ShantanuT01/DACTYL-Pretraining huggingface dataset:
Quantum Hall skyrmions are quantized solitons of a ferromagnetic O(3) sigma-model. The reference, classical, solutions depend upon the interaction between the electrons and exhibit completely different asymptotic profiles for the physical Coulomb interaction than for the model hard core interaction frequently used to generate variational wavefunctions. In this note we show, by means of numerical calculations on (large) finite size systems at nu=1, that this physically important difference, crucial for a sharp definition of their statistics, persists for the quantized skyrmions at n=1.
We obtained medium-resolution ultraviolet (UV) spectra between 1150 and 1450 Angstroms of the four UV-bright, infrared (IR)-luminous starburst galaxies IRAS F08339+6517, NGC 3256, NGC 6090, and NGC 7552 using the Cosmic Origins Spectrograph onboard the Hubble Space Telescope. The selected sightlines towards the starburst nuclei probe the properties of the recently formed massive stars and the physical conditions in the starburst-driven galactic superwinds. Despite being metal-rich and dusty, all four galaxies are strong Lyman-alpha emitters with equivalent widths ranging between 2 and 13 Angstroms. The UV spectra show strong P Cygni-type high-ionization features indicative of stellar winds and blueshifted low-ionization lines formed in the interstellar and circumgalactic medium. We detect outflowing gas with bulk velocities of about 400 km/s and maximum velocities of almost 900 km/s. These are among the highest values found in the local universe and comparable to outflow velocities found in luminous Lyman-break galaxies at intermediate and high redshift. The outflow velocities are unlikely to be high enough to cause escape of material from the galactic gravitational potential. However, the winds are significant for the evolution of the galaxies by transporting heavy elements from the starburst nuclei and enriching the galaxy halos. The derived mass outflow rates of ~100 Msol/yr are comparable to, or even higher than the star-formation rates. The outflows can quench star formation and ultimately regulate the starburst as has been suggested for high-redshift galaxies.
The $^1S_0$-pairing gap in semi-infinite nuclear matter is evaluated microscopically using the effective pairing interaction recently found explicitly in the coordinate representation starting from the separable form of the Paris NN-potential. Instead of direct iterative solution of the gap equation, a new method proposed by V.A.Khodel, V.V.Khodel and J.W.Clark was used which simplifies the procedure significantly. The gap $\Delta$ obtained in our calculations exibits a strong variation in the surface region with a pronounced maximum near the surface.
We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the polyharmonic operator in a half-space. Finally, we obtain explicit solutions to Cauchy-Dirichlet problems of iterated wave- and Klein-Gordon-operators in half-spaces.
We enumerate the state diagrams of the twist knot shadow which consist of the disjoint union of two trivial knots. The result coincides with the maximal number of regions into which the plane is divided by a given number of circles. We then establish a bijection between the state enumeration and this particular partition of the plane by means of binary words.
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented.
The velocity fluctuations in a spherical shell arising from sinusoidal perturbations of a Keplerian shear flow with a free amplitude parameter \epsilon are studied numerically by means of fully 3D nonlinear simulations. The investigations are performed at high Reynolds numbers, i.e.   3000 < Re < 5000. We find Taylor-Proudman columns of large eddies parallel to the rotation axis for sufficiently strong perturbations. An instability sets in at critical amplitudes with \epsilon_crit \propto Re^-1. The whole flow turns out to be almost axisymmetric and nonturbulent exhibiting, however, a very rich radial and latitudinal structure. The Reynolds stress <u'_r u'_\phi> is positive in the entire computational domain, from its Gaussian radial profile a positive viscosity-alpha of about 10^-4 is derived. The kinetic energy of the turbulent state is dominated by the azimuthal component <u_\phi'^2> whereas the other components are smaller by two orders of magnitude. Our simulations reveal, however, that these structures disappear as soon as the perturbations are switched off. We did not find an ``effective'' perturbation whose amplitude is such that the disturbance is sustained for large times (cf. Dauchot & Daviaud 1995) which is due to the effective violation of the Rayleigh stability criterion. The fluctuations rapidly smooth the original profile towards to pure Kepler flow which, therefore, proves to be stable in that sense.
It is well known that the Chern classes $c_i$ of a rank $n$ vector bundle on $\PP^N$, generated by global sections, are non-negative if $i\leq n$ and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers $c_i$ with $i\geq 4$ can be arbitrarily negative for reflexive sheaves of any rank; on the contrary for $i\leq 3$ we show positivity of the $c_i$ with weaker hypothesis. We obtain lower bounds for $c_1$, $c_2$ and $c_3$ for every reflexive sheaf $\FF$ which is generated by $H^0\FF$ on some non-empty open subset and completely classify sheaves for which either of them reach the minimum allowed, or some value close to it.
