ShantanuT01/DACTYL-Pretraining huggingface dataset:
We demonstrate a new design of graphene liquid cell consisting of a thin lithographically patterned hexagonal boron nitride crystal encapsulated from both sides with graphene windows. The ultra-thin window liquid cells produced have precisely controlled volumes and thicknesses, and are robust to repeated vacuum cycling. This technology enables exciting new opportunities for liquid cell studies, providing a reliable platform for high resolution transmission electron microscope imaging and spectral mapping. The presence of water was confirmed using electron energy loss spectroscopy (EELS) via the detection of the oxygen K-edge and measuring the thickness of full and empty cells. We demonstrate the imaging capabilities of these liquid cells by tracking the dynamic motion and interactions of small metal nanoparticles with diameters of 0.5-5 nm. We further present an order of magnitude improvement in the analytical capabilities compared to previous liquid cell data, with 1 nm spatial resolution elemental mapping achievable for liquid encapsulated bimetallic nanoparticles using energy dispersive X-ray spectroscopy (EDXS).
We investigate the quantum state generated by optical parametric down-conversion in a $\chi^{(2) } $ medium driven by two noncollinear light modes. The analysis shows the emergence of multipartite, namely 3- or 4-partite, entangled states in a subset of the spatio-temporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups: i) Non-critical phase-matching in a periodically poled Lithium Tantalate slab, characterized by a 3-mode entangled state among hot spots. ii) A type I setup in a Beta-Barium Borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a quadripartite entangled state. In both cases we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.
Understanding and predicting the thermodynamic properties of point defects in semiconductors and insulators would greatly aid in the design of novel materials and allow tuning the properties of existing ones. As a matter of fact, first-principles calculations based on density functional theory (DFT) and the supercell approach have become a standard tool for the study of point defects in solids. However, in the dilute limit, of most interest for the design of novel semiconductor materials, the raw DFT calculations require an extensive post-processing. Spinney is an open-source Python package developed with the aim of processing first-principles calculations to obtain several quantities of interest, such as the chemical potential limits that assure the thermodynamic stability of the defectladen system, defect charge transition levels, defect formation energies, including electrostatic corrections for finite-size effects, and defect and carrier concentrations. In this paper we demonstrate the capabilities of the Spinney code using c-BN, Mg-doped GaN, TiO2 and ZnO as examples.
We review the E(8) model of the M-theory 3-form and its applications to anomaly cancellation, Gauss laws, quantization of Page charge, and the 5-brane partition function. We discuss the potentially problematic behavior of the model under parity.
In "Proving that a genus 2 curve has complex multiplication", van Wamelen lists 19 curves of genus two over $\mathbf{Q}$ with complex multiplication (CM). For each of the 19 curves, the CM-field turns out to be cyclic Galois over $\mathbf{Q}$. The generic case of non-Galois quartic CM-fields did not feature in this list, as the field of definition in that case always contains a real quadratic field, known as the real quadratic subfield of the reflex field.   We extend van Wamelen's list to include curves of genus two defined over this real quadratic field. Our list therefore contains the smallest "generic" examples of CM curves of genus two.   We explain our methods for obtaining this list, including a new height-reduction algorithm for arbitrary hyperelliptic curves over totally real number fields. Unlike Van Wamelen, we also give a proof of our list, which is made possible by our implementation of denominator bounds of Lauter and Viray for Igusa class polynomials.
