ShantanuT01/DACTYL-Pretraining huggingface dataset:
This article concerns with the global H\"older regularity of weak solutions to a class of problems involving the fractional $(p,q)$-Laplacian, denoted by $(-\Delta)^{s_1}_{p}+(-\Delta)^{s_2}_{q}$, for $1<p,q<\infty$ and $s_1,s_2\in (0,1)$. We use a suitable Caccioppoli inequality and local boundedness result in order to prove the weak Harnack type inequality. Consequently, by employing a suitable iteration process, we establish the interior H\"older regularity for local weak solutions, which need not be assumed bounded. The global H\"older regularity result we prove expands and improves the regularity results of Giacomoni, Kumar and Sreenadh (arXiv: 2102.06080) to the subquadratic case (that is, $q<2$) and more general right hand side, which requires a different and new approach. Moreover, we establish a nonlocal Harnack type inequality for weak solutions, which is of independent interest.
We studied the influence of the trigonal distortion of the regular octahedron along the (111) direction, found in the $\rm CoO_2$ layers. Under such a distortion the $t_{2g}$ orbitals split into one $a_{1g}$ and two degenerated $e_g^\prime$ orbitals. We focused on the relative order of these orbitals. Using quantum chemical calculations of embedded clusters at different levels of theory, we analyzed the influence of the different effects not taken into account in the crystalline field theory; that is metal-ligand hybridization, long-range crystalline field, screening effects and orbital relaxation. We found that none of them are responsible for the relative order of the $t_{2g}$ orbitals. In fact, the trigonal distortion allows a mixing of the $t_{2g}$ and $e_g$ orbitals of the metallic atom. This hybridization is at the origin of the $a_{1g}$--$e_g^\prime$ relative order and of the incorrect prediction of the crystalline field theory.
We give a direct proof of well-posedness of solutions to general selection-mutation and structured population models with measures as initial data. This is motivated by the fact that some stationary states of these models are measures and not $L^1$ functions, so the measures are a more natural space to study their dynamics. Our techniques are based on distances between measures appearing in optimal transport and common arguments involving Picard iterations. These tools provide a simplification of previous approaches and are applicable or adaptable to a wide variety of models in population dynamics.
The wind braking model and its applications of magnetars are discussed. The decreasing torque of magnetars during outbursts, anti-glitch, and anti-correlations between radiation and timing are understandable in the wind braking model. Recent timing observations of magnetars are also consistent with the previous modeling. A magnetism-powered wind nebula and a braking index smaller than three are the two predictions. Besides isolated magnetars, there may also be accreting magnetars in binary systems and magnetars accreting from fallback disks. Observationally, ultra-luminous X-ray pulsars may be accreting magnetars, while super-slow magnetars may be magnetars with fallback disks in the past. Many works are needed for both isolated magnetars and accreting magnetars.
The goal of this article is to study the limit of the empirical distribution induced by a mutation-selection multi-allelic Moran model, whose dynamic is given by a continuous-time irreducible Markov chain. The rate matrix driving the mutation is assumed irreducible and the selection rates are assumed uniformly bounded. The paper is divided into two parts. The first one deals with processes with general selection rates. For this case we are able to prove the propagation of chaos in $\mathbb{L}^p$ over the compacts, with speed of convergence of order $1/\sqrt{N}$. Further on, we consider a specific type of selection that we call additive selection. Essentially, we assume that the selection rate can be decomposed as the sum of three terms: a term depending on the allelic type of the parent (which can be understood as selection at death), another term depending on the allelic type of the descendant (which can be understood as selection at birth) and a third term which is symmetric. Under this setting, our results include a uniform in time bound for the propagation on chaos in $\mathbb{L}^p$ of order $1/\sqrt{N}$, and the proof of the asymptotic normality with zero mean and explicit variance, for the approximation error between the empirical distribution and its limit, when the number of individuals tend towards infinity. Additionally, we explore the interpretation of the Moran model with additive selection as a particle process whose empirical distribution approximates a quasi-stationary distribution, in the same spirit as the Fleming\,--\,Viot particle systems. We then address the problem of minimising the asymptotic quadratic error, when the time and the number of particles go to infinity.
