ShantanuT01/DACTYL-Pretraining huggingface dataset:
Two-dimensional magnetic skyrmions are particle-like magnetic domains in magnetic thin films. The kinetic property of the magnetic skyrmions at finite temperature is well described by the Thiele equation, including a stochastic field and a finite mass. In this paper, the validity of the constant-mass approximation is examined by comparing the Fourier spectrum of Brownian motions described by the Thiele equation and the Landau-Lifshitz-Gilbert equation. Then, the 4-dimensional Fokker-Planck equation is derived from the Thiele equation with a mass-term. Consequently, an expression of the diffusion flow and diffusion constant in a tensor form is derived, extending Chandrasekhar's method for Thiele dynamics.
Globular cluster age estimates based on the absolute magnitude of the main sequence turn-off (\mvto) are generally considered to be the most reliable from a theoretical viewpoint. However, the difficulty in determining \mvto\ in observed colour-magnitude diagrams leads to a large error in the derived age. In this paper, we advocate the use of the absolute magnitude of the point which is brighter than the turn-off and 0.05 mag redder (\mvb) as a precision age indicator. It is easy to measure this point on observed colour-magnitude diagrams, leading to small observational error bars. Furthermore, an extensive Monte Carlo calculation indicates that the theoretical uncertainty in \mvb\ is similar to \mvto. As a result, ages derived using \mvb\ are at least a factor of 2 more precise than those derived using \mvto. This technique is applied to the globular cluster M68 and an age of $12.8\pm 0.3\,$Gyr is derived (assuming $\mvrr = 0.20\,\feh + 0.98$), indicating that M68 is a `young' globular cluster. A homogeneous set of globular cluster age estimates with this precision would provide unprecedented insight into the formation of the Galactic halo.
The variational theory of the perfect fluid with intrinsic spin and dilatonic charge (dilaton-spin fluid) is developed. The spin tensor obeys the classical Frenkel condition. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid, the Weyssenhoff-type evolution equation of the spin tensor and the conservation law of the dilatonic charge are derived. The expressions of the matter currents of the fluid (the canonical energy-momentum 3-form, the metric stress-energy 4-form and the dilaton-spin momentum 3-form) are obtained.
For nearly a decade, the COCO dataset has been the central test bed of research in object detection. According to the recent benchmarks, however, it seems that performance on this dataset has started to saturate. One possible reason can be that perhaps it is not large enough for training deep models. To address this limitation, here we introduce two complementary datasets to COCO: i) COCO_OI, composed of images from COCO and OpenImages (from their 80 classes in common) with 1,418,978 training bounding boxes over 380,111 images, and 41,893 validation bounding boxes over 18,299 images, and ii) ObjectNet_D containing objects in daily life situations (originally created for object recognition known as ObjectNet; 29 categories in common with COCO). The latter can be used to test the generalization ability of object detectors. We evaluate some models on these datasets and pinpoint the source of errors. We encourage the community to utilize these datasets for training and testing object detection models. Code and data is available at https://github.com/aliborji/COCO_OI.
Rare kaon processes appear to be particularly suitable to study the extensions of the standard model, especially if the possibility for eventual direct evidence becomes unlikely. In this review, we discuss processes that are important as a test of either the standard model or supergravity. Moreover, some of these are important even for both the standard model and for supergravity. Particular attention is paid to the reduction of uncertainties in the calculation, especially the ones coming from the confinement effects. Recent approaches, such as chiral perturbation theory, the large $N_c$-expansion, QCD sum rules and lattice QCD, are discussed. This is found to be the best strategy in view of the fact that supersymmetric effects are rather tiny.
To investigate the nature and properties of far-infrared (FIR) sources from the AKARI Deep Field South (ADF-S), we performed an extensive search for the counterparts of 1000 ADF-S objects brighter than 0.0301 Jy in the WIDE-S (90 $\mu$m) AKARI band in the public databases (NED and SIMBAD). We analyzed the properties of the resulting sample: statistic of the identified objects, number counts, redshift distribution and morphological types. We also made a crude analysis of the clustering properties of the sources and constructed spectral energy distributions (SEDs) of 47 selected objects with the best photometry. Among 1000 investigated ADF-S sources, 545 were identified at other wavelengths. From them, 518 are known galaxies, and 343 of them were not known previously as infra-red sources. We found redshifts of 48 extragalactic objects and morphological types of 77 galaxies. We conclude that the bright FIR point sources observed in the ADF-S are mostly nearby galaxies.Their properties are very similar to properties of the local population of optically bright galaxies, except an unusually high ratio of peculiar or interacting objects and a smaller percentage of elliptical galaxies. The percentage of lenticular galaxies is the same as in the optically bright population which suggests they may frequently contain a significant amount of cool dust. It is possible that source confusion plays a significant role in more than 34% of measurements. The SEDs display a variety of galaxy types, from very actively star forming to very quiescent. Thanks to the AKARI long wavelength bands it was revealed for the first time that these galaxies form a population of objects with very cool dust.
