ShantanuT01/DACTYL-Pretraining huggingface dataset:
Orbital memory is defined by two stable valencies that can be electrically switched and read-out. To explore the influence of an electric field on orbital memory, we studied the distance-dependent influence of an atomic Cu donor on the state favorability of an individual Co atom on black phosphorus. Using low temperature scanning tunneling microscopy/spectroscopy, we characterized the electronic properties of individual Cu donors, corroborating this behavior with ab initio calculations based on density functional theory. We studied the influence of an individual donor on the charging energy and stochastic behavior of an individual Co atom. We found a strong impact on the state favorability in the stochastic limit. These findings provide quantitative information about the influence of local electric fields on atomic orbital memory.
Building on recent work by Chandar et al. (2020), we construct X-ray luminosity functions (XLFs) for different classes of X-ray binary (XRB) donors in the nearby star-forming galaxy M83 through a novel methodology: rather than classifying low- vs. high-mass XRBs based on the scaling of the number of X-ray sources with stellar mass and star formation rate, respectively, we utilize multi-band Hubble Space Telescope imaging data to classify each Chandra-detected compact X-ray source as a low-mass (i.e. donor mass <~ 3 solar masses), high-mass (donor mass >~ 8 solar masses) or intermediate-mass XRB based on either the location of its candidate counterpart on optical color-magnitude diagrams or the age of its host star cluster. In addition to the the standard (single and/or truncated) power-law functional shape, we approximate the resulting XLFs with a Schechter function. We identify a marginally significant (at the 1-to-2 sigma level) exponential downturn for the high-mass XRB XLF, at logLx ~ 38.48^{+0.52}_{-0.33} (in log CGS units). In contrast, the low- and intermediate-mass XRB XLFs, as well as the total XLF of M83, are formally consistent with sampling statistics from a single power-law. Our method suggests a non-negligible contribution from low- and possibly intermediate-mass XRBs to the total XRB XLF of M83, i.e. between 20 and 50%, in broad agreement with X-ray based XLFs. More generally, we caution against considerable contamination from X-ray emitting supernova remnants to the published, X-ray based XLFs of M83, and possibly all actively star-forming galaxies.
We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating the dynamics at finite time steps, the algorithm can be expressed as alternating evolution under two non-commuting Hamiltonians. We show that each step of the algorithm updates the wavefunction in the direction of its local gradient, with an additional momentum-dependent displacement. For initial states in a superposition over many points, this method can therefore be interpreted as a coherent version of gradient descent, i.e., 'gradient descent in superposition.' This approach can be used for both constrained and unconstrained optimization. In terms of computational complexity, we show how variants of the algorithm can recover continuous-variable Grover search, and how a single iteration can replicate continuous-variable instantaneous quantum polynomial circuits. We also discuss how the algorithm can be adapted to solve discrete optimization problems. Finally, we test the algorithm through numerical simulation in optimizing the Styblinski-Tang function.
We investigate the variation of galaxy clustering with luminosity using the recently completed SSRS2 sample. Clustering measurements based on the two-point correlation function and the variance of counts in cells reveal the existence of a strong dependence of the clustering amplitude on luminosity for galaxies brighter than L*, while no significant variation is detected for fainter galaxies. We derive a relative bias versus magnitude relation which can be compared with theoretical predictions. Existing models of galaxy formation cannot adequately reproduce the simultaneous steep rise of biasing at high luminosities and the plateau at the low-luminosity end. Improved modeling of the halo-galaxy relation and larger samples including low luminosity galaxies are required to draw more definitive conclusions.
We show a general lower bound for Mean-value of Dirichlet polynomials
In the de Sitter gauge theory (DGT), the fundamental variables are the de Sitter (dS) connection and the gravitational Higgs/Goldstone field $\xi^A$. Previously, a model for DGT was analyzed, which generalizes the MacDowell--Mansouri gravity to have a variable cosmological constant $\Lambda=3/l^2$, where $l$ is related to $\xi^A$ by $\xi^A\xi_A=l^2$. It was shown that the model sourced by a perfect fluid does not support a radiation epoch and the accelerated expansion of the parity invariant universe. In this work, I consider a similar model, namely, the Stelle--West gravity, and couple it to a modified perfect fluid, such that the total Lagrangian 4-form is polynomial in the gravitational variables. The Lagrangian of the modified fluid has a nontrivial variational derivative with respect to $l$, and as a result, the problems encountered in the previous work no longer appear. Moreover, to explore the elegance of the general theory, as well as to write down the basic framework, I perform the Lagrange--Noether analysis for DGT sourced by a matter field, yielding the field equations and the identities with respect to the symmetries of the system. The resulted formula are dS covariant and do not rely on the existence of the metric field.