We investigate whether the formation mechanism of boxy and peanut-shaped (B/PS) bulges could depend on the gas content of the galaxy. We have performed N-body simulations with and without a gaseous component. In the second case star formation/feedback recipes have also been implemented to create new stellar populations. As in many previous studies, in our N-body collisionless simulation, the B/PS is due to the classical break in the z mirror symmetry lasting roughly 200 Myr. When a gaseous component and star formation recipes are added to the simulation, the bulge-growing mechanism is quite different. The young stellar population that is born in the thin gaseous disc rapidly populates vertical resonant orbits triggered by the combined effects of the linear horizontal and vertical ILRs. This leads to a B/PS bulge mainly made of stellar material younger than the surrounding population. The non-linear analysis of the orbital structure shows that the main orbit family responsible for the B/PS is not the same in the two cases. The 2:2:1 orbits prevail in the collisionless simulation whereas additional asymmetrical families contribute to the B/PS if a dissipative component is present and can form new stars. We found that 2:3:1 and 2:5:1 orbits trap a significant fraction of the mass. A flat ringed discy stellar component also appears simultaneously with the thickening of the young population. It is due to the star formation in a nuclear gaseous disc located in the central kpc, inside the ILR, and accumulated there by the torques exerted by the large-scale bar. Remarkably, it remains flat throughout the simulation although it develops a nuclear bar, leading to a double-barred galaxy. We predict that two populations of B/PS bulges could exist and even coexist in the same galaxy.
Magnetic spin resonance is a key non-invasive sensing and imaging technique across the life-, material- and fundamental sciences with further medical and commercial applications. Recent advances using paramagnetic color centers enable magnetic resonance down on the nanoscale, and sensitivity to single molecules is in sight. Ensemble sensing and wide field imaging improve sensitivity and acquisition speed, but may suffer from inhomogeneous spin control fields, produced by e.g. microstructures in integrated devices, and limited spatial resolution. Here we demonstrate multiplexed nuclear magnetic resonance imaging using diamond nitrogen-vacancy centers in such adverse conditions. We image thin films of calcium fluoride down to $1.2\,\mathrm{nm}$ in thickness with a spatial resolution of $250\,\mathrm{nm}$. This corresponds to a net moment of about 140 nuclear spins within the sensing radius of a given NV in the ensemble.
This paper is devoted to the detailed analysis of three-dimensional motions in $\mathbb{R}^3$ with orthogonal directions switching at Poisson times and moving with constant speed $c>0$. The study of the random position at an arbitrary time $t>0$ on the surface of the support, forming an octahedron $S_{ct}$, is completely carried out on the edges $E_{ct}$ and faces $F_{ct}$. In particular, the motion on the faces $F_{ct}$ is analysed by means of a transformation which reduces it to a three-directions planar random motion. This permits us to obtain an integral representation on $F_{ct}$ in terms of integral of products of first order Bessel functions. The investigation of the distribution of the position $p=p(t,x,y,z)$ inside $S_{ct}$ implied the derivation of a sixth-order partial differential equation governing $p$ (expressed in terms of the products of three D'Alembert operators). A number of results, also in explicit form, concern the time spent on each direction and the position reached by each coordinates as the motion devolpes. The analysis is carried out when the incoming direction is orthogonal to the ongoing one and also when all directions can be uniformely choosen at each Poisson event. If the switches are governed by homogeneus Poisson process many explicit results are obtained.
The kinetic approach to the formation of the filaments in the large-scale matter distribution in the Universe is considered within the Vlasov formalism. The structures arise due to the self-consistent dynamics, along with the repulsive term in the modified Newtonian gravity which includes the cosmological constant. That modified gravity enables one to describe the Hubble tension as a result of two flows, the local and global ones. The criteria for formation of non--stationary semi-periodic structures in a system of gravitating particles described by Vlasov--Poisson equations are obtained in the case of that repulsive term. The obtained dispersion relations for the Vlasov equation in the vicinity of the singular point of the modified gravitational potential demonstrate the possibility of the emergence of filaments as coherent complex states of relative equilibrium in non--stationary systems as structures of low dimensions (walls), and voids between them, of scales (diameters) defined by the balance between the gravity and repulsive term of the cosmological constant.
Based on a chain of BBGKI equations with a modified boundary condition that takes into account multiparticle correlations, kinetic equations in the approximate "pairs" collisions and in the polarization approximation, taking into account the interaction through the third particle, obtained. The specifics of the model representation of the pair potential of particle interaction through short-range and long-range parts were taken into account. In the case of the short-range potential in the form of the potential of solid spheres, the contribution of Enskog's revised theory to the complete integration of the collision of the kinetic equation is obtained. The collision integrals include paired quasi-equilibrium distribution functions that depend on the nonequilibrium mean values of the particle number density and the inverse temperature. The method of collective variables Yukhnovskii is applied for the calculation of pair quasi-equilibrium distribution function with an allocation of short-range and long-range parts in the potential of the interaction of particles. In this case, the system with short-range interaction is considered as a frame of reference.
