ShantanuT01/DACTYL-Pretraining huggingface dataset:
The nature of the "forbidden" local- and long-range polar order in nominally nonpolar paraelectric phases of ferroelectric materials has been an open question since the discovery of ferroelectricity in oxide perovskites (ABO3). A currently considered model suggests locally correlated displacements of B-site atoms along a subset of <111> cubic directions. Such offsite displacements have been confirmed experimentally, however, being essentially dynamic in nature they cannot account for the static nature of the symmetry-forbidden polarization implied by the macroscopic experiments. Here, in an atomically resolved study by aberration corrected scanning transmission electron microscopy (STEM) complemented by Raman spectroscopy, we reveal, directly visualize and quantitatively describe static, 2-4 nm large polar nanoclusters in the nominally nonpolar cubic phases of (Ba,Sr)TiO3 and BaTiO3. These results have implications on understanding of the atomic-scale structure of disordered materials, the origin of precursor states in ferroelectrics, and may help answering ambiguities on the dynamic-versus-static nature of nano-sized clusters.
Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR.   Earlier we have proposed some minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like 4-simplices or, say, cuboids into which ${\rm I \hspace{-3pt} R}^4$ can be decomposed.   Now we study some representation of this (discrete) theory, an analogue of the Cartan-Weyl connection-type form of the Hilbert-Einstein action in the usual continuum GR.
We extend the Altmann-Hausen presentation of normal affine algebraic C-varieties endowed with effective torus actions to the real setting. In particular, we focus on actions of quasi-split real tori, in which case we obtain a simpler presentation.
We present the spectroscopic characterization of the unusual high-amplitude very low mass pre-main-sequence periodic variable CHS7797. This study is based on optical medium-resolution (R=2200) spectroscopy in the 6450-8600 A range, carried out with GMOS-GEMINI-S in March 2011. Observations of CHS7797 have been carried out at two distinct phases of the 17.8d period, namely at maximum and four days before maximum. Four different spectral indices were used for the spectral classification at these two phases, all of them well-suited for spectral classification of young and obscured late M dwarfs. In addition, the gravity-sensitive NaI (8183/8195 A) and KI (7665/7699 A) doublet lines were used to confirm the young age of CHS7797. From the spectrum obtained at maximum light we derived a spectral type (SpT) of M6.05, while for the spectrum taken four days before maximum the derived SpT is M5.75. The derived SpTs confirm that CHS7797 has a mass in the stellar-substellar boundary mass range. In addition, the small differences in the derived SpTs at the two observed phases may provide indirect hints that CHS7797 is a binary system of similar mass components surrounded by a tilted circumbinary disk, a system similar to KH15D.
We investigate the role of correlations in the tetragonal and collapsed tetragonal phases of CaFe2As2 by performing charge self-consistent DFT+DMFT (density functional theory combined with dynamical mean-field theory) calculations. While the topology of the Fermi surface is basically unaffected by the inclusion of correlation effects, we find important orbital-dependent mass renormalizations which show good agreement with recent angle-resolved photoemission (ARPES) experiments. Moreover, we observe a markedly different behavior of these quantities between the low-pressure tetragonal and the high-pressure collapsed tetragonal phase. We attribute these effects to the increased hybridization between the iron- and arsenic orbitals as one enters the collapsed tetragonal phase.
A simple model explaining the experimental data on QDs luminescence blinking is suggested. The model does not assume the presence of the long-lived electron traps. The bleaching of the QD luminescence is a result of the Auger assisted radiationless relaxation of the excitation through the deep surface states. Possible ways of the experimental verification of the model are discussed.
The GeV light curve of a pulsar is an important probe to detect acceleration regions in its magnetosphere. Motivated by the recent reports on the observations of pulsars by {\it Fermi} Large Area Telescope (LAT), we restudy the two-pole caustic model and revise it to investigate the properties of the light curves in the GeV band. In the revised model, although acceleration gaps can extend from the star surface to the light cylinder along near the last open field lines, the extension of the gaps along the azimuthal direction is limited because of photon-photon pair production process. In such gaps, high-energy photons are emitted uniformly and tangentially to the field lines but cannot be efficiently produced along these field lines where the distances to the null charge surface are larger than $\sim0.9$ times of the distance of the light cylinder, and the effective azimuth extension of the gaps is about $230^\circ$. The model is applied to the four pulsars Vela, PSR J1028-5819, PSR J0205+6449, and PSR J2021+3651 whose light curves obtained with {\it Fermi} have been recently released. The model is successful in reproducing the general feature of the light curves for the four pulsars, and the radial distances of the radio pulse for the four pulsars are estimated.