We consider the steady-state Navier-Stokes equation in the whole space $\mathbb{R}^3$ driven by a forcing function $f$. The class of source functions $f$ under consideration yield the existence of at least one solution with finite Dirichlet integral ($\|\nabla U\|_2<\infty$). Under the additional assumptions that $f$ is absent of low modes and the ratio of $f$ to viscosity is sufficiently small in a natural norm we construct solutions which have finite energy (finite $L^2$ norm). These solutions are unique among all solutions with finite energy and finite Dirichlet integral. The constructed solutions are also shown to be stable in the following sense: If $U$ is such a solution then any viscous, incompressible flow in the whole space, driven by $f$ and starting with finite energy, will return to $U$.
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck equations, showing how the invariance condition on the underlying dynamics yields the existence and uniqueness, respectively in $L^\infty$ and in $L^1$. Then we apply this analysis to mean field games. We investigate further the regularity of solutions proving, under some extra conditions, that the value function is (globally) Lipschitz and semiconcave. This latter regularity eventually leads the distribution density to be bounded, under suitable conditions. The results are not restricted to smooth domains.
We consider the plasmon excitations in anisotropic two-dimensional Dirac systems, be it either anisotropic graphene or surfaces of topological insulators. Generalizing the exact density-density response function one finds a plasmon dispersion that is anisotropic already at the lowest frequencies. Asymptotic expressions are obtained for the dispersion in this regime. We show that the plasmon properties of the complete material class of anisotropic Dirac systems are characterized by just two dimensionless material parameters. The strong anisotropy can be used to guide the plasmon modes, introducing new functionalities to the field of Dirac plasmonics.
We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of $(2,4m)$-minimal superconformal models coupled to $2D$-supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of non-linear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.
Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show how a global $G \times \tilde G$ symmetry group may be realized by worldline degrees of freedom. The worldline action gives rise to vertex operators, which are compared to similar ones describing the coupling to gauge fields and gravity, thus exposing the color/kinematics interplay in this framework. The action is quantized by path integrals to find a worldline representation of the one-loop QFT effective action of the bi-adjoint scalar cubic theory. As simple applications, we recover the one-loop beta function of the theory in six dimensions, verifying its vanishing, and compute the self-energy correction to the propagator. The model is easily extendable to that of a particle carrying an arbitrary representation of direct products of global symmetry groups, including the multi-adjoint particle, whose one-loop beta function we reproduce as well.
We present new age and mass estimates for 920 stellar clusters in the Large Magellanic Cloud (LMC) based on previously published broad-band photometry and the stellar cluster analysis package, MASSCLEANage. Expressed in the generic fitting formula, d^{2}N/dM dt ~ M^{\alpha} t^{\beta}, the distribution of observed clusters is described by \alpha = -1.5 to -1.6 and \beta = -2.1 to -2.2. For 288 of these clusters, ages have recently been determined based on stellar photometric color-magnitude diagrams, allowing us to gauge the confidence of our ages. The results look very promising, opening up the possibility that this sample of 920 clusters, with reliable and consistent age, mass and photometric measures, might be used to constrain important characteristics about the stellar cluster population in the LMC. We also investigate a traditional age determination method that uses a \chi^2 minimization routine to fit observed cluster colors to standard infinite mass limit simple stellar population models. This reveals serious defects in the derived cluster age distribution using this method. The traditional \chi^2 minimization method, due to the variation of U,B,V,R colors, will always produce an overdensity of younger and older clusters, with an underdensity of clusters in the log(age/yr)=[7.0,7.5] range. Finally, we present a unique simulation aimed at illustrating and constraining the fading limit in observed cluster distributions that includes the complex effects of stochastic variations in the observed properties of stellar clusters.
Compressive isothermal turbulence is known to have a near lognormal density probability distribution function (PDF) with a width that scales with the sonic Mach number and nature of the turbulent driving (solenoidal vs compressive). However, the physical processes that mold the extreme high and low density structures in a turbulent medium can be different, with the densest structures being composed of strong shocks that evolve on shorter timescales than the low density fluid. The density PDF in a turbulent medium exhibits deviations from lognormal due to shocks, that increases with the sonic Mach number, which is often ignored in analytic models for turbulence and star formation. We develop a simple model for turbulence by treating it as a continuous Markov process, which explains both the density PDF and the transient timescales of structures as a function of density, using a framework developed in n Scannapieco & Safarzadeh (2018). Our analytic model depends on only a single parameter, the effective compressive sonic Mach number, and successfully describes the non-lognormal behavior seen in both 1D and 3D simulations of supersonic and subsonic compressive isothermal turbulence. The model quantifies the non-lognormal distribution of density structures in turbulent environments, and has application to star forming molecular clouds and star formation efficiencies.
