ShantanuT01/DACTYL-Pretraining huggingface dataset:
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness of critical traveling wave for the time-delayed degenerate diffusion equations, and obtained the reducing mechanism of time delay on critical wave speed. In this paper, we now are able to show the asymptotic spreading speed and its coincidence with the critical wave speed $c^*(m,r)$ of sharp wave, and prove that the initial perturbation or the boundary of the compact support of the solution propagates at the critical wave speed $c^*(m,r)$ for the time-delayed degenerate diffusion equations. Remarkably, different from the existing studies related to spreading speeds, the time delay and the degenerate diffusion lead to some essential difficulties in the analysis of the spreading speed, because the time-delay makes the critical speed of traveling waves slow down, and the degenerate diffusion causes the loss of regularity for the solutions. By a phase transform technique combined with the monotone method, we can determine the asymptotic spreading speed. Furthermore, we propose a brand-new sharp-profile-based difference scheme to handle large variation of degenerate diffusion $(u^m)_{xx}$ near the sharp edge and carry out some numerical simulations which perfectly confirm our theoretical results.
Non-diagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally-coupled paradigm of smoothly-varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and non-diagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the $k=0$ effective mass diverges, now becomes a transition line in the coupling constant plane - the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No 'self-trapping transition' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.
Context: Studying the problem of active region heating requires precise measurements of physical plasma parameters such as electron density, temperature etc. It is also important to understand the relationship of coronal structures with the magnetic field. The Extreme-ultraviolet Imaging Spectrometer (EIS) aboard Hinode provides a rare opportunity to derive electron density simultaneously at different temperatures.   Aims: MethodsWe study the density structure and characterise plasma in active regions and associated moss regions. In addition we study its relationship to the photospheric magnetic field.   Methods: We used data recorded by the EIS, together with magnetic field measurements from the Michelson Doppler Imager (MDI) aboard SoHO and images recorded with the Transition Region And Coronal Explorer (TRACE) and X-Ray Telescope (XRT/Hinode).   Results: We find that the hot core of the active region is densest with values as high as 10^10.5 cm^-3. The electron density estimated in specific regions in the active region moss decreases with increasing temperature. The moss areas were located primarily on one side of the active region, and they map the positive polarity regions almost exactly. The density within the moss region was highest at log T=5.8-6.1, with a value around 10^(10.0-10.5) cm^-3. The moss densities were highest in the strong positive magnetic field region. However, there was no such correlation for the negative polarity areas, where there was a large sunspot.
Alfv\'en waves are responsible for the transfer of magnetic energy in the magnetized plasma. They are involved in heating solar atmosphere and driving solar wind through various nonlinear processes. Since the magnetic field configurations directly affect the nonlinearity of Alfv\'en waves, it is important to investigate how they relate to the solar atmosphere and wind structure through the nonlinear propagation of Alfv\'en waves. In this study, we carried out the one-dimensional magnetohydrodynamic simulations to realize the above relation. The results show that when the nonlinearity of Alfv\'en waves in the chromosphere exceeds a critical value, the dynamics of the solar chromosphere (e.g., spicule) and the mass loss rate of solar wind tend to be independent of the energy input from the photosphere. In a situation where the Alfv\'en waves are highly nonlinear, the strong shear torsional flow generated in the chromosphere ``fractures'' the magnetic flux tube. This corresponds to the formation of chromospheric intermediate shocks, which limit the transmission of the Poynting flux into the corona by Alfv\'en waves and also inhibits the propagation of chromospheric slow shock.
The eROSITA X-ray telescope on board the Spectrum-Roentgen-Gamma (SRG) mission will measure the position and properties of about 100,000 clusters of galaxies and 3 million active galactic nuclei over the full sky. To study the statistical properties of this ongoing survey, it is key to estimate the selection function accurately. We create a set of full sky light-cones using the MultiDark and UNIT dark matter only N-body simulations. We present a novel method to predict the X-ray emission of galaxy clusters. Given a set of dark matter halo properties (mass, redshift, ellipticity, offset parameter), we construct an X-ray emissivity profile and image for each halo in the light-cone. We follow the eROSITA scanning strategy to produce a list of X-ray photons on the full sky. We predict scaling relations for the model clusters, which are in good agreement with the literature. The predicted number density of clusters as a function of flux also agrees with previous measurements. Finally, we obtain a scatter of 0.21 (0.07, 0.25) for the X-ray luminosity -- mass (temperature -- mass, luminosity -- temperature) model scaling relations. We provide catalogues with the model photons emitted by clusters and active galactic nuclei. These catalogues will aid the eROSITA end to end simulation flow analysis and in particular the source detection process and cataloguing methods.
Based on a realistic model for the rho meson in free space we investigate it's medium modifications in a hot hadron gas generated by hadronic rescattering processes, i.e. renormalization of intermediate two-pion states as well as direct rho meson scattering off hadrons. Within the vector dominance model the resulting in-medium rho spectral function is applied to calculate $e^+e^-$ spectra as recently measured in heavy-ion collisions at CERN-SpS energies in the CERES experiment.
An exact solution of Einstein-Cartan-Maxwell (ECM) field equations representing a charged domain wall given by the jump on the electric charge and spin density across the wall is obtained from the Riemannian theory of distributions. The Gauss-Coddazzi equations are used to show that spin, charge and Cartan torsion increases the repulsive character of the domain wall. Taub and Vilenkin walls are discussed as well as their relations to wormhole geometry. The electric and torsion fields are constants at the wall.
