ShantanuT01/DACTYL-Pretraining huggingface dataset:
The cointercalation of sodium with the solvent organic molecule into graphite can resolve difficulty of forming the stage-I Na-graphite intercalation compound, which is a predominant anode of Na-ion battery. To clarify the mechanism of such cointercalation, we investigate the atomistic structure, energetics, electrochemical properties, ion and electron conductance, and charge transferring upon de/intercalation of the solvated Na-diglyme ion into graphite with {\it ab initio} calculations. It is found that the Na(digl)$_2$C$_n$ compound has the negatively lowest intercalation energy at $n\approx$21, the solvated Na(digl)$_2$ ion diffuses fast in the interlayer space, and their electronic conductance can be enhanced compared to graphite. The calculations reveal that the diglyme molecules as well as Na atom donates electrons to the graphene layer, resulting in the formation of ionic bonding between the graphene layer and the moiety of diglyme molecule. This work will contribute to the development of innovative anode materials for alkali-ion battery applications.
We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This result provides a unified way to understand known formulae for various geometric situations such as blowups, Cayley's trick, projectivizations, Grassmannian bundles, flops from Springer type resolutions, as well as provide new phenomena such as formulae for Grassmannain type flips/flops and virtual flips. We also give applications to blowups of determinantal ideals, moduli spaces of linear series on curves, and Hilbert schemes of points on surfaces.
A stochastic model of the chemical enrichment of metal-poor systems by core-collapse (Type II) supernovae is presented, allowing for large-scale mixing of the enriched material by turbulent motions and cloud collisions in the interstellar medium. Infall of pristine material is taken into account by following the evolution of the gas density in the medium. Analytical expressions were derived for the number of stars enriched by a given number of supernovae, as well as for the amount of mass with which the ejected material from a supernova is mixed before being locked up in a subsequently formed star. It is shown that for reasonable values of the gas density (~0.1 cm-3) and of the supernova rate (~0.25 kpc-3 Myr-1) of the Galactic halo, the resulting metallicity distributions of the extreme Population II stars show a distinct cut-off at [Fe/H] ~= -4. In fact, by assuming no low-mass Population III stars were able to form out of the primordial interstellar medium, the derived fraction of stars below [Fe/H] = -4 is in agreement with observations. Moreover, the probability is high that even the most metal-poor stars observed to date have been enriched by several contributing supernovae. This partly explains the relatively small star-to-star scatter in many chemical-abundance ratios for stars down to [Fe/H] = -4, as recently found in several observational studies. Contribution from the thermonuclear (Type Ia) supernovae is found to be negligible over almost the entire extremely metal-poor regime. (***abridged***)
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is completely determined by the response of the likelihood to changes in parameters. Under the assumption that the likelihood is a Gaussian distribution, the Jeffreys prior is a constant, i.e. flat. However, if one parameter is constrained by physical considerations, the Gaussian approximation fails and the flat prior is no longer the Jeffreys prior.   In this paper we compute the correct Jeffreys prior for a multivariate normal distribution constrained in one dimension, and we apply it to the sum of neutrino masses $\Sigma m_\nu$ and the tensor-to-scalar ratio $r$. We find that one-dimensional marginalised posteriors for these two parameters change considerably and that the 68% and 95% Bayesian upper limits increase by 9% and 4% respectively for $\Sigma m_\nu$ and 22% and 3% for $r$. Adding the prior to an existing chain can be done as a trivial importance sampling in the final step of the analysis proces.
An equivalence graph is a disjoint union of cliques, and the equivalence number $\mathit{eq}(G)$ of a graph $G$ is the minimum number of equivalence subgraphs needed to cover the edges of $G$. We consider the equivalence number of a line graph, giving improved upper and lower bounds: $\frac 13 \log_2\log_2 \chi(G) < \mathit{eq}(L(G)) \leq 2\log_2\log_2 \chi(G) + 2$. This disproves a recent conjecture that $\mathit{eq}(L(G))$ is at most three for triangle-free $G$; indeed it can be arbitrarily large.   To bound $\mathit{eq}(L(G))$ we bound the closely-related invariant $\sigma(G)$, which is the minimum number of orientations of $G$ such that for any two edges $e,f$ incident to some vertex $v$, both $e$ and $f$ are oriented out of $v$ in some orientation. When $G$ is triangle-free, $\sigma(G)=\mathit{eq}(L(G))$. We prove that even when $G$ is triangle-free, it is NP-complete to decide whether or not $\sigma(G)\leq 3$.
