ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present magnetohydrodynamic simulation of the evolution from quasi-equilibrium to onset of eruption of a twisted, prominence-forming coronal magnetic flux rope underlying a corona streamer. The flux rope is built up by an imposed flux emergence at the lower boundary. During the quasi-static phase of the evolution, we find the formation of a prominence-cavity system with qualitative features resembling observations, as shown by the synthetic SDO/AIA EUV images with the flux rope observed above the limb viewed nearly along its axis. The cavity contains substructures including ``U''-shaped or horn-liked features extending from the prominence enclosing a central ``cavity'' on top of the prominence. The prominence condensations form in the dips of the highly twisted field lines due to runaway radiative cooling and the cavity is formed by the density depleted portions of the prominence-carrying field lines extending up from the dips. The prominence ``horns'' are threaded by twisted field lines containing shallow dips, where the prominence condensations have evaporated to coronal temperatures. The central ``cavity'' enclosed by the horns is found to correspond to a central hot and dense core containing twisted field lines that do not have dips. The flux rope eventually erupts as its central part rises quasi-statically to a critical height consistent with the onset of the torus instability. The erupting flux rope accelerates to a fast speed of nearly 900 km/s and the associated prominence eruption shows significant rotational motion and a kinked morphology.
By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H\"{o}lder continuous drift coefficients. An example is also provided to explain our result.
The ability to handle outliers is essential for performing the perspective-n-point (PnP) approach in practical applications, but conventional RANSAC+P3P or P4P methods have high time complexities. We propose a fast PnP solution named R1PPnP to handle outliers by utilizing a soft re-weighting mechanism and the 1-point RANSAC scheme. We first present a PnP algorithm, which serves as the core of R1PPnP, for solving the PnP problem in outlier-free situations. The core algorithm is an optimal process minimizing an objective function conducted with a random control point. Then, to reduce the impact of outliers, we propose a reprojection error-based re-weighting method and integrate it into the core algorithm. Finally, we employ the 1-point RANSAC scheme to try different control points. Experiments with synthetic and real-world data demonstrate that R1PPnP is faster than RANSAC+P3P or P4P methods especially when the percentage of outliers is large, and is accurate. Besides, comparisons with outlier-free synthetic data show that R1PPnP is among the most accurate and fast PnP solutions, which usually serve as the final refinement step of RANSAC+P3P or P4P. Compared with REPPnP, which is the state-of-the-art PnP algorithm with an explicit outliers-handling mechanism, R1PPnP is slower but does not suffer from the percentage of outliers limitation as REPPnP.
Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.
N-doped SrO seems to be one of the model systems for d^0 magnetism, in which magnetism (or ideally, ferromagnetism) was ascribed to the localized N 2p spins mediated by delocalized O 2p holes. Here we offer a different view, using density functional calculations. We find that N-doped SrO with solely substitutional N impurities as widely assumed in the literature is unstable, and instead that a pairing state of substitutional and interstitial N impurities is significantly more stable and has a much lower formation energy than the former by 6.7 eV. The stable (N_{sub}-N_{int})^{2-} dimers behave like a charged (N_2)^{2-} molecule and have each a molecular spin=1. However, their spin-polarized molecular levels lie well inside the wide band gap of SrO and thus the exchange interaction is negligibly weak. As a consequence, N-doped SrO could not be ferromagnetic but paramagnetic.
We study properties of ultra-cold bosonic atoms in one, two and three dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose Hubbard model in parabolic confinement potentials. Local phase structures of the atoms are shown to be accessible via a well defined local compressibility, quantifying a global response of the system to a local perturbation. An indicator for the presence of extended Mott plateaux is shown to stem from the shape of the coherent component of the momentum distribution function, amenable to experimental detection. Additional fine structures in the momentum distribution are found to appear unrelated to the local phase structure, disproving previous claims. We discuss limitations of local potential approximations for confined Bose gases, and the absence of quantum criticality and critical slowing down in parabolic confinement potentials, thus accounting for the fast dynamics in establishing phase coherence in current experiments. In contrast, we find that flat confinement potentials allow quantum critical behavior to be observed already on moderately sized optical lattices. Our results furthermore demonstrate, that the experimental detection of the Mott transition would be significantly eased in flat confinement potentials.