A study of the luminous dipping LMXB X1624-490 was made using BeppoSAX. From modelling the MECS radial profile in several energy bands, the optical depth to dust scattering at 1 keV was found to be 2.4+/-0.4. The non-dip and dip spectra of X1624-490 in the energy band 1-100 keV are well-described by emission consisting of a point-like blackbody from the neutron star plus extended Comptonized emission from an ADC. The blackbody temperature was 1.31+/-0.07 keV and the Comptonized emission had photon power law index 2.0+0.5/-0.7 and cut-off energy ~12 keV. Good fits to the dip spectra were obtained by allowing the Comptonized emission to be progressively covered by an extended absorber while the blackbody was rapidly absorbed and a constant halo component accounted for dust scattering into the line-of-sight. From the dip ingress time, a diameter of the extended Comptonized emission region of 5.3+/-0.8x10^10 cm was derived, consistent with a hot, X-ray emitting corona extending to ~50% of the accretion disk radius. The source luminosity for a distance of 15 kpc is 7.3x10^37 erg/s, an appreciable fraction of the Eddington limit making X1624-490 the most luminous dipping LMXB. The half-height of the blackbody emitting region on the neutron star of 6.8+/-1.8 km agrees well with the half-height of the radiatively supported inner accretion disk of 6.3+/-2.9 km. Together with similar agreement recently obtained for 13 other LMXB in an ASCA survey (Church & Balucinska-Church 2000), this strongly supports the identification of the neutron star as the origin of the blackbody emission in LMXB and suggests a mechanism in which the disk height is the main factor determining the level of blackbody emission. Finally, from RXTE ASM data, we derive an improved orbital period of 20.87+/-0.01 hr.
The recent observational, theoretical, and numerical progress made in understanding stellar magnetism is discussed. Particularly, this review will cover the physical processes thought to be at the origin of these magnetic fields and their variability, namely dynamo action arising from the interaction between convection, rotation, radiation and magnetic fields. Some care will be taken to cover recent analytical advances regarding the dynamics and magnetism of radiative interiors, including some thoughts on the role of a tachocline. Moreover, recent and rapidly advancing numerical modeling of convective dynamos will be discussed, looking at rapidly rotating convective systems, grand minima and scaling laws for magnetic field strength. These topics are linked to observations or their observational implications.
More than forty years ago, axion was postulated as an elementary particle with a low mass and weak interaction in particle physics to solve the strong $\mathcal{CP}$ (charge conjugation and parity) puzzle. Axions are also considered as a possible component of dark matter of the universe. However, the existence of axions in nature has not been confirmed. Interestingly, axions arise as pseudoscalar fields derived from the Chern-Simons theory in condensed matter physics. In antiferromagnetic insulators, the axion field can become dynamical induced by spin-wave excitations and exhibits rich exotic phenomena, such as, the chiral magnetic effect, axionic polariton and so on. However, the study of the dynamical axion field is rare due to the lack of real materials. Recently, MnBi$_2$Te$_4$ was discovered to be an antiferromagnetic topological insulator with a quantized axion field protected by the inversion symmetry $\mathcal{P}$ and the magnetic-crystalline symmetry $\mathcal{S}$. Here, we studied MnBi$_2$Te$_4$ films in which both the $\mathcal{P}$ and $\mathcal{S}$ symmetries are spontaneously broken and found that the dynamical axion field and largely tunable dynamical magnetoelectric effects can be realized through tuning the thickness of MnBi$_2$Te$_4$ films, the temperature and the element substitution. Our results open a broad avenue to study axion dynamics in antiferromagnetic topological insulator MnBi$_2$Te$_4$ and related materials, and also is hopeful to promote the research of dark matter.
Let $\{p_n\}_{n\ge 1}$ be the sequence of primes and $\vartheta(x) = \sum_{p \leq x} \log p$, where $p$ runs over the primes not exceeding $x$, be the Chebyshev $\vartheta$-function. In this note we derive lower and upper bounds for $\vartheta(p_n)/n$ by comparing it with $\log p_{n+1}$ and deduce that $\vartheta(p_n)/n=\log p_{n+1}\left(1-\frac{1}{\log n}+\frac{\log\log n}{\log^2 n}\left(1+o(1)\right)\right).$
Recently, self-attention operators have shown superior performance as a stand-alone building block for vision models. However, existing self-attention models are often hand-designed, modified from CNNs, and obtained by stacking one operator only. A wider range of architecture space which combines different self-attention operators and convolution is rarely explored. In this paper, we explore this novel architecture space with weight-sharing Neural Architecture Search (NAS) algorithms. The result architecture is named TrioNet for combining convolution, local self-attention, and global (axial) self-attention operators. In order to effectively search in this huge architecture space, we propose Hierarchical Sampling for better training of the supernet. In addition, we propose a novel weight-sharing strategy, Multi-head Sharing, specifically for multi-head self-attention operators. Our searched TrioNet that combines self-attention and convolution outperforms all stand-alone models with fewer FLOPs on ImageNet classification where self-attention performs better than convolution. Furthermore, on various small datasets, we observe inferior performance for self-attention models, but our TrioNet is still able to match the best operator, convolution in this case. Our code is available at https://github.com/phj128/TrioNet.