With their relatively fast variability time-scales, Galactic X-ray binaries provide an excellent laboratory to explore the physics of accretion and related phenomena, most notably outflows, over different regimes. After comparing the phenomenology of jets in black hole X-ray binary systems to that of neutron stars, here I discuss the role of the jet at very low Eddington ratios, and present preliminary results obtained by fitting the broadband spectral energy distribution of a quiescent black hole binary with a `maximally jet-dominated' model.
The IceCube Upgrade, planned for deployment in the 2022/2023 South Pole Summer, will involve deployment of a greater density of optical modules (vertically spaced ~3 m). Improvements in the calibration of optical sensors and an enhanced understanding of the optical properties of the deep glacial ice, due to the more closely-spaced modules, are projected to have a large impact on neutrino reconstruction. A new optical sensor module called the "Dual optical sensors in an Ellipsoid glass for Gen2" (D-Egg), is planned for installation in both the IceCube Upgrade and IceCube-Gen2, and has both an upward and downward facing 8" high quantum efficiency PMT. The D-Egg modules will make use of a downward-facing LED calibration system to measure the optical properties of the refrozen drill holes ("hole ice"). An inner section of the hole ice contains some impurities, which modify the optical properties of the ice; this area is known as the "bubble column". The measurement of this "hole ice" is critical both for the upgraded IceCube detector as well as the current generation IceCube, as refrozen ice contributes significant systematic uncertainties to the reconstruction of low energy neutrinos. A simulation was performed, where the size and optical properties of the bubble column were varied. A log likelihood function is constructed from the geometry of the D-Eggs and properties of the hole ice. The minimization recovers best fit values close to the Monte Carlo truth.
This article is devoted to examples of (orbifold) K\"ahler groups from the perspective of the so-called Shafarevich conjecture on holomorphic convexity. It aims at pointing out that every quasi-projective complex manifold with an 'interesting' fundamental group gives rise to interesting instances of this long-standing open question. Complements of line arrangements are one of the better known classes of quasi-projective complex surfaces with an interesting fundamental group. We solve the corresponding instance of the Shafarevich conjecture partially giving a proof that the universal covering surface of a Hirzebruch's covering surface with equal weights is holomorphically convex. The final section reduces the Shafarevich conjecture to a question related to the Serre problem.
We have directly observed spin-dependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by $\pi$ causes displacement of the $\sigma^{+}$- and $\sigma^{-}$-lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.
We propose a method to synthesize the inverse Compton (IC) gamma-ray image of a supernova remnant starting from the radio (or hard X-ray) map and using results of the spatially resolved X-ray spectral analysis. The method is successfully applied to SN 1006. We found that synthesized IC gamma-ray images of SN 1006 show morphology in nice agreement with that reported by the H.E.S.S. collaboration. The good correlation found between the observed very-high energy gamma-ray and X-ray/radio appearance can be considered as an evidence that the gamma-ray emission of SN 1006 observed by H.E.S.S. is leptonic in origin, though the hadronic origin may not be excluded.
On the base of the simplest model of a modulation of 3D Gaussian field in $k$-space we produce a set of simulations to bring out the effects of a modulating function $f_{\rm mod} (k)=f_1 (k) + f_2 (k)$ on power spectra of radial (shell-like) distributions of cosmological objects, where a model function $f_1 (k)$ reproduces the smoothed power spectrum of underlying 3D density fluctuations, while $f_2 (k)$ is a wiggling function imitating the baryon acoustic oscillations (BAO). It is shown that some excess of realizations of simulated radial distributions actually displays quasi-periodical components with periods about a characteristic scale $2\pi/k \sim 100~h^{-1}$~Mpc detected as power-spectrum peaks in vicinity of the first maximum of the modulation function $f_2 (k)$. We revised our previous estimations of the significance of such peaks and found that they were largely overestimated. Thereby quasi-periodical components appearing in some radial distributions of matter are likely to be stochastic (rather than determinative), while the amplitudes of the respective spectral peaks can be quite noticeable. They are partly enhanced by smooth part of the modulating function $f_1(k)$ and, to a far lesser extent, by effects of the BAO (i.e. $f_2(k)$). The results of the simulations match quite well with statistical properties of the radial distributions of the brightest cluster galaxies (BCGs).
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
We propose a method of determining the shape of a two-dimensional magnetic skyrmion, which can be parameterized as the position dependence of the orientation of the local magnetic moment, by using the expansion in terms of the eigenfunctions of the Schr\"{o}dinger equation of a harmonic oscillator. A variational calculation is done, up to the next-to-next-to-leading order. This result is verified by a lattice simulation based on Landau-Lifshitz-Gilbert equation. Our method is also applied to the dissipative matrix in the Thiele equation as well as two interacting skyrmions in a bilayer system.