We consider the entropy of four-dimensional near-extremal N=2 black holes. Without R^2-terms, the Bekenstein-Hawking entropy formula has the structure of the extremal black holes entropy with a shift of the charges depending on the non-extremality parameter and the moduli at infinity. We derive a generalized Wald entropy formula for non-extremal N=2 black holes with R^2-terms. We construct a class of small near-extremal horizon solutions with R^2-terms. In this case the entropy is the same as in the extremal case to order O(mu^2), and does not exhibit the charge shift behavior.
The nature of an emerging class of rapidly fading supernovae (RFSNe)--characterized by their short-lived light curve duration, but varying widely in peak brightness--remains puzzling. Whether the RFSNe arise from low-mass thermonuclear eruptions on white dwarfs or from the core collapse of massive stars is still a matter of dispute. We explore the possibility that the explosion of hydrogen-free massive stars could produce bright but rapidly fading transients if the effective pre-supernova radii are large and if little or no radioactive nickel is ejected. The source of radiation is then purely due to shock cooling. We study this model of RFSNe using spherically symmetric hydrodynamics and radiation transport calculations of the explosion of stripped stars embedded in helium-dominated winds or shells of various masses and extent. We present a parameter study showing how the properties of the circumstellar envelopes affect the dynamics of the explosion and can lead to a diversity of light curves. We also explore the dynamics of the fallback of the innermost stellar layers, which might be able to remove radioactive nickel from the ejecta, making the rapid decline in the late time light curve possible. We provide scaling relations that describe how the duration and luminosity of these events depend on the supernova kinetic energy and the mass and radius of the circumstellar material.
We construct weak solutions to a class of distribution dependent SDE, of type   $dX(t)=b\left( X(t), \displaystyle\frac{d\mathcal{L}_{X(t)}}{dx}(X(t))\right) dt+\sigma\left( X(t),\displaystyle\frac{d\mathcal{L}_{X(t)}}{dt}(X(t))\right) dW(t)$   for possibly degenerate diffusion matrices $\sigma$ with $X(0)$ having a given law, which has a density with respect to Lebesgue measure, $dx$. Here ${\mathcal{L}}_{X(t)}$ denotes the law of $X(t)$. Our approach is to first solve the corresponding nonlinear Fokker-Planck equations and then use the well known superposition principle to obtain weak solutions of the above SDE.
CONTEXT. The ESO archive of FORS1 spectropolarimetric observations may be used to create a homogeneous database of magnetic field measurements. However, no systematic comparison of FORS field measurements to those obtained with other instruments has been undertaken so far. AIMS. We exploit the FORS archive of circular spectropolarimetric data to examine in a general way how reliable and accurate field detections obtained with FORS are. METHODS. We examine the observations of Ap and Bp stars, on the grounds that almost all of the unambiguous detections of magnetic fields in the FORS1 archive are in these kinds of stars. We assess the overall quality of the FORS1 magnetic data by examining the consistency of field detections with what is known from previous measurements obtained with other instruments, and we look at patterns of internal consistency. RESULTS. FORS1 magnetic measurements are fully consistent with those made with other instruments, and the internal consistency of the data is excellent. However, it is important to recognise that each choice of grism and wavelength window constitutes a distinct instrumental measuring system, and that simultaneous field measurements in different instrumental systems may produce field strength values that differ up to 20 %, or more. Furthermore, we found that field measurements using hydrogen lines only yield results that meaningfully reflect the field strength as sampled specifically by lines of hydrogen for stars with effective temperatures above about 9000 K. CONCLUSIONS. In general the magnetic field measurements of Ap and Bp stars obtained with FORS1 are of excellent quality, accuracy and precision, and FORS1 provides an extremely useful example that offers valuable lessons for field measurements with other low- resolution Cassegrain spectropolarimeters.
We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level $k=2$, which in the large $N$ limit is holographically dual to weakly coupled M-theory on $AdS_4\times S^7/\mathbb{Z}_2$. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the corresponding terms in the 11d M-theory S-matrix by taking the flat space limit, which is not sensitive to these contact terms. We then conjecturally fix these contact terms by analytically continuing the inversion formula below its expected range of convergence, and verify this conjecture using supersymmetric localization. Finally, we compare some of the 1-loop CFT data to non-perturbative in $N$ bounds from the numerical conformal bootstrap, which we compute at unprecedently high accuracy, and find that the 1-loop corrections saturate the bounds in the large $N$ regime, which extends the previously observed match at tree level.