We give a characterisation of the singular points of the free boundary $\partial \{u>0\}$ for viscosity solutions of the nonlinear equation \begin{equation}F(D^2 u)=-\chi_{\{u>0\}},\tag{0.1} \end{equation} where $F$ is a fully nonlinear elliptic operator and $\chi$ the characteristic function. The equation (0.1) models the propagation of a nerve impulse along an axon.   We analyse the structure of the free boundary $\partial\{ u>0\}$ near the singular points where $u$ and $\nabla u$ vanish simultaneously. Our method uses the stratification approach developed in [DK18].   In particular, when $n=2$ we show that near a rank-2 flat singular free boundary point $\partial\{ u>0\}$ is a union of four $C^1$ arcs tangential to a pair of crossing lines. Moreover, if $F$ is linear then the singular set of $\partial\{ u>0\}$ is the union of degenerate and rank-2 flat points.   We also provide an application of the boundary Harnack principles to study the higher order flat degenerate points and show that if $\{u<0\}$ is a cone then the blow-ups of $u$ are homogeneous functions.
In recent years, constant applied potential molecular dynamics has allowed to study the structure and dynamics of the electrochemical double-layer of a large variety of nanoscale capacitors. Nevertheless it remained impossible to simulate polarized electrodes at fixed total charge. Here we show that combining a constant potential electrode with a finite electric displacement fills this gap by allowing to simulate open circuit conditions. The method can be extended by applying an electric displacement ramp to perform computational amperometry experiments at different current intensities. As in experiments, the full capacitance of the system is obtained at low intensity, but this quantity decreases when the applied ramp becomes too fast with respect to the microscopic dynamics of the liquid.
In some recent papers some sufficiency conditions for the occurrence of a $\mathbb{Z}_2$-symmetry breaking phase transition ($\mathbb{Z}_2$-SBPT) have been showed starting from geometric-topological concepts of potential energy landscapes. In particular, a $\mathbb{Z}_2$-SBPT can be triggered by double-well potentials, or in an equivalent way, by dumbbell-shaped equipotential surfaces. In this paper we introduce two models with a $\mathbb{Z}_2$-SBPT which, due to their essential feature, show in the clearest way the generating-mechanism of a $\mathbb{Z}_2$-SBPT above mentioned. These models, despite they cannot be considered physical models, have all the features of such models with the same kind of SBPT. At the end of the paper, the $\phi^4$ model is revisited in the light of this approach. In particular, the landscape of one of the model introduced here is turned out to be equivalent to that of the mean-field $\phi^4$ model in a simplified version.
The main theorem, I.a, is the existence for excellent Deligne-Mumford champ of characteristic zero of a resolution functor independent of the resolution process itself. Perceived wisdom was that this was impossible, but the counterexamples overlooked the possibility of using weighted blow ups. The fundamental local calculations take place in complete local rings, and are elementary in nature, while being self contained and wholly independent of Hironaka's methods and all derivatives thereof, i.e. existing technology. Nevertheless Abramovich, Temkin, and Wlodarczyk, [ATW], have varied existing technology to obtain an even shorter proof of principalisation, I.f, in the geometric case. Excellent patching is more technical than varieties over a field, and whence easier geometric arguments are pointed out when they exist.