We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N-body dark matter halos. We consider halos generated from LCDM simulations of gravitational clustering, as well as isolated, spherical collapses. The logarithmic density slopes gamma = d(log rho)/d(log r) of the LCDM halos are found to vary as power-laws in radius, reaching values of gamma ~ -1 at the innermost resolved radii (~0.01 r_virial). This behavior is significantly different from that of broken power-law models like the NFW profile, but similar to that of models like de Vaucouleurs'. Accordingly, we compare the N-body density profiles with various parametric models to find which provide the best fit. We consider an NFW-like model with arbitrary inner slope; Dehnen & McLaughlin's anisotropic model; Einasto's model (identical in functional form to Sersic's model but fit to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sersic's R^{1/n} law. Overall, the best-fitting model to the LCDM halos is Einasto's, although the Prugniel-Simien and Dehnen-McLaughlin models also perform well. With regard to the spherical collapse halos, both the Prugniel-Simien and Einasto models describe the density profiles well, with an rms scatter some four times smaller than that obtained with either the NFW-like model or the 3-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass.
We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of positive real numbers indexed by the unit vectors of Z^d. We prove that, as soon as these weights are nonsymmetric, the random walk in this random environment is transient in a direction with positive probability. In dimension 2, this result can be strenghened to an almost sure directional transience thanks to the 0-1 law from [ZM01]. Our proof relies on the property of stability of Dirichlet environment by time reversal proved in [Sa09]. In a first part of this paper, we also give a probabilistic proof of this property as an alternative to the change of variable computation used in that article.
Conductivity and permittivity of the quasi-one-dimensionsional organic transfer salt (TMTTF)2PF6 have been measured at low frequencies (10^3-10^7 Hz) between room temperature down to below the temperature of transition into the spin-Peierls state. We interpret the huge real part of the dielectric permittivity (up to 10^6) in the localized state as the realization in this compound of a charge ordered state of Wigner crystal type due to long range Coulomb interaction.
We study a cluster of quantum dots defined within silicene that host confined electron states with spin and valley degrees of freedom. Atomistic tight-binding and continuum Dirac approximation are applied for few-electron system in quest for spontaneous valley polarization driven by inter-dot tunneling and electron-electron interaction, i.e. a valley counterpart of itinerary Nagaoka ferromagnetic ordering recently identified in GaAs square cluster of quantum dots with three excess electrons [P. Dehollain, {\it et al.}, Nature {\bf 579}, 528 (2020)]. We find that for Hamiltonian without intrinsic-spin orbit coupling -- similar to the one of graphene with staggered potential -- the valley polarization in the ground-state can be observed in a range of inter-dot spacing provided that the spin of the system is frozen by external magnetic field. The inter-valley scattering effects are negligible for cluster geometry that supports the valley polarized ground-state. In presence of a strong intrinsic spin-orbit coupling that is characteristic to graphene no external magnetic field is necessary for observation of ground-state that is polarized in both spin and valley. The effective magnetic field due to the spin-orbit interaction produces a perfect anticorrelation of the spin and valley isospin components in the degenerate ground-state.
We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative geometry defined by a spectral triple, and study its quantization. In particular, we consider a simple model based on a finite dimensional spectral triple (A, H, D), which mimics certain aspects of the spectral formulation of general relativity. We find the physical phase space, which is the space of the onshell Dirac operators compatible with A and H. We define a natural symplectic structure over this phase space and construct the corresponding quantum theory using a covariant canonical quantization approach. We show that the Connes distance between certain two states over the algebra A (two ``spacetime points''), which is an arbitrary positive number in the classical noncommutative geometry, turns out to be discrete in the quantum theory, and we compute its spectrum. The quantum states of the noncommutative geometry form a Hilbert space K. D is promoted to an operator *D on the direct product *H of H and K. The triple (A, *H, *D) can be viewed as the quantization of the family of the triples (A, H, D).
We show that if the neighbor complex, as defined by H.~Scarf, of an infinite subset of $\Z^n$ has finite dimension, then each vertex has finitely many neighbors.
We study spin transport in forward and reverse biased junctions between a ferromagnetic metal and a degenerate semiconductor with a delta-doped layer near the interface at relatively low temperatures. We show that spin polarization of electrons in the semiconductor, Pn, near the interface increases both with the forward and reverse current and reaches saturation at certain relatively large current while the spin injection coefficient, Gamma, increases with reverse current and decreases with the forward current. We analyze the condition for efficient spin polarization of electrons in degenerate semiconductor near interface with ferromagnet. We compare the accumulation of spin polarized electrons in degenerate semiconductors at low temperatures with that in nondegenerate semiconductors at relatively high, room temperatures.