Upsampling videos of human activity is an interesting yet challenging task with many potential applications ranging from gaming to entertainment and sports broadcasting. The main difficulty in synthesizing video frames in this setting stems from the highly complex and non-linear nature of human motion and the complex appearance and texture of the body. We propose to address these issues in a motion-guided frame-upsampling framework that is capable of producing realistic human motion and appearance. A novel motion model is trained to inference the non-linear skeletal motion between frames by leveraging a large-scale motion-capture dataset (AMASS). The high-frame-rate pose predictions are then used by a neural rendering pipeline to produce the full-frame output, taking the pose and background consistency into consideration. Our pipeline only requires low-frame-rate videos and unpaired human motion data but does not require high-frame-rate videos for training. Furthermore, we contribute the first evaluation dataset that consists of high-quality and high-frame-rate videos of human activities for this task. Compared with state-of-the-art video interpolation techniques, our method produces in-between frames with better quality and accuracy, which is evident by state-of-the-art results on pixel-level, distributional metrics and comparative user evaluations. Our code and the collected dataset are available at https://git.io/Render-In-Between.
For large dimensional non-Hermitian random matrices $X$ with real or complex independent, identically distributed, centered entries, we consider the fluctuations of $f(X)$ as a matrix where $f$ is an analytic function around the spectrum of $X$. We prove that for a generic bounded square matrix $A$, the quantity $\mathrm{Tr}f(X)A$ exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of $A$. We find a new formula for the variance of the traceless part that involves the Frobenius norm of $A$ and the $L^{2}$-norm of $f$ on the boundary of the limiting spectrum.
Hydrodynamical simulations of galaxy formation such as the Illustris simulations have progressed to a state where they approximately reproduce the observed stellar mass function from high to low redshift. This in principle allows self-consistent models of reionization that exploit the accurate representation of the diffuse gas distribution together with the realistic growth of galaxies provided by these simulations, within a representative cosmological volume. In this work, we apply and compare two radiative transfer algorithms implemented in a GPU-accelerated code to the $106.5\,{\rm Mpc}$ wide volume of Illustris in postprocessing in order to investigate the reionization transition predicted by this model. We find that the first generation of galaxies formed by Illustris is just about able to reionize the universe by redshift $z\sim 7$, provided quite optimistic assumptions about the escape fraction and the resolution limitations are made. Our most optimistic model finds an optical depth of $\tau\simeq 0.065$, which is in very good agreement with recent Planck 2015 determinations. Furthermore, we show that moment-based approaches for radiative transfer with the M1 closure give broadly consistent results with our angular-resolved radiative transfer scheme. In our favoured fiducial model, 20\% of the hydrogen is reionized by redshift $z=9.20$, and this rapidly climbs to 80\% by redshift $z=6.92$. It then takes until $z=6.24$ before 99\% of the hydrogen is ionized. On average, reionization proceeds `inside-out' in our models, with a size distribution of reionized bubbles that progressively features regions of ever larger size while the abundance of small bubbles stays fairly constant.
We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing crossing paths and exibiting dependence before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.
The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin, and respects Kramers degeneracy for time-reversal invariant systems. It is tested for various models, in particular the Lipkin-Meshkov-Glick model, and found to agree very well with exact results.
We present a high-resolution spectral analysis of Betelgeuse (M2 Iab). Between 1998 January and 1999 March four spatially resolved raster scans (http://cfa-www.harvard.edu/cfa/ep/pressrel/alobel0100.html) have been obtained with the STIS on the Hubble Space Telescope. The near-UV echelle spectra reveal double-peaked permitted emission lines of neutral and singly ionized metals, with self-absorbed line cores. We observe reversals in the intensity of both emission line components when scanning across the UV disk, for four unsaturated lines of Si I, Fe I, Al II], and Fe II. We model the Si I lam2516 resonance line with detailed non-LTE radiative transport calculations in spherical geometry, and constrain the mean velocity structure in the projected aperture area, for each scan position on the chromospheric disk. We infer the spatial velocity structure of Betelgeuse's extended chromosphere, which reveals localized upflows in the western front hemisphere in 1998 September, that expand further toward the eastern hemisphere in 1999 March. The spatial scans exhibit simultaneous up- and downflows across the lower chromosphere with mean velocities of ~2 km/s. We infer non-radial (or non-coherent) mass movements during certain phases of the stellar variability cycle from these subsonic flows. We present a discussion of constructing semi-empiric models for the chromosphere of this cool supergiant, and of its temporal variability.