The unprecedented depth and area surveyed by the Subaru Strategic Program with the Hyper Suprime-Cam (HSC-SSP) have enabled us to construct and publish the largest distant cluster sample out to $z\sim 1$ to date. In this exploratory study of cluster galaxy evolution from $z=1$ to $z=0.3$, we investigate the stellar mass assembly history of brightest cluster galaxies (BCGs), evolution of stellar mass and luminosity distributions, stellar mass surface density profile, as well as the population of radio galaxies. Our analysis is the first high redshift application of the top N richest cluster selection, which is shown to allow us to trace the cluster galaxy evolution faithfully. Over the 230 deg$^2$ area of the current HSC-SSP footprint, selecting the top 100 clusters in each of the 4 redshift bins allows us to observe the buildup of galaxy population in descendants of clusters whose $z\approx 1$ mass is about $2\times 10^{14}\,M_\odot$. Our stellar mass is derived from a machine-learning algorithm, which is found to be unbiased and accurate with respect to the COSMOS data. We find very mild stellar mass growth in BCGs (about 35% between $z=1$ and 0.3), and no evidence for evolution in both the total stellar mass-cluster mass correlation and the shape of the stellar mass surface density profile. We also present the first measurement of the radio luminosity distribution in clusters out to $z\sim 1$, and show hints of changes in the dominant accretion mode powering the cluster radio galaxies at $z\sim 0.8$.
We consider an $L^2$-Wasserstein type distance $\rho$ on the configuration space $\Gamma_X$ over a Riemannian manifold $X$, and we prove that $\rho$-Lipschitz functions are contained in a Dirichlet space associated with a measure on $\Gamma_X$ satisfying some general assumptions. These assumptions are in particular fulfilled by a large class of tempered grandcanonical Gibbs measures with respect to a superstable lower regular pair potential. As an application we prove a criterion in terms of $\rho$ for a set to be exceptional. This result immediately implies, for instance, a quasi-sure version of the spatial ergodic theorem. We also show that $\rho$ is optimal in the sense that it is the intrinsic metric of our Dirichlet form.
We present the redshift catalogs for the X-ray sources detected in the Chandra Deep Field North (CDF-N), the Chandra Large Area Synoptic X-ray Survey (CLASXS), and the Chandra Lockman Area North Survey (CLANS). The catalogs for the CDF-N and CLASXS fields include redshifts from previous work, while the redshifts for the CLANS field are all new. For fluxes above 10^-14 ergs cm^-2 s^-1 (2-8 keV) we have redshifts for 76% of the sources. We extend the redshift information for the full sample using photometric redshifts. The goal of the OPTX Project is to use these three surveys, which are among the most spectroscopically complete surveys to date, to analyze the effect of spectral type on the shape and evolution of the X-ray luminosity functions and to compare the optical spectral types with the X-ray spectral properties.   We also present the CLANS X-ray catalog. The nine ACIS-I fields cover a solid angle of ~0.6 square degrees and reach fluxes of 7x10^-16 ergs cm^-2 s^-1 (0.5-2 keV) and 3.5x10^-15 ergs cm^-2 s^-1 (2-8 keV). We find a total of 761 X-ray point sources. Additionally, we present the optical and infrared photometric catalog for the CLANS X-ray sources, as well as updated optical and infrared photometric catalogs for the X-ray sources in the CLASXS and CDF-N fields.   The CLANS and CLASXS surveys bridge the gap between the ultradeep pencil-beam surveys, such as the CDFs, and the shallower, very large-area surveys. As a result, they probe the X-ray sources that contribute the bulk of the 2-8 keV X-ray background and cover the flux range of the observed break in the logN-logS distribution. We construct differential number counts for each individual field and for the full sample.
We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the positions of neighboring atoms as well. Using the Lanczos algorithm for the numerical evaluation of eigenvalues of large sparse matrices, we calculate the bilayer single-electron spectrum for commensurate twist angles in the range $1^{\circ}\lesssim\theta\lesssim30^{\circ}$. We show that at certain angles $\theta$ greater than $\theta_{c}\approx1.89^{\circ}$ the electronic spectrum acquires a finite gap, whose value could be as large as $80$ meV. However, in an infinitely large and perfectly clean sample the gap as a function of $\theta$ behaves non-monotonously, demonstrating exponentially-large jumps for very small variations of $\theta$. This sensitivity to the angle makes it impossible to predict the gap value for a given sample, since in experiment $\theta$ is always known with certain error. To establish the connection with experiments, we demonstrate that for a system of finite size $\tilde L$ the gap becomes a smooth function of the twist angle. If the sample is infinite, but disorder is present, we expect that the electron mean-free path plays the same role as $\tilde L$. In the regime of small angles $\theta<\theta_c$, the system is a metal with a well-defined Fermi surface which is reduced to Fermi points for some values of $\theta$. The density of states in the metallic phase varies smoothly with $\theta$.