We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to modulus of full fields, which consist of sums of incident and scattering fields. These full fields are the interference fields generated by point sources. We introduce a set of auxiliary point sources for solving the inverse problems and demonstrate that the corresponding data allow us to solve the inverse problems in a way similar to the case of measurements of scattering waves.
We present the influence of spin correlation on the metal-insulator transitions (MIT) in two-orbital Hubbard models by the Kotliar-Ruckenstein slave-boson approach. In the asymmetric half-filling situation, the two orbits simultaneously transit from conducting to insulating states with the increase of Coulomb correlation, accompanied by a paramagnetic (PM)-antiferromagnetic (AFM) transition. The orbital selective Mott transition found in the PM condition is completely suppressed over a wide correlation range, though it may exist in the systems away from half-filling. In the insulating state, the system crosses over from a partially-polarized spin-gapped phase in the intermediate correlation regime to an almost fully-polarized Mott insulating phase in the strong correlation regime. These results demonstrate that the spin modulation to the quasiparticle spectra brings much rich and more interesting MIT scenario in multi-orbital correlated systems.
We present three-dimensional self-gravitating smoothed-particle hydrodynamics (SPH) simulations of an isothermal gaseous disc interacting with an embedded planet. Discs of varying stability are simulated with planets ranging from 10 Earth-masses to 2 Jupiter-masses. The SPH technique provides the large dynamic range needed to accurately capture the large scale behavior of the disc as well as the small scale interaction of the planet with surrounding material. Most runs used 10^5 gas particles, giving us the spatial resolution required to observe the formation of planets. We find four regions in parameter space: low-mass planets undergo Type I migration; higher-mass planets can form a gap; the gravitational instability mode of planet formation in marginally stable discs can be triggered by embedded planets; discs that are completely unstable can fragment to form many planets. The disc stability is the most important factor in determing which interaction a system will exhibit. For the stable disc cases, our migration and accretion time-scales are shorter and scale differently than previously suggested.
If E(z,s) is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z,s) has a "Siegel zero." That is E(z,\beta)=0 for a real number \beta just to the left of one. We give a generalization of this result to Eisenstein series formed with real valued automorphic forms on a finite central covering of the adele points of a connected reductive algebraic group over a global field.
A closed plane meander of order n is a closed self-avoiding loop intersecting an infinite line 2n times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. This allows us to calculate the number of closed meanders up to n=24. The algorithm is easily modified to enumerate various systems of closed meanders, semi-meanders or open meanders.
The Lefschetz algebra $L^*(X)$ of a smooth complex projective variety $X$ is the subalgebra of the cohomology algebra of $X$ generated by divisor classes. We construct smooth complex projective varieties whose Lefschetz algebras do not satisfy analogues of the hard Lefschetz theorem and Poincar\'e duality.
The spin dynamics of a quasi one dimensional $S=1$ bond alternating spin-gap antiferromagnet Ni(C$_9$H$_{24}$N$_4$)NO$_2$(ClO$_4$) (abbreviated as NTENP) is studied by means of electron spin resonance (ESR) technique. Five modes of ESR transitions are observed and identified: transitions between singlet ground state and excited triplet states, three modes of transitions between spin sublevels of collective triplet states and antiferromagnetic resonance absorption in the field-induced antiferromagnetically ordered phase. Singlet-triplet and intra-triplet modes demonstrate a doublet structure which is due to two maxima in the density of magnon states in the low-frequency range. A joint analysis of the observed spectra and other experimental results allows to test the applicability of the fermionic and bosonic models. We conclude that the fermionic approach is more appropriate for the particular case of NTENP.
Most ultraluminous X-ray sources (ULXs) are believed to be X-ray binary systems, but previous observational and theoretical studies tend to prefer a black hole rather than a neutron star accretor. The recent discovery of 1.37 s pulsations from the ULX M82 X-2 has established its nature as a magnetized neutron star. In this work we model the formation history of neutron star ULXs in an M82- or Milky Way-like galaxy, by use of both binary population synthesis and detailed binary evolution calculations. We find that the birthrate is around $10^{-4}\, \rm yr^{-1}$ for the incipient X-ray binaries in both cases. We demonstrate the distribution of the ULX population in the donor mass - orbital period plane. Our results suggest that, compared with black hole X-ray binaries, neutron star X-ray binaries may significantly contribute to the ULX population, and high-mass and intermediate-mass X-ray binaries dominate the neutron star ULX population in M82- and Milky Way-like galaxies, respectively.