The main purpose of this work is to provide a Hilbertian functional framework for the analysis of the planar Navier-Stokes (NS) equations either in vorticity or in stream function formulation. The fluid is assumed to occupy a bounded possibly multiply connected domain. The velocity field satisfies either homogeneous (no-slip boundary conditions) or prescribed Dirichlet boundary conditions. We prove that the analysis of the 2D Navier-Stokes equations can be carried out in terms of the so-called nonprimitive variables only (vorticity field and stream function) without resorting to the classical NS theory (stated in primitive variables, i.e. velocity and pressure fields). Both approaches (in primitive and nonprimitive variables) are shown to be equivalent for weak (Leray) and strong (Kato) solutions. Explicit Bernoulli-like formulas are derived and allow recovering the pressure field from the vorticity fields or the stream function. In the last section, the functional framework described earlier leads to a simplified rephrasing of the vorticity dynamics, as introduced by Maekawa in [52]. At this level of regularity, the vorticity equation splits into a coupling between a parabolic and an elliptic equation corresponding respectively to the non-harmonic and harmonic parts of the vorticity equation. By exploiting this structure it is possible to prove new existence and uniqueness results, as well as the exponential decay of the palinstrophy (that is, loosely speaking, the $H^1$ norm of the vorticity) for large time, an estimate which was not known so far.
We report on observations of the nova-like cataclysmic variable AE Aqr performed by MAGIC. The observations were part of a quasi-simultaneous multi-wavelength campaign carried out between 2012 May and June covering the optical, UV, X-ray and gamma-ray ranges. MAGIC conducted the campaign and observed the source during 12 hours. The other instruments involved were KVA, Skinakas, and Vidojevica in the optic and Swift in the X-ray. We also used optical data from the AAVSO. The goals were to: monitor the variability of the source at different wavelengths, perform gamma-ray studies coincident with the highest states of the source at the other wavelengths, and confirm or rule out previous claims of detection of very-high-energy emission from this object. We report on a search for steady TeV emission during the whole observation, for variable TeV emission coincident with the highest optical and X-ray states and periodic TeV emission at the 33.08 s rotation period (30.23 mHz rotation frequency) of the white dwarf and its first harmonic (60.46 mHz rotation frequency). These are the first observations under good weather conditions performed by the present generation of IACTs for this object.
We prove that classical jittered sampling of the $d$-dimensional unit cube does not yield the smallest expected $\mathcal{L}_2$-discrepancy among all stratified samples with $N=m^d$ points. Our counterexample can be given explicitly and consists of convex partitioning sets of equal volume.
It is a long-standing question of Stanley whether or not the chromatic symmetric function (CSF) distinguishes unrooted trees. Previously, the best computational result, due to Russell, proved that it distinguishes all trees with at most $25$ vertices. In this paper, we present a novel probabilistic algorithm which may be used to check more efficiently that the CSF distinguishes a set of trees. Applying it, we verify that the CSF distinguishes all trees with up to $29$ vertices.
Submillimetre galaxies (SMGs) have long posed a challenge for theorists, and self-consistently reproducing the properties of the SMG population in a large-volume cosmological hydrodynamical simulation has not yet been achieved. We use a scaling relation derived from previous simulations plus radiative transfer calculations to predict the submm flux densities of simulated SMGs drawn from cosmological simulations from the Illustris and IllustrisTNG projects based on the simulated galaxies' star formation rates (SFRs) and dust masses and compare the predicted number counts with observations. We find that the predicted SMG number counts based on IllustrisTNG are significantly less than observed (more than 1 dex at $S_{850} \gtrsim 4$ mJy). The simulation from the original Illustris project yields more SMGs than IllustrisTNG: the predicted counts are consistent with those observed at both $S_{850} \lesssim 5$ mJy and $S_{850} \gtrsim 9$ mJy and only a factor of $\sim 2$ lower than observed at intermediate flux densities. The redshift distribution of SMGs with $S_{850} > 3$ mJy in IllustrisTNG is consistent with the observed distribution, whereas the Illustris redshift distribution peaks at significantly lower redshift (1.5 vs. 2.8). We demonstrate that IllustrisTNG hosts fewer SMGs than Illustris because in the former, high-mass ($M_{\star} \sim 10^{11} \, \text{M}_{\odot}$) $z \sim 2-3$ galaxies have lower dust masses and SFRs than in Illustris owing to differences in the sub-grid models for stellar or/and active galactic nucleus (AGN) feedback between the two simulations (we unfortunately cannot isolate the specific cause(s) post hoc). Our results demonstrate that because our method enables predicting SMG number counts in post-processing with a negligible computational expense, SMGs can provide useful constraints for tuning sub-grid models in future large-volume cosmological simulations.
