromagnetic state of EuGa$_{4}$. $^{69,71}$Ga zero-field NMR spectra were also observed below $T_{\rm{N}}$. The internal field and nuclear quadrupole frequency are estimated from a simulation of the spectra by the exact diagonalization of the nuclear spin Hamiltonian matrix. The asymmetrically split zero-field NMR spectra were explained by considering a configuration of the magnetic moments of Eu$^{2+}$ lying in the basal $ab$-plane. The temperature dependence of the internal field, which is proportional to the sublattice magnetization, can be explained by the Brillouin function with $J=S=7/2$
Let f be a G-function (in the sense of Siegel), and x be an algebraic number; assume that the value f(x) is a real number. As a special case of a more general result, we show that f(x) can be written as g(1), where g is a G-function with rational coefficients and arbitrarily large radius of convergence. As an application, we prove that quotients of such values are exactly the numbers which can be written as limits of sequences a(n)/b(n), where the generating series of both sequences are G-functions with rational coefficients. This result provides a general setting for irrationality proofs in the style of Apery for zeta(3), and gives answers to questions asked by T. Rivoal in [Approximations rationnelles des valeurs de la fonction Gamma aux rationnels : le cas des puissances, Acta Arith. 142 (2010), no. 4, 347-365].
We study the simplified Hubbard (SH) model in the presence of a transverse field in the infinite dimension limit. The relevant one-particle Green's functions of the model are obtained by means a perturbative treatment of the hopping and of the transverse field around the atomic limit. We consider an analytical solution for the impurity problem. It is shown that this solution is very accurate in describing the spectral properties of the heavy-particles of the SH for intermediate and strong values of the on-site Coulomb interaction $U$. We find that for large values of $U$ an insulator-metal transition takes place as a function of the transverse field. We analyze the metallic phase through the behavior of the density of states and of the optical conductivity and static resistivity. Our results for the latter quantity agree with what is observed in experiments on $Bi_2Sr_2CuO_y$.
In analogy with the semi-Fibonacci partitions studied recently by Andrews, we define semi-Pell compositions and semi-$m$-Pell compositions. We find that these are in bijection with certain weakly unimodal $m$-ary compositions. We give generating functions, bijective proofs, and a number of unexpected congruences for these objects.
We report a discovery of a double radio relic in the cluster merger ZwCl1447.2+2619 ($z=0.376$) with uGMRT observations at $420\rm~MHz$ and $700\rm~MHz$. The linear sizes of the northern and southern relics are $\sim0.3~$Mpc and $\sim1.2~$Mpc, respectively, which is consistent with the theoretical expectation that a larger relic is produced in the less massive subcluster side. However, ZwCl1447.2+2619 is unlike other known double radio relic systems, where the larger relics are much more luminous by several factors. In this merger the higher surface brightness of the smaller northern relic makes its total radio luminosity comparable to that of the much larger southern relic. The surface brightness ratio $\sim0.1$ between the two radio relics differs significantly from the relation observed in other double radio relic systems. From our radio spectral analysis, we find that both relics signify similar weak shocks with Mach numbers of $2.9\pm0.8$ and $2.0\pm0.7$ for the northern and southern relics, respectively. Moreover, the northern relic is connected to a discrete radio source with an optical counterpart, which indicates the possible presence of cosmic ray injection and re-acceleration. Therefore, we propose that this atypical surface brightness ratio can be explained with the particle acceleration efficiency precipitously dropping in the weak shock regime and/or with re-acceleration of fossil cosmic rays. Our multi-wavelength analysis and numerical simulation suggest that ZwCl1447.2+2619 is a post-merger, which has experienced a near head-on collision $\sim0.7\rm~Gyr$ ago.
We have searched the entire ROSAT archive for useful observations to study X-ray emission from Galactic planetary nebulae (PNs). The search yields a sample of 63 PNs, which we call the ROSAT PN sample. About 20-25% of this sample show X-ray emission; these include 13 definite detections and three possible detections (at a 2-sigma level). All X-ray sources in these PNs are concentrated near the central stars. Only A 30, BD+30 3639, and NGC 6543 are marginally resolved by the ROSAT instruments. Three types of X-ray spectra are seen in PNs. Type 1 consists of only soft X-ray emission (<0.5 keV), peaks at 0.1-0.2 keV, and can be fitted by blackbody models at temperatures 1-2 10^5 K. Type 2 consists of harder X-ray emission, peaks at >0.5 keV, and can be fitted by thin plasma emission models at temperatures of a few 10^6 K. Type 3 is a composite of a bright Type 1 component and a fainter Type 2 component. Unresolved soft sources with Type 1 spectra or the soft component of Type 3 spectra are most likely photospheric emission from the hot central stars. Absorption cross sections are large for these soft-energy photons; therefore, only large, tenuous, evolved PNs with hot central stars and small absorption column densities have been detected. The origin of hard X-ray emission from PNs is uncertain. PNs with Type 2 spectra are small, dense, young nebulae with relatively cool (<<10^5 K) central stars, while PNs with Type 3 X-ray spectra are large, tenuous, evolved nebulae with hot central stars. The hard X-ray luminosities are also different between these two types of PNs, indicating perhaps different origins of their hard X-ray emission. Future Chandra and XMM observations with high spatial and spectral resolution will help to understand the origin of hard X-ray emission from PNs.