We performed time resolved spectroscopy of 1H0707-495 and IRAS 13224-3809 using long XMM-Newton observations. These are strongly variable narrow line Seyfert 1 galaxies and show broad features around 1 keV that has been interpreted as relativistically broad Fe L$\alpha$ lines. Such features are not clearly observed in other AGN despite sometimes having high iron abundance required by the best fitted blurred reflection models. Given the importance of these lines, we explore the possibility if rapid variability of spectral parameters may introduce broad bumps/dips artificially in the time averaged spectrum, which may then be mistaken as broadened lines. We tested this hypothesis by performing time resolved spectroscopy using long (> 100 ks) XMM-Newton observations and by dividing it into segments with typical exposure of few ks. We extracted spectra from each such segment and modelled using a two component phenomenological model consisting of a power law to represent hard component and a black body to represent the soft emission. As expected both the sources showed variations in the spectral parameters. Using these variation trends, we simulated model spectra for each segment and then co-added to get a combined simulated spectrum. In the simulated spectra, we found no broad features below 1 keV and in particular no deviation near 0.9 keV as seen in the real average spectra. This implies that the broad Fe L? line that is seen in the spectra of these sources is not an artifact of the variation of spectral components and hence providing evidence that the line is indeed genuine.
Using the modularity technique of Wiles, we study the Hecke algebra of weight 2 and prime level N localized at the Eisenstein primes. On the way, we recover some results of Mazur ("Modular Curves and the Eisenstein Ideal") from a deformation theoretic point of view. Combining some of our results with a theorem of Merel, we obtain new information about the p-part of the class groups of Q(N^(1/p)), where p and N are prime, and N = 1 mod p.
In this paper we study elliptic equations with a nonlinear conormal derivative boundary condition involving nonstandard growth terms. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds for weak solutions of such problems.
We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $\Omega$-deformed sphere, $S^2_\Omega$, which is a one-parameter deformation of the $A$-twisted sphere. We provide an exact formula for the $S^2_\Omega$ supersymmetric correlation functions using supersymmetric localization. The contribution of each instanton sector is given in terms of a Jeffrey-Kirwan residue on the Coulomb branch. In the limit of vanishing $\Omega$-deformation, the localization formula greatly simplifies the computation of $A$-twisted correlation functions, and leads to new results for non-abelian theories. We discuss a number of examples and comment on the $\epsilon_\Omega$-deformation of the quantum cohomology relations. Finally, we present a complementary Higgs branch localization scheme in the special case of abelian gauge groups.
We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when $t\to\infty$, the distribution of particles is Gaussian. However, the convergence to this limit is ultraslow, hence it is practically unattainable. Here we obtain an analytical solution for the Lorentz gas' kinetics on physically relevant timescales, and find that the density in its far tails decays as a universal power law of exponent $-3$. We also show that the arrangement of scatterers is imprinted in the shape of the distribution.
In this note we shall continue our study on the initial value problem associated for the generalized derivative Schr\"odinger (gDNLS) equation $$ \partial_tu=i\partial_x^2u + \mu\,|u|^{\alpha}\partial_x u, \hskip10pt x,t\in\mathbb{R}, \hskip5pt 0<\alpha \le 1\;\; {\rm and}\;\; |\mu|=1. $$ Inspiring by Cazenave-Naumkin's works we shall establish the local well-posedness for a class of data of arbitrary size in an appropriate weighted Sobolev space, thus removing the size restriction on the data required in our previous work. The main new tool in the proof is the homogeneous and inhomogeneous versions of the Kato smoothing effect for the linear Schr\"odinger equation with lower order variable coefficients established by Kenig-Ponce-Vega.
Diffusion models (DMs) have achieved state-of-the-art results for image synthesis tasks as well as density estimation. Applied in the latent space of a powerful pretrained autoencoder (LDM), their immense computational requirements can be significantly reduced without sacrificing sampling quality. However, DMs and LDMs lack a semantically meaningful representation space as the diffusion process gradually destroys information in the latent variables. We introduce a framework for learning such representations with diffusion models (LRDM). To that end, a LDM is conditioned on the representation extracted from the clean image by a separate encoder. In particular, the DM and the representation encoder are trained jointly in order to learn rich representations specific to the generative denoising process. By introducing a tractable representation prior, we can efficiently sample from the representation distribution for unconditional image synthesis without training of any additional model. We demonstrate that i) competitive image generation results can be achieved with image-parameterized LDMs, ii) LRDMs are capable of learning semantically meaningful representations, allowing for faithful image reconstructions and semantic interpolations. Our implementation is available at https://github.com/jeremiastraub/diffusion.