Developing quantum computers for real-world applications requires understanding theoretical sources of quantum advantage and applying those insights to design more powerful machines. Toward that end, we introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis (CCPHASE$(\theta)$). We estimate the process fidelity for this scheme via Cycle Benchmarking of $\mathcal{F}=87.1\pm0.8\%$, higher than reference two-qubit gate decompositions. CCPHASE$(\theta)$ is anticipated to have broad experimental implications, and we report a blueprint demonstration for solving a class of binary constraint satisfaction problems whose construction is consistent with a path to quantum advantage.
The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently-introduced approach based on density-functional perturbation theory (DFPT) for the calculation of the on-site Hubbard $U$ to also compute the inter-site Hubbard $V$. DFPT allows to reduce significantly computational costs, improve numerical accuracy, and fully automate the calculation of the Hubbard parameters by recasting the linear response of a localized perturbation into an array of monochromatic perturbations that can be calculated in the primitive cell. In addition, here we generalize the entire formalism from norm-conserving to ultrasoft and projector-augmented wave formulations, and to metallic ground states. After benchmarking DFPT against the conventional real-space Hubbard linear response in a supercell, we demonstrate the effectiveness of the present extended Hubbard formulation in determining the equilibrium crystal structure of Li$_x$MnPO$_4$ (x=0,1) and the subtle energetics of Li intercalation.
We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no second Neumann eigenfunction with an interior critical point, then there exists a convex quadrilateral with an unstable critical point. We also show that each critical point of a second-Neumann eigenfunction on a Lip-1 polygon with no orthogonal sides is an acute vertex.
Galaxies with 'rows' in Vorontsov-Velyaminov's terminology stand out among the variety of spiral galactic patterns. A characteristic feature of such objects is the sequence of straight-line segments that forms the spiral arm. In 2001 A. Chernin and co-authors published a catalog of such galaxies which includes 204 objects from the Palomar Atlas. In this paper, we supplement the catalog with 276 objects based on an analysis of all the galaxies from the New General Catalogue and Index Catalogue. The total number of NGC and IC galaxies with rows is 406, including the objects of Chernin et al. (2001). The use of more recent galaxy images allowed us to detect more 'rows' on average, compared with the catalog of Chernin et al. When comparing the principal galaxy properties we found no significant differences between galaxies with rows and all S-type NGC/IC galaxies.We discuss twomechanisms for the formation of polygonal structures based on numerical gas-dynamic and collisionless N-body calculations, which demonstrate that a spiral pattern with rows is a transient stage in the evolution of galaxies and a system with a powerful spiral structure can pass through this stage. The hypothesis of A. Chernin et al. (2001) that the occurrence frequency of interacting galaxies is twice higher among galaxies with rows is not confirmed for the combined set of 480 galaxies. The presence of a central stellar bar appears to be a favorable factor for the formation of a system of 'rows'.
We prove the $W^{1,2}_p$-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when $p\in (1,2]$. We also consider the corresponding Neumann problem in a half space when $p\in [2,\infty)$. Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions.
We present arguments that reinforce the hybrid interpretation of pi(1800) and we establish that the rho(1450) and the omega(1420) can be interpreted as radial-hybrid mixtures. Some questions for future experiments are raised.
A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function Z. A formula for internal energy E and that of heat capacity C are derived from derivatives of the partition function. We also derive a formula for the exchange probability in the replica exchange Monte Carlo method. By combining the formulae with the Stochastic Cutoff method, we can greatly reduce the computational time to perform internal energy and heat capacity measurements and the replica exchange Monte Carlo method in long-range interacting systems. Numerical simulations in three dimensional magnetic dipolar systems show the validity and efficiency of the method.
Validation of image segmentation methods is of critical importance. Probabilistic image segmentation is increasingly popular as it captures uncertainty in the results. Image segmentation methods that support multi-region (as opposed to binary) delineation are more favourable as they capture interactions between the different objects in the image. The Dice similarity coefficient (DSC) has been a popular metric for evaluating the accuracy of automated or semi-automated segmentation methods by comparing their results to the ground truth. In this work, we develop an extension of the DSC to multi-region probabilistic segmentations (with unordered labels). We use bipartite graph matching to establish label correspondences and propose two functions that extend the DSC, one based on absolute probability differences and one based on the Aitchison distance. These provide a robust and accurate measure of multi-region probabilistic segmentation accuracy.