We investigate the local density of states and Friedel oscillation in graphene around a well localized impurity in Born approximation. In our analytical calculations Green's function technique has been used taking into account both the localized atomic wavefunctions in a tight-binding scheme and the corresponding symmetries of the lattice. As a result we obtained long wavelength oscillations in the density of electrons with long range behavior proportional to the inverse square of the distance from the impurity. These leading oscillations are out of phase on nearby lattice sites (in fact for an extended defect they cancel each other within one unit cell), therefore a probe with resolution worse than a few unit cells will experience only the next to leading inverse cube decay of density oscillations even for a short range scatterer.
We present NH3 observations of the B5 region in Perseus obtained with the Green Bank Telescope (GBT). The map covers a region large enough (~11'x14') that it contains the entire dense core observed in previous dust continuum surveys. The dense gas traced by NH3(1,1) covers a much larger area than the dust continuum features found in bolometer observations. The velocity dispersion in the central region of the core is small, presenting subsonic non-thermal motions which are independent of scale. However, it is thanks to the coverage and high sensitivity of the observations that we present the detection, for the first time, of the transition between the coherent core and the dense but more turbulent gas surrounding it. This transition is sharp, increasing the velocity dispersion by a factor of 2 in less than 0.04 pc (the 31" beam size at the distance of Perseus, ~250 pc). The change in velocity dispersion at the transition is ~3 km/s/pc. The existence of the transition provides a natural definition of dense core: the region with nearly-constant subsonic non-thermal velocity dispersion. From the analysis presented here we can not confirm nor rule out a corresponding sharp density transition.
Preface, introduction and contents to the book "Theory of Quantum Transport at Nanoscale", published in 2016 by Springer, the author version.
This paper gives a rather concrete description of the category Rep(G) for certain flat commutative affine group schemes G over a discrete valuation ring such that the general fiber of G is the multiplicative group.
We present X-ray spectral fits to a recently obtained Chandra grating spectrum of Eta Carinae, one of the most massive and powerful stars in the Galaxy and which is strongly suspected to be a colliding wind binary system. Hydrodynamic models of colliding winds are used to generate synthetic X-ray spectra for a range of mass-loss rates and wind velocities. They are then fitted against newly acquired Chandra grating data. We find that due to the low velocity of the primary wind (~500 km/s), most of the observed X-ray emission appears to arise from the shocked wind of the companion star. We use the duration of the lightcurve minimum to fix the wind momentum ratio at 0.2. We are then able to obtain a good fit to the data by varying the mass-loss rate of the companion and the terminal velocity of its wind. We find that Mdot ~ 1e-5 Msol/yr and v ~ 3000 km/s. With observationally determined values of ~500-700 km/s for the velocity of the primary wind, our fit implies a primary mass-loss rate of Mdot ~ 2.5e-4 Msol/yr. This value is smaller than commonly inferred, although we note that a lower mass-loss rate can reduce some of the problems noted by Hillier et al. (2001) when a value as high as 1e-3 Msol/yr is used. The wind parameters of the companion are indicative of a massive star which may or may not be evolved. The line strengths appear to show slightly sub-solar abundances, although this needs further confirmation. Based on the over-estimation of the X-ray line strengths in our model, and re-interpretation of the HST/FOS results, it appears that the homunculus nebula was produced by the primary star.
We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a previous approach are made, showing where its assumption of uniform local fields breaks down for networks with nodes of low degree.
We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylindrical radius R_j. We find that equilibria in which the Lorentz factor \gamma(R) increases monotonically with increasing radius R are stable. On the other hand, equilibria in which \gamma(R) reaches a maximum value at an intermediate radius and then declines to a smaller value \gamma_j at R_j are unstable. The most rapidly growing mode is an m=1 kink instability which has a growth rate ~ (0.4 / \gamma_j) (c/R_j). The e-folding length of the equivalent convected instability is ~2.5 \gamma_j R_j. For a typical jet with an opening angle \theta_j ~ few / \gamma_j, the mode amplitude grows weakly with increasing distance from the base of the jet, much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion.
An unusual atomic scale chemical fluctuation in LaSrVMoO$_6$, in terms of narrow patches of La,V and Sr,Mo-rich phases, has been probed in detail to understand the origin of such a chemical state. Exhaustive tuning of the equilibrium synthesis parameters showed that the extent of phase separation can never be melted down below an unit cell dimension making it impossible to achieve the conventional $B$-site ordered structure, which establishes that the observed `inhomogeneous' patch-like structure with minimum dimension of few angstroms is a reality in LaSrVMoO$_6$. Therefore, another type of local chemical order, hitherto unknown in double perovskites, gets introduced here. X-ray diffraction, electron microscopy elemental mapping, magnetic, and various spectroscopic studies have been carried out on samples, synthesized under different conditions. These experimental results in conjunction with {\it ab-initio} electronic structure calculation revealed that it is the energy stability, gained by typical La-O covalency as in LaVO$_3$, that leads to the preferential La,V and Sr,Mo ionic proximity, and the consequent patchy structure.