In this work, we analyse coordinated observations spanning chromospheric, TR and coronal temperatures at very high resolution which reveal essential characteristics of thermally unstable plasmas. Coronal rain is found to be a highly multi-thermal phenomenon with a high degree of co-spatiality in the multi-wavelength emission. EUV darkening and quasi-periodic intensity variations are found to be strongly correlated to coronal rain showers. Progressive cooling of coronal rain is observed, leading to a height dependence of the emission. A fast-slow two-step catastrophic cooling progression is found, which may reflect the transition to optically thick plasma states. The intermittent and clumpy appearance of coronal rain at coronal heights becomes more continuous and persistent at chromospheric heights just before impact, mainly due to a funnel effect from the observed expansion of the magnetic field. Strong density inhomogeneities on spatial scales of 0.2"-0.5" are found, in which TR to chromospheric temperature transition occurs at the lowest detectable scales. The shape of the distribution of coronal rain widths is found to be independent of temperature with peaks close to the resolution limit of each telescope, ranging from 0.2" to 0.8". However we find a sharp increase of clump numbers at the coolest wavelengths and especially at higher resolution, suggesting that the bulk of the rain distribution remains undetected. Rain clumps appear organised in strands in both chromospheric and TR temperatures, suggesting an important role of thermal instability in the shaping of fundamental loop substructure. We further find structure reminiscent of the MHD thermal mode. Rain core densities are estimated to vary between 2x10^{10} cm^{-3} and 2.5x10^{11} cm^{-3} leading to significant downward mass fluxes per loop of 1-5x10^{9} g s^{-1}, suggesting a major role in the chromosphere-corona mass cycle.
Some strong field effects on test particle motion associated with the propagation of a plane electromagnetic wave in the exact theory of general relativity are investigated. Two different profiles of the associated radiation flux are considered in comparison, corresponding to either constant or oscillating electric and magnetic fields with respect to a natural family of observers. These are the most common situations to be experimentally explored, and have a well known counterpart in the flat spacetime limit. The resulting line elements are determined by a single metric function, which turns out to be expressed in terms of standard trigonometric functions in the case of a constant radiation flux, and in terms of special functions in the case of oscillating flux, leading to different features of test particle motion. The world line deviation between both uncharged and charged particles on different spacetime trajectories due to the combined effect of gravitational and electromagnetic forces is studied. The interaction of charged particles with the background radiation field is also discussed through a general relativistic description of the inverse Compton effect. Motion as well as deviation effects on particles endowed with spin are studied too. Special situations may occur in which the direction of the spin vector change during the interaction, leading to obsevables effects like spin-flip.
Systems operating out of equilibrium exchange energy and matter with the environment, thus producing entropy in their surroundings. Since the entropy production depends on the current flowing throughout the system, its quantification is affected by the level of coarse-graining we adopt. In particular, it has been shown that the description of a system via a Fokker-Planck equation (FPE) lead to an underestimation of the entropy production with respect to the corresponding one in terms of microscopic transition rates. Moreover, such a correction can be derived exactly. Here we review this derivation, generalizing it when different prescriptions to derive the FPE from a Langevin equation are adopted. Then, some open problems about Gaussian transition rates and underdamped limit are discussed. In the second part of the manuscript we present a new approach to dealing with the discrepancy in entropy production due to the coarse graining by introducing enough microscopic variables to correctly estimate the entropy production within the FPE description. We show that any discrete state system can be described by making explicit the contribution of each microscopic current.
We have carried-out multi-configuration Breit-Pauli AUTOSTRUCTURE calculations for the dielectronic recombination (DR) of Fe^{8+} - Fe^{12+} ions. We obtain total DR rate coefficients for the initial ground-level which are an order of magnitude larger than those corresponding to radiative recombination (RR), at temperatures where Fe 3p^q (q=2-6) ions are abundant in photoionized plasmas. The resultant total (DR+RR) rate coefficients are then an order of magnitude larger than those currently in use by photoionized plasma modeling codes such as CLOUDY, ION and XSTAR. These rate coefficients, together with our previous results for q=0 and 1, are critical for determining the ionization balance of the M-shell Fe ions which give rise to the prominent unresolved-transition-array X-ray absorption feature found in the spectrum of many active galactic nuclei. This feature is poorly described by CLOUDY and ION, necessitating an ad hoc modification to the low-temperature DR rate coefficients. Such modifications are no longer necessary and a rigorous approach to such modeling can now take place using these data.
The quest to discover the most distant galaxies has developed rapidly in the last decade. We are now exploring redshifts of 6 and beyond, when the Universe was less than a billion years old, an epoch when the previously-neutral intergalactic medium was reionized. The continuing discovery of galaxies at progressively higher and higher redshifts has been driven by the availability of large telescopes on the ground and in space, improvements in detector technology, and new search strategies. Over the past 4 years, the Lyman break technique has been shown to be effective in isolating z~6 star-forming i'-drop galaxies through spectroscopic confirmation with large ground-based telescopes (Keck, Gemini and the ESO VLTs). Narrow-band imaging, notably with the wide field of the Subaru telescope, has also produced samples of Lyman-alpha emitters at these redshifts. A The discovery of this i'-drop galaxy population has been used to infer the global star formation rate density at this epoch (z~6), and we are now beginning to constrain the contribution to reionization of the UV flux from these galaxies. Infrared data from the Spitzer Space Telescope has been used to determine the spectral energy distributions (SEDs) from the rest-frame UV to the optical, and constrain the previous star formation histories, masses and ages. The indications are that much of the stellar mass of these galaxies might have formed in vigorous bursts at z>6. The next big advances would be to test the population synthesis modelling of these z~6 galaxies through spectroscopy of the rest-frame optical (rather than crude broad-band SEDs), and also to push the observational horizon for galaxies further to directly explore star formation during the reionization epoch. JWST is likely to have a profound impact on realising these goals.