Giant molecular clouds contain supersonic turbulence that can locally heat small fractions of gas to over 100 K. We run shock models for low-velocity, C-type shocks propagating into gas with densities between 10^3 and 10^5 cm^(-3) and find that CO lines are the most important cooling lines. Comparison to photodissociation region (PDR) models indicates that mid-J CO lines (J = 8-7 and higher) should be dominated by emission from shocked gas. In Papers I and II we presented CO J = 3-2, 8-7, and 9-8 observations toward four primarily quiescent clumps within infrared dark clouds. Here we fit PDR models to the combined spectral line energy distributions and show that the PDR models that best fit the low-J CO emission underpredict the mid-J CO emission by orders of magnitude, strongly hinting at a hot gas component within these clumps. The low-J CO data clearly show that the integrated intensities of both the CO J = 8-7 and 9-8 lines are anomalously high, such that the line ratio can be used to characterize the hot gas component. Shock models are reasonably consistent with the observed mid-J CO emission, with models with densities near 10^(4.5) cm^(-3) providing the best agreement. Where this mid-J CO is detected, the mean volume filling factor of the hot gas is 0.1%. Much of the observed mid-J CO emission, however, is also associated with known protostars and may be due to protostellar feedback.
The proton spin dependent structure function $g_1^p$ is analysed using the unified scheme incorporating both Altarelli-Parisi evolution and the double $ln^2(1/x)$ effects at low $x$. The latter are found to be very important in the region of $x$ which can possibly be probed at HERA. Predictions for the polarized gluon distribution $\Delta G(x)$ at low $x$ are also given.
Under the hypothesis of convergence in probability of a sequence of c\`{a}dl\`{a}g processes $(X^n)\_n$ to a c\`{a}dl\`{a}g process $X$, we are interested in the convergence of corresponding values in optimal stopping and also in the convergence of optimal stopping times. We give results under hypothesis of inclusion of filtrations or convergence of filtrations.
Based on the Szekeres-Pirani gravitational compass we suggest the addition of a fourth, non-coplanar mass/mirror to the presently existing laser based gravitational wave observatories, enabling them to operate omnidirectionally, to filter out ambiguous interpretations and to point out the direction of the gravitational wave source.
We present an experimental analysis of quadrature entanglement produced from a pair of amplitude squeezed beams. The correlation matrix of the state is characterized within a set of reasonable assumptions, and the strength of the entanglement is gauged using measures of the degree of inseparability and the degree of EPR paradox. We introduce controlled decoherence in the form of optical loss to the entangled state, and demonstrate qualitative differences in the response of the degrees of inseparability and EPR paradox to this loss. The entanglement is represented on a photon number diagram that provides an intuitive and physically relevant description of the state. We calculate efficacy contours for several quantum information protocols on this diagram, and use them to predict the effectiveness of our entanglement in those protocols.
This work explains how to utilize earlier results by P. Diaconis, K. Houston-Edwards and the second author to estimate probabilities related to the 4-player gambler ruin problem. For instance, we show that the probability that a very dominant player (i.e., a player starting with all but 3 chips distributed among the remaining players) is first to loose is of order $N^{-\alpha}$ where $\alpha$ is approximately $5.68$. In the $3$-player game, this probability is or order $N^{-3}$. We note it is futile to attempt to give heuristic/intuitive explanations for the value of $\alpha$. This value is obtained via an explicit formula relating $\alpha$ to the Dirichlet eigenvalue $\lambda$ (zero boundary condition) of the spherical Laplacian in the equilateral spherical triangle on the unit sphere $\mathbb S^2$ that corresponds to a unit simplex with one vertex placed at the origin in Euclidean $3$-space. The value of $\lambda$ is estimated using a finite-difference-type algorithm developed by Grady Wright.