We study the collapse of a circular loop of cosmic string. The gravitational field of the string is treated using the weak field approximation. The gravitational radiation from the loop is evaluated numerically. The memtric of the loop near the point of collapse is found analytically.
We derive a general formula for the correlation function of two identical particles with the inclusion of multiple elastic scatterings in the medium in which the two particles are produced. This formula involves the propagator of the particle in the medium. As illustration of the effect we apply the formula to the special case where the scatterers are static, localized 2-body potentials. In this illustration both $R^2_{\rm side}$ and $R^2_{\rm out}$ are increased by an amount proportional to the square of the spatial density of scatterers and to the differential cross section. Specific numbers are used to show the expected magnitude of the rescattering effect on kaon interferometry.
Monolayer graphene aligned with hexagonal boron nitride (hBN) develops a gap at the charge neutrality point (CNP). This gap has previously been extensively studied by electrical transport through thermal activation measurements. Here, we report the determination of the gap size at the CNP of graphene/hBN superlattice through photocurrent spectroscopy study. We demonstrate two distinct measurement approaches to extract the gap size. A maximum of ~ 14 meV gap is observed for devices with a twist angle of less than 1 degree. This value is significantly smaller than that obtained from thermal activation measurements, yet larger than the theoretically predicted single-particle gap. Our results suggest that lattice relaxation and moderate electron-electron interaction effects may enhance the CNP gap in hBN/graphene superlattice.
Pulsating low-mass white dwarf stars are white dwarfs with stellar masses between 0.30~M$_{\odot}$ and 0.45~M$_{\odot}$ that show photometric variability due to gravity-mode pulsations. Within this mass range, they can harbour both a helium- and hybrid-core, depending if the progenitor experienced helium-core burning during the pre-white dwarf evolution. SDSS J115219.99$+$024814.4 is an eclipsing binary system where both components are low-mass white dwarfs, with stellar masses of 0.362$\pm$0.014~M$_{\odot}$ and 0.325$\pm$0.013~M$_{\odot}$. In particular, the less massive component is a pulsating star, showing at least three pulsation periods of $\sim$1314 s, $\sim$1069 s and $\sim$582.9 s. This opens the way to use asteroseismology as a tool to uncover its inner chemical structure, in combination with the information obtained using the light-curve modelling of the eclipses. To this end, using binary evolutionary models leading to helium- and hybrid-core white dwarfs, we compute adiabatic pulsations for $\ell=1$ and $\ell=2$ gravity modes with \texttt{Gyre}. We found that the pulsating component of the SDSS J115219.99$+$024814.4 system must have a hydrogen envelope thinner that the value obtained from binary evolution computations, independently of the inner composition. Finally, from our asteroseismological study, we find a best fit model characterised by T$_{\rm e ff}=10\, 917$ K, M=0.338~M$_{\odot}$, M$_{\rm H}=10^{-6}$~M$_{\odot}$ with the inner composition of a hybrid WD.
The origin of the solar wind is one of the most important unresolved prob- lems in space and solar physics. We report here the first spectroscopic signatures of the nascent fast solar wind on the basis of observations made by the EUV Imaging Spectrometer (EIS) on Hinode in a polar coronal hole, in which patches of blueshift are clearly present on dopplergrams of coronal emission lines with a formation temperature of lg(T/K)=6.0. The corresponding upflow is associated with open field lines in the coronal hole, and seems to start in the solar transition region and becomes more prominent with increasing temperature. This temperature-dependent plasma outflow is interpreted as evidence of the nascent fast solar wind in the polar coronal hole. The patches with significant upflows are still isolated in the upper transition region but merge in the corona, in agreement with the scenario of solar wind outflow being guided by expanding magnetic funnels.
A model describing nuclear collisions at intermediate energies is presented and the results are compared with recently measured double differential cross sections in C-C reactions at 95 MeV/nucleon. Results show the key role played by geometrical effects and the memory of the entrance channel, in particular the momentum distributions of the two incoming nuclei. Special attention is paid to the description of processes occurring at mid-rapidity. To this end, a random particle production mechanism by means of a coalescence process in velocity space is considered in the overlap region of the two interacting nuclei.
The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions [arXiv:1305.4370] are expressed in terms of new complex polynomials, and in the Klein-Gordon case they are expressed in term of Ince polynomials [arXiv:1306.0097]. In each case these solutions form a doubly infinite discrete set, parametrized by quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation (which may be considered as a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma). These solutions describe a high-contrast periodic structure of the particle density on the plasma length scale, and they may have relevance in the study of novel acceleration mechanisms.