ShantanuT01/DACTYL-Pretraining huggingface dataset:
The purpose of this note is to show that in characteristic two there exists a smooth Fano variety for which the square of the anti-canonical bundle violates Kodaira vanishing. This is used in turn to construct non-Cohen-Macaulay canonical singularities in characteristic two.
We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII_{0}, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII_{0} cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII_{0} cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.
We report a first principles theoretical investigation of quantum transport in monolayer WSe2 field effect transistor (FET). Due to a strong spin-orbit interaction (SOI) and the atomic structure of the two-dimensional (2D) lattice, monolayer WSe2 has an interesting electronic structure that exhibits Zeeman-like up-down spin texture near the K and K' points of the Brillouin zone. In a FET, the gate electric field induces an extra, externally tunable SOI that re-orients the spins into a Rashba-like texture thereby realizing electric control of the spin. Quantum transport is modulated by the spin texture, namely by if the spin orientation of the carrier after the gated channel region, matches or miss-matches that of the FET drain electrode. The carrier current in the FET is labelled both the spin index and the valley index, realizing spintronics and valleytronics in the same device.
The recent discovery of magnetism in atomically thin layers of van der Waals (vdW) crystals has created new opportunities for exploring magnetic phenomena in the two-dimensional (2D) limit. In most 2D magnets studied to date the c-axis is an easy axis, so that at zero applied field the polarization of each layer is perpendicular to the plane. Here, we demonstrate that atomically thin CrCl3 is a layered antiferromagnetic insulator with an easy-plane normal to the c-axis, that is the polarization is in the plane of each layer and has no preferred direction within it. Ligand field photoluminescence at 870 nm is observed down to the monolayer limit, demonstrating its insulating properties. We investigate the in-plane magnetic order using tunneling magnetoresistance in graphene/CrCl3/graphene tunnel junctions, establishing that the interlayer coupling is antiferromagnetic down to the bilayer. From the temperature dependence of the magnetoresistance we obtain an effective magnetic phase diagram for the bilayer. Our result shows that CrCl3 should be useful for studying the physics of 2D phase transitions and for making new kinds of vdW spintronic devices.
We derive a new microscopic spin Hamiltonian for Rashba-coupled double exchange metals. The Hamiltonian consists of anisotropic interactions of the Dzyaloshinskii-Moriya (DM) and Kitaev form, in addition to the standard isotropic term. We validate the spin Hamiltonian by comparing results with those on the exact spin-fermion model, and present its phase diagram using large scale Monte Carlo simulations. In addition to ferromagnetic, planar spiral and flux states, the model hosts skyrmion crystal and classical spin-liquid states characterized, respectively, by multiple peaks and a diffuse ring pattern in the spin structure factor. The filamentary domain wall structures in the spin-liquid state are in remarkable agreement with experimental data on thin films of MnSi-type B20 metals and transition metals and their alloys.
An integer partition of $n$ is a decreasing sequence of positive integers that add up to $[n]$. Back in $1979$ Macdonald posed a question about the limit value of the probability that two partitions chosen uniformly at random, and independently of each other, are comparable in terms of the dominance order. In $1982$ Wilf conjectured that the uniformly random partition is a size-ordered degree sequence of a simple graph with the limit probability $0$. In $1997$ we showed that in both, seemingly unrelated, cases the limit probabilities are indeed zero, but our method left open the problem of convergence rates. The main result in this paper is that each of the probabilities is $e^{-0.11\log n/\log\log n}$, at most. A key element of the argument is a local limit theorem, with convergence rate, for the joint distribution of the $[n^{1/4-\varepsilon}]$ tallest columns and the $[n^{1/4-\varepsilon}]$ longest rows of the Young diagram representing the random partition.
The equation of state of strange matter build of the u,d,s quarks in the framework of the MIT bag model is studied. The scaling relations with bag constant are discussed and applied to the determination of maximum frequency of a particle in stable circular orbit around strange star. The highest QPO frequency of 1.33 kHz observed so far is consistent with the strange stars models for which the maximum QPO frequency is 1.7-2.4 kHz depending on the strange quark mass and the QCD coupling constant. The linear approximation of the equation of state is found and the parameters of this EOS are determined as a functions of strange quark mass, QCD coupling constant and bag constant. This approximation reproduces exact results within an error of the order of 1% and can be used for the complete study of the properties of strange stars including microscopic stability of strange matter and determination of the total baryon number of the star.