We consider a singular limit problem for the Navier-Stokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the ``horizontal'' variables containing an extra term that accounts for compressibility in the original system.
Von Renesse and the author (Ann. Prob. '09) developed a second order calculus on the Wasserstein space P([0,1]) of probability measures on the unit interval. The basic objects of interest had been Dirichlet form, semigroup and continuous Markov process, called Wasserstein diffusion. The goal of this paper is to derive approximations of these objects on the infinite dimensional space P([0, 1]) in terms of appropriate objects on finite dimensional spaces. In particular, we will approximate the Wasserstein diffusion in terms of interacting systems of Brownian motions.
We investigate the spectral evolution in different metal phthalocyanine molecules on NbSe$_2$ surface using scanning tunnelling microscopy (STM) as a function of the coupling with the substrate. For manganese phthalocyanine (MnPc), we demonstrate a smooth spectral crossover from Yu-Shiba-Rusinov (YSR) bound states to spin-flip excitations. This has not been observed previously and it is in contrast to simple theoretical expectations. We corroborate the experimental findings using numerical renormalization group calculations. Our results provide fundamental new insight on the behavior of atomic scale magnetic/SC hybrid systems, which is important for e.g. engineered topological superconductors and spin logic devices.
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
We consider dynamical percolation on the complete graph $K_n$, where each edge refreshes its state at rate $\mu \ll 1/n$, and is then declared open with probability $p = \lambda/n$ where $\lambda > 1$. We study a random walk on this dynamical environment which jumps at rate $1/n$ along every open edge. We show that the mixing time of the full system exhibits cutoff at $\log n/\mu$. We do this by showing that the random walk component mixes faster than the environment process; along the way, we control the time it takes for the walk to become isolated.
We fix $d \geq 2$ and denote $\mathcal S$ the semi-group of $d \times d$ matrices with non negative entries. We consider a sequence $(A_n, B_n)_{n \geq 1} $ of i. i. d. random variables with values in $\mathcal S\times \mathbb R_+^d$ and study the asymptotic behavior of the Markov chain $(X_n)_{n \geq 0}$ on $ \mathbb R_+^d$ defined by:   \[   \forall n \geq 0, \qquad X_{n+1}=A_{n+1}X_n+B_{n+1},   \] where $X_0$ is a fixed random variable. We assume that the Lyapunov exponent of the matrices $A_n$ equals $0$ and prove, under quite general hypotheses, that there exists a unique (infinite) Radon measure $\lambda$ on $(\mathbb R^+)^d$ which is invariant for the chain $(X_n)_{n \geq 0}$. The existence of $\lambda$ relies on a recent work by T.D.C. Pham about fluctuations of the norm of product of random matrices . Its unicity is a consequence of a general property, called "local contractivity", highlighted about 20 years ago by M. Babillot, Ph. Bougerol et L. Elie in the case of the one dimensional affine recursion .
Recent detections of complex organic molecules in dark clouds have rekindled interest in the astrochemical modeling of these environments. Because of its relative closeness and rich molecular complexity, TMC-1 has been extensively observed to study the chemical processes taking place in dark clouds. We use local thermodynamical equilibrium radiative transfer modeling coupled with a Bayesian statistical method which takes into account outliers to analyze the data from the Nobeyama spectral survey of TMC-1 between 8 and 50 GHz. We compute the abundance relative to molecular hydrogen of 57 molecules, including 19 isotopologues in TMC-1 along with their associated uncertainty. The new results are in general agreement with previous abundance determination from Ohishi & Kaifu and the values reported in the review from Agundez & Wakelam. However, in some cases, large opacity and low signal to noise effects allow only upper or lower limits to be derived, respectively.
In this paper, we proved that for an affine variety V in A^n; O_V is a sheaf of regular functions and the ringed space pair (V;O_V ) is a locally ringed space.
We consider critical percolation on Galton-Watson trees and prove quenched analogues of classical theorems of critical branching processes. We show that the probability critical percolation reaches depth $n$ is asymptotic to a tree-dependent constant times $n^{-1}$. Similarly, conditioned on critical percolation reaching depth $n$, the number of vertices at depth $n$ in the critical percolation cluster almost surely converges in distribution to an exponential random variable with mean depending only on the offspring distribution. The incipient infinite cluster (IIC) is constructed for a.e. Galton-Watson tree and we prove a limit law for the number of vertices in the IIC at depth $n$, again depending only on the offspring distribution. Provided the offspring distribution used to generate these Galton-Watson trees has all finite moments, each of these results holds almost-surely.