It is shown that distance powers of an integral Cayley graph over an abelian group are again integral Cayley graphs over that group. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum.
Observations of quiescent dwarfs and low surface brightness galaxies suggest that continuous low rate star formation is likely to occur, during the quiescent phases between bursts, in dwarf galaxies. We thus have used a spectrophotometric model to reproduce the observed abundances in IZw 18, assuming only a low constant star formation rate. We conclude that such a continuous low star formation rate cannot be neglected, especially when considering the chemical evolution of very metal poor objects.
We report the structural and magnetic characterization of La-substituted Gd$_{1-x}$La$_x$RhIn$_5$ ($x\leq$ 0.50) antiferromagnetic (AFM) compounds. The magnetic responses of pure GdRhIn$_5$ are well described by a $S=7/2$ Heisenberg model. When Gd$^{3+}$ ions are substituted by La$^{3+}$, the maximum of the susceptibility and the inflection point of the magnetic specific heat are systematically shifted to lower temperatures accompanied by a broadening of the transition. The data is qualitatively explained by a phenomenological model which incorporates a distribution of magnetic regions with different transition temperatures ($T_N$). The universal behaviour of the low temperature specific heat is found for La (vacancies) concentrations below $x=0.40$ which is consistent with spin wave excitations. For $x=0.5$ this universal behaviour is lost. The sharp second order transition of GdRhIn$_5$ is destroyed, as seen in the specific heat data, contrary to what is expected for a Heisenberg model. The results are discussed in the context of the magnetic behavior observed for the La-substituted (Ce,Tb,Nd)RhIn$_5$ compounds.
We consider the classical theory of the Dirac massive particle in the Riemann-Cartan spacetime. We demonstrate that the translational and the Lorentz gravitational moments, obtained by means of the Gordon type decompositions of the canonical energy-momentum and spin currents, are consistently coupled to torsion and curvature, as expected.
We considered a model for the prompt phase of Gamma-Ray Burst (GRB) emission arising from a magnetized jet undergoing gradual energy dissipation due to magnetic reconnection. The dissipated magnetic energy is translated to bulk kinetic energy and to acceleration of particles. The energy in these particles is released via synchrotron radiation as they gyrate around the strong magnetic fields in the jet. At small radii, the optical depth is large, and the radiation is reprocessed through Comptonization into a narrow, strongly peaked, component. At larger distances the optical depth becomes small and radiation escapes the jet with a non-thermal distribution. The obtained spectra typically peak around $\approx 300$keV (as observed) and with spectral indices below and above the peak that are, for a broad range of the model parameters, close to the observed values. The small radius of dissipation causes the emission to become self absorbed at a few keV and can sufficiently suppress the optical and X-ray fluxes within the limits required by observations (Beniamini & Piran 2014).
In a recent work, Duong, Ghoul and Zaag determined the gradient profile for blowup solutions of standard semilinear heat equation with power nonlinearities in the (supposed to be) generic case. Their method refines the constructive techniques introduced by Bricmont and Kupiainen and further developed by Merle and Zaag. In this paper, we extend their refinement to the problem about the reconnection of vortex lines with the boundary in a type-II superconductor under planar approximation, a physical model derived by Chapman, Hunton and Ockendon featuring the finite time quenching for the nonlinear heat equation $$\frac{\partial h}{\partial t}=\frac{\partial^2 h}{\partial x^2}+e^{-h}-\frac{1}{h^\beta},\quad\beta>0$$ subject to initial boundary value conditions $$h(\cdot,0)=h_0>0,\quad h(\pm1,t)=1.$$ We derive the intermediate extinction profile with refined asymptotics, and with extinction time $T$ and extinction point $0$, the gradient profile behaves as $x\rightarrow0$ like $$\lim_{t\rightarrow T}\,(\nabla h)(x,t)\quad\sim\quad\frac{1}{\sqrt{2\beta}}\frac{x}{|x|}\frac{1}{\sqrt{|\log|x||}}\left[\frac{(\beta+1)^2}{8\beta}\frac{|x|^2}{|\log|x||}\right]^{\frac{1}{\beta+1}-\frac12},$$ agreeing with the gradient of the extinction profile previously derived by Merle and Zaag. Our result holds with general boundary conditions and in higher dimensions.