We prove that function fields of varieties of dimension at least two over an algebraic closure of a finite field are determined, modulo purely inseparable extensions, by the quotient by the second term in the lower central series of their pro-$\ell$ Galois groups.
We study the one-loop effective action for $N$ 4D conformally invariant scalars on the spherically symmetric background. The main part of effective action is given by integration of 4D conformal anomaly. This effective action (in large $N$ approximation and partial curvature expansion) is applied to investigate the quantum evolution of Schwarzschild-de Sitter (SdS) black holes of maximal mass. We find that the effect (recently discovered by Bousso and Hawking for $N$ minimal scalars and another approximate effective action) of anti-evaporation of nearly maximal SdS (Nariai) black holes takes also place in the model under consideration. Careful treatment of quantum corrections and perturbations modes of Nariai black hole is given being quite complicated. It is shown that exists also perturbation where black hole radius shrinks, i.e. black hole evaporates. We point out that our result holds for wide class of models including conformal scalars, spinors and vectors. Hence,anti-evaporation of SdS black holes is rather general effect which should be taken into account in quantum gravity considerations.
We give in this Chapter an overview of the problem of neutron star mass distribution, the issue of the maximum mass as inferred from the existing sample and the new gravitational wave events, and the connection with the formation events. It is shown that at least two different mass-scales (and possibly three) are favored by Bayesian and frequentist analysis, and the resulting maximum mass on empirical grounds only is $\sim 2.5 M_{\odot}$, making room for an interpretation of the lighter component of the GW190408 merger as a neutron star (as suggested by the GW event population analysis). We discuss in some length the challenges for a theoretical construction of a stiff equation of state and the status of available supernova explosions (single and binary simulations) and AIC expected to provide the masses at birth.
We derive expressions for the critical density for jamming in a hyper-rhomboid system of arbitrary shape in any dimension for the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models. We find that changing the system's shape without altering its total volume or particle density may induce jamming. We also find a transition between shapes in which the correlation length between jammed particles is infinite, and shapes that have a finite correlation length.
For a complex toric variety $X$ the logarithmic absolute value induces a natural retraction of $X$ onto the set of its non-negative points and this retraction can be identified with a quotient of $X(\mathbb{C})$ by its big real torus. We prove an analogous result in the non-Archimedean world: The Kajiwara-Payne tropicalization map is a non-Archimedean analytic stack quotient of $X^{an}$ by its big affinoid torus. Along the way, we provide foundations for a geometric theory of non-Archimedean analytic stacks, particularly focussing on analytic groupoids and their quotients, the process of analytification, and the underlying topological spaces of analytic stacks.
Properties of galaxies vary systematically with the mass of their parent dark matter halos. This basic galaxy - halo connection shows a fair amount of scatter whose origin is not fully understood. Here, we study how differences in the halo assembly history affect central galaxies in low mass (M_halo < 10^12 M_sun) halos at z=2-6 with the help of the MassiveFIRE suite of cosmological simulations. In contrast to previous works that tie galaxy properties to halo concentration and halo formation redshift, we focus on halo growth rate as a measure of assembly history. We find that, at fixed halo mass, faster growing halos tend to have lower stellar masses and higher SFRs per unit stellar mass but similar overall SFRs. We provide a simple explanation for these findings with the help of an analytic model that captures approximately the behavior of our hydrodynamical simulations. Specifically, among halos of a given current mass, quickly growing halos have lower stellar masses (and thus higher sSFRs) because they were less massive and had comparably lower cold gas masses and SFRs in the past than slowly growing halos. By combining these findings with estimates for the scatter of the halo growth rate, we show that variations in growth rate at fixed halo mass may largely explain the scatter of the stellar mass - halo mass relation. In contrast, halo growth variations likely play only a minor role in the scatter of the star forming sequence in low mass galaxies.