We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework is given as an abstract "martingale formulation", which encompasses a broad range of standard control problems. Under appropriate conditions we show that the set of admissible controls gives rise to a certain class of controlled special semimartingales. Our results generalise both the standard controlled It\^o- and L\'evy-diffusion settings as we allow ourselves to locally control not only the drift and diffusion coefficients, but also the jump intensity measure of the jumps. As an illustration, we present a few examples with explicit solutions.
We study a solution of the Einstein-Gauus-Bonnet theory in 5 dimensions coupled to a Maxwell field, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.
A domino covering of a board is saturated if no domino is redundant. We introduce the concept of a fragment tiling and show that a minimal fragment tiling always corresponds to a maximal saturated domino covering. The size of a minimal fragment tiling is the domination number of the board. We define a class of regular boards and show that for these boards the domination number gives the size of a minimal X-pentomino covering. Natural sequences that count maximal saturated domino coverings of square and rectangular boards are obtained. These include the new sequences A193764, A193765, A193766, A193767, and A193768 of OEIS.
I review recent observations on the evolution of quasars, describe new surveys for quasars at z > 5 and for quasars at z > 3.3 down to luminosities corresponding to L* galaxies, and note the possible connection between the evolution of the star formation rate in young galaxies and the evolution of quasars.
The purpose of this paper is to study radial solutions for steady hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary. The existence and uniqueness of radial subsonic solution, and the existence of radial supersonic solutions are derived by using the energy method and the compactness method, but under a general condition of the doping profile. In particular, for radial supersonic solutions, it is more difficult to get the related estimates by the effect of high dimensional space and the sonic boundary, so we apply a special iteration to complete the proofs. The results obtained essentially improve and develop the previous studies in the one-dimensional case.
We use the timescale distribution of ~3000 microlensing events measured by the OGLE-III survey, together with accurate new made-to-measure dynamical models of the Galactic bulge/bar region, to measure the IMF in the inner Milky Way. The timescale of each event depends on the mass of the lensing object, together with the relative distances and velocities of the lens and source. The dynamical model provides statistically these distances and velocities allowing us to constrain the lens mass function, and from this to infer the IMF. Parameterising the IMF as a broken power-law, we find slopes in the main sequence $\alpha_{\rm ms}=1.31\pm0.10|_{\rm stat}\pm0.10|_{\rm sys}$ and brown dwarf region $\alpha_{\rm bd}=-0.7\pm0.9|_{\rm stat}\pm0.8|_{\rm sys}$ where we use a fiducial 50% binary fraction, and the systematic uncertainty covers the range of binary fractions 0-100%. Similarly for a log-normal IMF we conclude $M_c=(0.17\pm0.02|_{\rm stat}\pm0.01|_{\rm sys})M_\odot$ and $\sigma_m=0.49\pm0.07|_{\rm stat}\pm0.06|_{\rm sys}$. These values are very similar to a Kroupa or Chabrier IMF respectively, showing that the IMF in the bulge is indistinguishable from that measured locally, despite the lenses lying in the inner Milky Way where the stars are mostly ~10Gyr old and formed on a fast $\alpha$-element enhanced timescale. This therefore constrains models of IMF variation that depend on the properties of the collapsing gas cloud.
The parity violating asymmetry $A_{PV}$ in $^{208}$Pb, recently measured by the PREX-2 collaboration, is studied using modern relativistic (covariant) and non-relativistic energy density functionals. We first assess the theoretical uncertainty on $A_{PV}$ which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability $\alpha_D$ of $^{208}$Pb. We then add the quantified value of $A_{PV}$ together with $\alpha_D$ to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in $^{208}$Pb $r_\mathrm{skin} =0.19\pm 0.02$\,fm and the symmetry-energy slope $L=54\pm 8$\,MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. We also make a prediction for the $A_{PV}$ value in $^{48}$Ca that will be soon available from the CREX measurement.