The surface functionalization of diamond has been extensively studied through a variety of techniques, such as oxidation. Several oxygen groups have been correspondingly detected on the oxidized diamond, such as COC (ester), CO (ketonic), and COH (hydroxyl). However, the composition and relative concentration of these groups on diamond surfaces can be affected by the type of oxygenation treatment and the diamond surface quality. To investigate the stability of the oxygenated groups at specific diamond surfaces, we evaluated through fully atomistic reactive molecular mechanics (FARMM) simulations, using the ReaxFF force field, the formation energies of CO, COC, and COH groups on pristine and defective diamond surfaces (110), (111), and (311). According to our findings, the COH group has the lowest formation energy on a perfect (110) surface, while the COC is favored on a defective surface. As for the (111) surface, the COC group is the most stable for both pristine and defective surfaces. Similarly, COC group is also the most stable one on the defective/perfect (311) surface. In this way, our results suggest that if in a diamond film the (110) surface is the major exposed facet, the most adsorbed oxygen group could be either COH or COC, in which the COC would depend on the level of surface defects.
We present a computational random walk method of measuring the isothermal pressure of the lattice gas with and without the excluded volume interaction. The method is based on the discretization of the exact thermodynamic relation for the pressure. The simulation results are in excellent agreement with the theoretical predictions.
We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth, shown to describe their large population limits in arXiv:1303.3939. The proof relies on a novel coupling argument for binary branching diffusions based on optimal transport, which allows us to sharply mimic the trajectory of the interacting binary branching population by certain system of independent particles with suitably distributed random space-time births. We are thus able to derive an optimal convergence rate, in the dual bounded-Lipschitz distance on finite measures, for the empirical measure of the population, from the convergence rate in 2-Wasserstein distance of empirical distributions of i.i.d. samples. Our approach and results extend techniques and ideas on propagation of chaos from kinetic models to stochastic systems of interacting branching populations, and appear to be new in this setting, even in the simple case of pure binary branching diffusions.
Based on first-principles calculations, we discover a two-dimensional layered antiferromagnetic (AFM) electride Gd$_2$O, where anionic excess electrons exist in the interstitial spaces between positively charged cationic layers. It is revealed that each cationic layer composed of three-atom-thick Gd$-$O$-$Gd stacks has in-plane ferromagnetic and out-of-plane AFM superexchange interactions between the localized Gd 4$f$ spins through O 2$p$ orbitals. Furthermore, the interlayer superexchange mediated by the hybridized Gd-5$d$ and interstitial-$s$-like states involves intimate couplings between the spin, lattice, and charge degrees of freedom, thereby inducing simultaneous magnetic, structural, and electronic phase transitions. The resulting ground state with the simple hexagonal lattice hosts massless Dirac fermions protected by nonsymmorphic magnetic symmetry, as well as massive Dirac fermions. We thus demonstrate that the anionic excess electrons in Gd$_2$O play a crucial role in the emergence of magnetic Dirac semimetal states, therefore offering an intriguing interplay between 2D magnetic electrides and topological physics.
We consider several physical scenarios where black holes within classical gravity theories including $R^2$ and Ricci-squared corrections and formulated \`a la Palatini can be analytically studied.
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible consequences to cosmology, and in particular to the missing-mass problem.
For supernova powered by the conversion of kinetic energy into radiation due to the interactions of the ejecta with a dense circumstellar shell, we show that there could be X-ray analogues of optically super-luminous SNe with comparable luminosities and energetics. We consider X-ray emission from the forward shock of SNe ejecta colliding into an optically-thin CSM shell, derive simple expressions for the X-ray luminosity as a function of the circumstellar shell characteristics, and discuss the different regimes in which the shock will be radiative or adiabatic, and whether the emission will be dominated by free-free radiation or line-cooling. We find that even with normal supernova explosion energies of 10^51 erg, there exists CSM shell configurations that can liberate a large fraction of the explosion energy in X-rays, producing unabsorbed X-ray luminosities approaching 10^44 erg/s events lasting a few months, or even 10^45 erg/s flashes lasting days. Although the large column density of the circumstellar shell can absorb most of the flux from the initial shock, the most luminous events produce hard X-rays that are less susceptible to photoelectric absorption, and can counteract such losses by completely ionizing the intervening material. Regardless, once the shock traverses the entire circumstellar shell, the full luminosity could be available to observers.
In the paper, we first classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $\deg_zv\leq 1$. After that, we generalize the structure of $H$ to $H=\big(H_1(x_1,x_2,\ldots,x_n),\allowbreak b_3x_3+\cdots+b_nx_n+H_2^{(0)}(x_2),H_3(x_1,x_2),\ldots,H_n(x_1,x_2)\big)$.