We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential.
Intriguing work on observations of 4.83 GHz formaldehyde (H2CO) absorptions and 4.87 GHz H110a radio recombination lines (RRLs) towards 6.7 GHz methanol (CH3OH) maser sources is presented. Methanol masers provide ideal sites to probe the earliest stages of massive star formation, while 4.8 GHz formaldehyde absorptions are accurate probes of physical conditions in dense $(10^{3} - 10^{5} cm^{-3})$ and low temperature molecular clouds towards massive star forming regions. The work is aimed at studying feature similarities between the formaldehyde absorptions and the methanol masers so as to expand knowledge of events and physical conditions in massive star forming regions. A total of 176 methanol maser sources were observed for formaldehyde absorptions, and formaldehyde absorptions were detected 138 of them. 53 of the formaldehyde absorptions were newly detected. We noted a poor correlation between the methanol and formaldehyde intensities, an indication that the signals (though arise from about the same regions) are enhanced by different mechanisms. Our results show higher detection rates of the formaldehyde lines for sources with stronger methanol signals. The strongest formaldehyde absorptions were associated with IRAS sources and IRDCs that have developed HII regions, and that do not have EGOs.
Interfacial adhesion between graphene and a SiO2 substrate is studied by density functional theory (DFT) with dispersion corrections. The results demonstrate the van der Waals (vdW) interaction as the predominate mechanism for the graphene/SiO2 interface. It is found that the interaction strength is strongly influenced by changes of the SiO2 surface structures due to surface reactions with water. The adhesion energy is reduced when the reconstructed SiO2 surface is hydroxylated, and further reduced when covered by a monolayer of adsorbed water molecules. Thus, the effect of humidity may help explain the wide variation of adhesion energies measured in recent experiments between graphene and SiO2. Moreover, it is noted that vdW forces are required to accurately model the graphene/SiO2 interface with DFT and that the adhesion energy is underestimated by empirical force fields commonly used in atomistic simulations.
In this short article, we state a Hopf type lemma for fractional equations and the outline of its proof. We believe that it will become a powerful tool in applying the method of moving planes on fractional equations to obtain qualitative properties of solutions.
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown to involve a squared Dirac operator for the free case, whose essential self-adjointness is proved by using the Weyl limit point-limit circle criterion, and a `perturbation' resulting from the potential. One then finds that a potential of Coulomb type in the Dirac equation leads to a potential term in the above second-order equations which is not even infinitesimally form-bounded with respect to the free operator. Moreover, the conditions ensuring essential self-adjointness of the second-order operators in the interacting case are changed with respect to the free case, i.e. they are expressed by a majorization involving the parameter in the Coulomb potential and the angular momentum quantum number. The same methods are applied to the analysis of coupled eigenvalue equations when the anomalous magnetic moment of the electron is not neglected.
We discuss symmetry-driven squeezing and coherent states of few-particle systems in magnetic fields. An operator approach using canonical transformations and the SU(1,1) algebras is developed for considering Coulomb correlations in the lowest Landau levels.
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian-Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville theorem of conservation of phase density distribution must be modified to allow time evolution of phase density and consequently the Boltzmann H theorem. We argue that the gap between the regular Newtonian dynamics and the random dynamics was not considered in the criticisms of the H theorem.
We investigate the assembly history of massive disk galaxies and describe how they shape their morphology through cosmic time. Using SHARDS and HST data, we modeled the surface brightness distribution of 91 massive galaxies at redshift $0.14<z\leq 1$ in the wavelength range $0.5-1.6$ $\mu$m, deriving the uncontaminated spectral energy distributions of their bulges and disks separately. This spectrophotometric decomposition allows us to compare the stellar populations properties of each component in individual galaxies. We find that the majority of massive galaxies ($\sim85\%$) builds inside-out, growing their extended stellar disk around the central spheroid. Some bulges and disks could start forming at similar epochs, but these bulges grow more rapidly than their disks, assembling $80\%$ of their mass in $\sim0.7$ Gyr and $\sim3.5$ Gyr, respectively. Moreover, we infer that both older bulges and older disks are more massive and compact than younger stellar structures. In particular, we find that bulges display a bimodal distribution of mass-weighted ages, i.e., they form in two waves. In contrast, our analysis of the disk components indicates that they form at $z\sim1$ for both first and second-wave bulges. This translates to first-wave bulges taking longer in acquiring a stellar disk ($5.2$ Gyr) compared to second-wave less-compact spheroids ($0.7$ Gyr). We do not find distinct properties (e.g., mass, star formation timescale, and mass surface density) for the disks in both types of galaxies. We conclude that the bulge mass and compactness mainly regulate the timing of the stellar disk growth, driving the morphological evolution of massive disk galaxies.