We consider a Vicsek model of self-propelled particles with bounded confidence, where each particle interacts only with neighbors that have a similar direction. Depending on parameters, the system exhibits a continuous or discontinuous polar phase transition from the isotropic phase to a phase with a preferred direction. In a recent paper [1] the von Mises distribution was proposed as an ansatz for polar ordering. In the present system the time evolution of the angular distribution can be solved in Fourier space. We compare the results of the Fourier analysis with the ones obtained by using the von Mises distribution ansatz. In the latter case the qualitative behavior of the system is recovered correctly. However, quantitatively there are serious deviations. We introduce an extended von Mises distribution ansatz such that a second term takes care of the next two Fourier modes. With the extended ansatz we find much better quantitative agreement. As an alternative approach we also use a Gaussian and a geometric series ansatz in Fourier space. The geometric series ansatz is analytically handable but fails for very weak noise, the Gaussian ansatz yields better results but it is not analytically treatable.
We present a theoretical model that explains the high energy phenomenology of the neighborhood of SNR IC 443, as observed with the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescope and the Energetic Gamma-Ray Experiment Telescope (EGRET). We interpret MAGIC J0616+225 as delayed TeV emission of cosmic-rays diffusing from IC 443 and interacting with a known cloud located at a distance of about 20 pc in the foreground of the remnant. This scenario naturally explains the displacement between EGRET and MAGIC sources, their fluxes, and their spectra. We compare this model with others recently presented, and discuss how it can be tested with observations by the Gamma-ray Large Area Telescope (GLAST).
Recently, the laser experiments BMV and GammeV, searching for light shining through walls, have published data and calculated new limits on the allowed masses and couplings for axion-like particles. In this note we point out that these experiments can serve to constrain a much wider variety of hidden-sector particles such as, e.g., minicharged particles and hidden-sector photons. The new experiments improve the existing bounds from the older BFRT experiment by a factor of two. Moreover, we use the new PVLAS constraints on a possible rotation and ellipticity of light after it has passed through a strong magnetic field to constrain pure minicharged particle models. For masses <~0.05 eV, the charge is now restricted to be less than (3-4)x10^(-7) times the electron electric charge. This is the best laboratory bound and comparable to bounds inferred from the energy spectrum of the cosmic microwave background.
We investigate the Smith-Purcell emission produced by electron- or ion-beam-driven coherent excitation of nuclei arranged in periodic crystal lattices. The excitation and subsequent radiative decay of the nuclei can leave the target in the initial ground state after $\gamma$-ray emission, thus generating a coherent superposition of the far-field photon amplitude emanating from different nuclei that results in sharp angular patterns at spectrally narrow nuclear transition energies. We focus on Fe-57 as an example of two-level nuclear lossy system giving rise to Smith-Purcell emission at 14.4\,keV with a characteristic delay of 1.2\,ns relative to the excitation time. These properties enable a clean separation from faster and spectrally broader emission mechanisms, such as bremsstrahlung. Besides its fundamental interest, our study holds potential for the design of high-energy, narrow-band, highly-directive photon sources, as well as a means to store energy in the form of nuclear excitations.
In this short note, we observe that Theorem 3.1 in arXiv:1508.00682 for semiorthogonal indecomposability of the derived category of smooth DM stacks based on the canonical bundle can be extended to the case of projective varieties with Cohen-Macaulay singularities. As a consequence, all projective curves of positive arithmetic genus have weakly indecomposable bounded derived categories and indecomposable categories of perfect complexes. Here weak indecomposablility refers to the admissibility of components.
Thermodynamical properties of the nuclear matter at sub-saturation densities were investigated using a simple van der Waals-like equation of state with an additional term representing the symmetry energy. First-order isospin-asymmetric liquid-gas phase transition appears restricted to isolated isospin-asymmetric systems while the symmetric systems will undergo fragmentation decay resembling the second-order phase transition. The density dependence of the symmetry energy scaling with the Fermi energy satisfactorily describes the symmetry energy at sub-saturation nuclear densities. The deconfinement-confinement phase transition from the quark-gluon plasma to the confined quark matter appears in the isolated systems continuous in energy density while discontinuous in quark density. A transitional state of the confined quark matter has a negative pressure and after hadronization an explosion scenario can take place which can offer explanation for the HBT puzzle as a signature of the phase transition.
Recently, we have established the generalized Li's criterion equivalent to the Riemann hypothesis, viz. demonstrated that the sums over all non-trivial Riemann function zeroes k_n,a=Sum_rho(1-(1-((rho-a)/(rho+a-1))^n) for any real a not equal to 1/2 are non-negative if and only if the Riemann hypothesis holds true; arXiv:1304.7895 (2013); Ukrainian Math. J., V.66, N3, 371-383 (2014). An arithmetic interpretation of this generalized Li's criterion is given here.
Using the Calogero-Moser model and the Nakamura equations for a multi-partite quantum system, we prove an inequality between the mean bi-partite entanglement rate of change under the variation of a critical parameter and the level-curvature. This provides an upper bound for the rate of production or distraction of entanglement induced dynamically. We then investigate the dependence of the upper bound on the degree of chaos of the system, which in turn, through the inequality, gives a measure of the stability of the entangled state. Our analytical results are supported with extensive numerical calculations.