Three types of blow-up for a fourth-order degenerate reaction-diffusion equation are studied by a combination of analytic and numerical methods. At the critical values of parameters, there occurs a variational problem with a countable set of solutions obtained by Lysternik--Shnirelman category theory, which then are extended to neighbouring values of parameters by a homotopy-like approach.
We examine closed timelike curves (CTCs) and "effective" superluminal travel in a spacetime containing naked line singularities, which we call "wires". Each wire may be straight-line singularity or a ring singularity. The Weak Energy Condition (WEC) is preserved in all well-defined regions of the spacetime. (The singularities themselves are not well-defined, so the WEC is undefined there, but it is never explicitly violated.) Parallel to the wire, "effective" superluminal travel is possible, in that the wire may be used as a shortcut between distant regions of spacetime. Our purpose in presenting the superluminal aspects of the wire is to dispel the commonly held view that explicit WEC violation is necessary for effective superluminal travel, whereas in truth the strictures against superluminal travel are more complicated. We also demonstrate how the existence of such "wires" could create CTCs. We present a model spacetime which contains two wires which are free to move relative to each other. This spacetime is asymptotically flat: It becomes a Minkowski spacetime a finite distance away from each of the wires. The CTCs under investigation do not need to enter the wires' singularities, and can be confined to regions that are weak-field: This means that if these wires were physically possible, they would present causality problems even in nonsingular, energetically realistic regions of the spacetime. We conclude that the Weak Energy Condition alone is not sufficient to prevent superluminal travel in asymptotically flat spacetimes.
In this paper, we are concerned with the following equation involving higher-order fractional Lapalacian \begin{equation*} \left\{\begin{aligned} &(-\Delta)^{p+{\frac{\alpha}{2}}}u(x)=u_+^\gamma~~ \mbox{ in }\mathbb{R}^n,\\ &\int_{\mathbb{R}^n}u_+^\gamma dx<+\infty, \end{aligned}\right. \end{equation*} where $p\geq 1$ is an integer, $0<\alp<2$, $n> 2p+\alpha$ and $\gamma \in (1,\frac{n}{n-2p-\alp})$. We establish an integral representation formula for any nonconstant classical solution satisfying certain growth at infinity. From this we prove that these solutions are radially symmetric about some point in $\R^n$ and monotone decreasing in the radial direction via method of moving planes in integral forms.
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background.   However, exact vacuum solutions with double duality properties exhibit a `vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of `dark energy' as well as `dark matter' modeled by a torsion induced quintaxion.
We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples, including recently found double elliptic Hamiltonians. We consider as basic the notion of self-duality, while the duality in integrable systems (of the Toda/Calogero/Ruijsenaars type) comes as a derivative notion (degenerations of self-dual systems). This is a talk presented at the Workshop "Classical and Quantum Integrable Systems", Protvino, January, 2001.
Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. For simple models of decoherence, this method can be applied even when the decoherence time is comparable to the oscillation period of the system.
The quasar SDSS J105041.35+345631.3 (z = 0.272) has broad emission lines blueshifted by 3500 km/s relative to the narrow lines and the host galaxy. Such an object may be a candidate for a recoiling supermassive black hole, binary black hole, a superposition of two objects, or an unusual geometry for the broad emission-line region. The absence of narrow lines at the broad line redshift argues against superposition. New Keck spectra of J1050+3546 place tight constraints on the binary model. The combination of large velocity shift and symmetrical H-beta profile, as well as aspects of the narrow line spectrum, make J1050+3546 an interesting candidate for black hole recoil. Other aspects of the spectrum, however, suggest that the object is most likely an extreme case of a ``double-peaked emitter.'' We discuss possible observational tests to determine the true nature of this exceptional object.
A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for the $\alpha$+${}^6$He cluster system, so finding a model spectrum for ${}^{10}$Be to more than 10 MeV excitation. Three states of ${}^6$He are included and the resonance character of the two excited states taken into account in finding solutions. A model Hamiltonian has been found that gives very good agreement with the known bound states and with some low-lying resonances of ${}^{10}$Be. More resonance states are predicted than have as yet been observed. The method also yields $S$-matrices which we have used to evaluate low-energy ${}^6$He-$\alpha$ scattering cross sections. Reasonable reproduction of low-energy differential cross sections and of energy variation of cross sections measured at fixed scattering angles is found.
Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of $[n]:=\{1,...,n\}$ that contains no subposet P. This problem has been studied intensively in recent years, and it is conjectured that $\pi(P):= \lim_{n\rightarrow\infty} La(n,P)/{n choose n/2}$ exists for general posets P, and, moreover, it is an integer. For $k\ge2$ let $\D_k$ denote the $k$-diamond poset $\{A< B_1,...,B_k < C\}$. We study the average number of times a random full chain meets a $P$-free family, called the Lubell function, and use it for $P=\D_k$ to determine $\pi(\D_k)$ for infinitely many values $k$. A stubborn open problem is to show that $\pi(\D_2)=2$; here we make progress by proving $\pi(\D_2)\le 2 3/11$ (if it exists).
We present preliminary results of BeppoSAX AO1 observations of 3C 273 performed in January 1997. We also present a close comparison with data obtained during the satellite SVP, in July 1996. On average, the AO1 flux is about a factor 2 higher than the flux detected during the SVP, and roughly on the middle of the historical X-ray flux range. Power law fits with galactic absorption to all observations yield spectral indices in the range 1.53-1.6, with the spectrum extending from 0.2 to at least up to 200 keV without any significant slope change. The broad band spectrum appears basically featureless, marking a clear difference from the SVP data, where an absorption feature at low energy and a fluorescence iron emission line are present. The lack of cold/warm matter signatures in our data may indicate that, at this "high" level of luminosity, the featureless continuum produced in a relativistic jet overwhelms any thermal and/or reprocessing component, while the two components were at least comparable during the "low" state of July 1996.
Although the anchor-based detectors have taken a big step forward in pedestrian detection, the overall performance of algorithm still needs further improvement for practical applications, \emph{e.g.}, a good trade-off between the accuracy and efficiency. To this end, this paper proposes a series of systematic optimization strategies for the detection pipeline of one-stage detector, forming a single shot anchor-based detector (SADet) for efficient and accurate pedestrian detection, which includes three main improvements. Firstly, we optimize the sample generation process by assigning soft tags to the outlier samples to generate semi-positive samples with continuous tag value between $0$ and $1$, which not only produces more valid samples, but also strengthens the robustness of the model. Secondly, a novel Center-$IoU$ loss is applied as a new regression loss for bounding box regression, which not only retains the good characteristics of IoU loss, but also solves some defects of it. Thirdly, we also design Cosine-NMS for the postprocess of predicted bounding boxes, and further propose adaptive anchor matching to enable the model to adaptively match the anchor boxes to full or visible bounding boxes according to the degree of occlusion, making the NMS and anchor matching algorithms more suitable for occluded pedestrian detection. Though structurally simple, it presents state-of-the-art result and real-time speed of $20$ FPS for VGA-resolution images ($640 \times 480$) on challenging pedestrian detection benchmarks, i.e., CityPersons, Caltech, and human detection benchmark CrowdHuman, leading to a new attractive pedestrian detector.
The neutron capture cross section of the unstable nucleus $^{186}$Re is studied by investigating the inverse photodisintegration reaction $^{187}$Re($\gamma$,n). The special interest of the {\it s}-process branching point $^{186}$Re is related to the question of possible {\it s}-process contributions to the abundance of the {\it r}-process chronometer nucleus ^{187}$Re. We use the photoactivation technique to measure photodisintegration rates. Our experimental results are in good agreement with two different statistical model calculations. Although the cross sections predicted by both models for the inverse reaction $^{186}$Re(n,$\gamma$) is too low to remove the overproduction of $^{186}$Os; the two predicted neutron-capture cross sections differ by a factor of 2.4; this calls for future theoretical study.
Because of the disappearance of its accretion disk since the time period around 2012 November--December, XSS J12270-4859 has recently been identified as, in addition to PSR J1023+0038, another transitional millisecond pulsar binary. We have carried out detailed analysis of the Fermi Large Area Telescope data for the binary. While both spectra before and after the disk-disappearance transition are well described by an exponentially cut-off power law, typical for pulsars' emission in the Fermi's 0.2-300 GeV, a factor of 2 flux decrease related to the transition is detected. A weak orbital modulation is seen, but only detectable in the after-transition data, same to that found at X-rays. In the long-term light curve of the source before the transition, a factor of 3 flux variations are seen. Comparing to the properties of J1023+0038, we disucss the implications from these results. We suggest that since the modulation is aligned with that at X-rays in orbital phase, it possibly arises due to the occultation of the gamma-ray emitting region by the companion. The origin of the variations in the long-term light curve is not clear, because the source field also contains unidentified radio or X-ray sources and their contamination can not be excluded. Multi-wavelength observations of the source field will help identify the origin of the variations by detecting any related flux changes from the in-field sources.