In this work, we investigate the correspondence between the Erez-Rosen and Hartle-Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe the gravitational field of static objects. Since both the Erez-Rosen and the Hartle-Thorne solutions are particular solutions of a more general solution, the Zipoy-Voorhees transformation is applied to the exact Erez-Rosen metric in order to obtain a generalized solution in terms of the Zipoy-Voorhees parameter $\delta=1+sq$. The Geroch-Hansen multipole moments of the generalized Erez-Rosen metric are calculated to find the definition of the total mass and quadrupole moment in terms of the mass $m$, quadrupole $q$ and Zipoy-Voorhees $\delta$ parameters. The coordinate transformations between the metrics are found in the approximation of $\sim$q. It is shown that the Zipoy-Voorhees parameter is equal to $\delta=1-q$ with $s=-1$. This result is in agreement with previous results in the literature.
In order to assess inelastic effects on two fermion entanglement production, we address an exactly solvable two-particle scattering problem where the target is an excitable scatterer. Useful entanglement, as measured by the two particle concurrence, is obtained from post-selection of oppositely scattered particle states. The $S$ matrix formalism is generalized in order to address non-unitary evolution in the propagating channels. We find the striking result that inelasticity can actually increase concurrence as compared to the elastic case by increasing the uncertainty of the single particle subspace. Concurrence zeros are controlled by either single particle resonance energies or total reflection conditions that ascertain precisely one of the electron states. Concurrence minima also occur and are controlled by entangled resonance situations were the electron becomes entangled with the scatterer, and thus does not give up full information of its state. In this model, exciting the scatterer can never fully destroy phase coherence due to an intrinsic limit to the probability of inelastic events.
We perform time-dependent simulations of spin exchange for an electron pair in laterally coupled quantum dots. The calculation is based on configuration interaction scheme accounting for spin-orbit (SO) coupling and electron-electron interaction in a numerically exact way. Noninteracting electrons exchange orientations of their spins in a manner that can be understood by interdot tunneling associated with spin precession in an effective SO magnetic field that results in anisotropy of the spin swap. The Coulomb interaction blocks the electron transfer between the dots but the spin transfer and spin precession due to SO coupling is still observed. The electron-electron interaction additionally induces an appearance of spin components in the direction of the effective SO magnetic field which are opposite in both dots. Simulations indicate that the isotropy of the spin swap is restored for equal Dresselhaus and Rashba constants and properly oriented dots.
During the September-October 2008 outburst of the accreting millisecond pulsar SAX J1808.4-3658, the source was observed by both Suzaku and XMM-Newton approximately 1 day apart. Spectral analysis reveals a broad relativistic Fe K-alpha emission line which is present in both data-sets, as has recently been reported for other neutron star low-mass X-ray binaries. The properties of the Fe K line observed during each observation are very similar. From modeling the Fe line, we determine the inner accretion disk radius to be 13.2 +/- 2.5 GM/c^2. The inner disk radius measured from the Fe K line suggests that the accretion disk is not very receded in the island state. If the inner disk (as measured by the Fe line) is truncated at the magnetospheric radius this implies a magnetic field strength of ~3E8 G at the magnetic poles, consistent with other independent estimates.
We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky(ST). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but go well beyond.We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.
We study the problem of identification of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a fixed Markov process $M$ on a Riemannian manifold $X$. The main problem arising here is a possible collapse of the system, in the sense that, though the initial configuration of particles is locally finite, there could exist a compact set in $X$ such that, with probability one, infinitely many particles will arrive at this set at some time $t>0$. We assume that $X$ has infinite volume and, for each $\alpha\ge1$, we consider the set $\Theta_\alpha$ of all infinite configurations in $X$ for which the number of particles in a compact set is bounded by a constant times the $\alpha$-th power of the volume of the set. We find quite general conditions on the process $M$ which guarantee that the corresponding infinite particle process can start at each configuration from $\Theta_\alpha$, will never leave $\Theta_\alpha$, and has cadlag (or, even, continuous) sample paths in the vague topology. We consider the following examples of applications of our results: Brownian motion on the configuration space, free Glauber dynamics on the configuration space (or a birth-and-death process in $X$), and free Kawasaki dynamics on the configuration space. We also show that if $X=\mathbb R^d$, then for a wide class of starting distributions, the (non-equilibrium) free Glauber dynamics is a scaling limit of (non-equilibrium) free Kawasaki dynamics.