Dwarf spheroidal galaxies of the Local Group obey a relationship between the line-of-sight velocity dispersion and half-light radius, although there are a number of dwarfs that lie beneath this relation with suppressed velocity dispersion. The most discrepant of these (in the Milky Way) is the `feeble giant' Crater II. Using analytic arguments supported by controlled numerical simulations of tidally-stripped flattened two-component dwarf galaxies, we investigate interpretations of Crater II within standard galaxy formation theory. Heavy tidal disruption is necessary to explain the velocity-dispersion suppression which is plausible if the proper motion of Crater II is $(\mu_{\alpha*},\mu_\delta)=(-0.21\pm0.09,-0.24\pm0.09)\mathrm{mas\,yr}^{-1}$. Furthermore, we demonstrate that the velocity dispersion of tidally-disrupted systems is solely a function of the total mass loss even for weakly-embedded and flattened systems. The half-light radius evolution depends more sensitively on orbital phase and the properties of the dark matter profile. The half-light radius of weakly-embedded cusped systems rapidly decreases producing some tension with the Crater II observations. This tension is alleviated by cored dark matter profiles, in which the half-light radius can grow after tidal disruption. The evolution of flattened galaxies is characterised by two competing effects: tidal shocking makes the central regions rounder whilst tidal distortion produces a prolate tidally-locked outer envelope. After $\sim70$ per cent of the central mass is lost, tidal distortion becomes the dominant effect and the shape of the central regions of the galaxy tends to a universal prolate shape irrespective of the initial shape.
In the Minimal Supersymmetric Standard Model, the higgsinos can have masses around the electroweak scale, while the other supersymmetric particles have TeV-scale masses. This happens in models of gauge-mediated SUSY breaking with a high messenger scale, which are motivated from string theory. For particular choices of the messenger field content, multi-TeV squark and gluino masses naturally lead to a much lower electroweak scale, somewhat similar to focus point supersymmetry. They also induce Higgs masses of 124-126 GeV, while making the discovery of supersymmetry at the LHC unlikely. The light higgsinos will be difficult to see at the LHC but may eventually be discovered at a linear collider.
For fixed positive integers $r, k$ and $\ell$ with $1 \leq \ell < r$ and an $r$-uniform hypergraph $H$, let $\kappa (H, k,\ell)$ denote the number of $k$-colorings of the set of hyperedges of $H$ for which any two hyperedges in the same color class intersect in at least $\ell$ elements. Consider the function $\KC(n,r,k,\ell)=\max_{H\in{\mathcal H}_{n}} \kappa (H, k,\ell) $, where the maximum runs over the family ${\mathcal H}_n$ of all $r$-uniform hypergraphs on $n$ vertices. In this paper, we determine the asymptotic behavior of the function $\KC(n,r,k,\ell)$ for every fixed $r$, $k$ and $\ell$ and describe the extremal hypergraphs. This variant of a problem of Erd\H{o}s and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erd\H{o}s--Ko--Rado Theorem on intersecting systems of sets [Intersection Theorems for Systems of Finite Sets, Quarterly Journal of Mathematics, Oxford Series, Series 2, {\bf 12} (1961), 313--320].
We investigate how the X-ray circumgalactic medium (CGM) of present-day galaxies depends on galaxy morphology and azimuthal angle using mock observations generated from the EAGLE cosmological hydrodynamic simulation. By creating mock stacks of {\it eROSITA}-observed galaxies oriented to be edge-on, we make several observationally-testable predictions for galaxies in the stellar mass range $M_\star=10^{10.7-11.2}\;$M$_{\odot}$. The soft X-ray CGM of disc galaxies is between 60 and 100\% brighter along the semi-major axis compared to the semi-minor axis, between 10-30 kpc. This azimuthal dependence is a consequence of the hot ($T>10^6$ K) CGM being non-spherical: specifically it is flattened along the minor axis such that denser and more luminous gas resides in the disc plane and co-rotates with the galaxy. Outflows enrich and heat the CGM preferentially perpendicular to the disc, but we do not find an observationally-detectable signature along the semi-minor axis. Spheroidal galaxies have hotter CGMs than disc galaxies related to spheroids residing at higher halos masses, which may be measurable through hardness ratios spanning the $0.2-1.5$ keV band. While spheroids appear to have brighter CGMs than discs for the selected fixed $M_\star$ bin, this owes to spheroids having higher stellar and halo masses within that $M_\star$ bin, and obscures the fact that both simulated populations have similar total CGM luminosities at the exact same $M_\star$. Discs have brighter emission inside 20 kpc and more steeply declining profiles with radius than spheroids. We predict that the {\it eROSITA} 4-year all-sky survey should detect many of the signatures we predict here, although targeted follow-up observations of highly inclined nearby discs after the survey may be necessary to observe some of our azimuthally-dependent predictions.