We present the discovery of molecular hydrogen (H_2), including the presence of vibrationally-excited H_2^* in the optical spectrum of the afterglow of GRB 120815A at z=2.36 obtained with X-shooter at the VLT. Simultaneous photometric broad-band data from GROND and X-ray observations by Swift/XRT place further constraints on the amount and nature of dust along the sightline. The galactic environment of GRB 120815A is characterized by a strong DLA with log(N(H)/cm^-2) = 21.95 +/- 0.10, prominent H_2 absorption in the Lyman-Werner bands (log(N(H_2)/cm^-2) = 20.53 +/- 0.13) and thus a molecular gas fraction log f(H_2)=-1.14 +/- 0.15. The distance d between the absorbing neutral gas and GRB 120815A is constrained via photo-excitation modeling of fine-structure and meta-stable transitions of FeII and NiII to d = 0.5 +/- 0.1 kpc. The DLA metallicity ([Zn/H] = -1.15 +/- 0.12), visual extinction (A_V < 0.15 mag) and dust depletion ([Zn/Fe] = 1.01 +/- 0.10) are intermediate between the values of well-studied, H_2-deficient GRB-DLAs observed at high spectral resolution, and the approximately solar metallicity, highly-obscured and H_2-rich GRB 080607 sightline. With respect to N(H), metallicity, as well as dust-extinction and depletion, GRB 120815A is fairly representative of the average properties of GRB-DLAs. This demonstrates that molecular hydrogen is present in at least a fraction of the more typical GRB-DLAs, and H_2 and H_2^* are probably more wide-spread among GRB-selected systems than the few examples of previous detections would suggest.
In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity $\omega_0$ and the circulation $\gamma$ of the initial flow around the obstacle. We prove that, if $\gamma$ is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity $\omega_0 + \gamma \delta$, where $\delta$ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in [Comm P.D.E. 28 (2003) 349-379], where the effect of the small obstacle appears in the coefficients of the PDE and not only on the initial data. The main ingredients of the proof are $L^p-L^q$ estimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato's fixed point method, energy estimates, renormalization and interpolation.
We study the effects of local environmental conditions affecting the diffuse interstellar band (DIB) carriers within the Upper Scorpius subgroup of the Sco OB2 association. We obtained optical spectra with FEROS, and measured the equivalent widths of five DIBs (at 5780, 5797, 6196, 6379, and 6613 Angstrom) as well as those of absorption lines of di-atomic molecules (CH, CH+, CN) and atoms (KI, CaI) towards 89 targets in the direction of Upper Scorpius. We construct a simple radiative transfer and chemical network model of the diffuse interstellar medium (ISM) sheet in front of Upp Sco to infer the effective radiation field. Both the interstellar radiation field strength, I_UV, and the molecular hydrogen fraction, f_H2, have been derived for 55 sightlines probing the Upp Sco ISM. We discuss the relations between DIB strengths, CH and CH+ line strengths, E(B-V), I_UV, and f_H2. The ratio between the 5780 and 5797 DIBs reveals a (spatial) dependence on the local environment in terms of cloud density and exposure to the interstellar radiation field, reflecting the molecular nature of these DIB carriers.
We examine the mechanism for generating a mass for a U(1) vector field introduced by Stueckelberg. First, it is shown that renormalization of the vector mass is identical to the renormalization of the vector field on account of gauge invariance. We then consider how the vector mass affects the effective potential in scalar quantum electrodynamics at one-loop order. The possibility of extending this mechanism to couple, in a gauge invariant way, a charged vector field to the photon is discussed.
We study slowly rotating four-dimensional black holes with flat horizon structure in scale-dependent gravity. First we obtain the solution, and then we study thermodynamic properties as well as the invariants of the theory. The impact of the scale-dependent parameter is investigated in detail. We find that the scale-dependent solution exhibits a single singularity at the origin, also present in the classical solution.
We present the second XMM-Newton observation (85 ks) of the narrow-line Seyfert 1 galaxy (NLS1) I Zw 1 and describe its mean spectral and timing characteristics. On average, I Zw 1 is ~35 per cent dimmer in 2005 than in the shorter (20 ks) 2002 observation. Between the two epochs the intrinsic absorption column density diminished, but there were also subtle changes in the continuum shape. Considering the blurred ionised reflection model, the long-term changes can be associated with a varying contribution of the power law component relative to the total spectrum. Examination of normalised light curves indicates that the high-energy variations are quite structured and that there are delays, but only in some parts of the light curve. Interestingly, a hard X-ray lag first appears during the most-distinct structure in the mean light curve, a flux dip ~25 ks into the observation. The previously discovered broad, ionised Fe Ka line shows significant variations over the course of the 2005 observation. The amplitude of the variations is 25-45 per cent and they are unlikely due to changes in the Fe ka-producing region, but perhaps arise from orbital motion around the black hole or obscuration in the broad iron line-emitting region. The 2002 data are re-examined for variability of the Fe Ka line at that epoch. There is evidence of energy and flux variations that are associated with a hard X-ray flare that occurred during that observation.
The mid-infrared ratio [NeIII]15.6mum/[NeII]12.8mum is a strong diagnostic of the ionization state of emission line objects, due to its use of only strong neon emission lines only weakly affected by extinction. However this ratio is not available to ground-based telescopes as only a few spectroscopic windows are available in the MIR. To deal with this problem we aimed to verify if there exists a conversion law between ground-accessible, strong MIR line ratio [SIV]/[NeII] and the diagnostic [NeIII]/[NeII] ratio that can serve as a reference for future ground-based observations. We collated the [SIV]10.5mum, [NeII]12.8mum, [NeIII]15.6\mum and [SIII]18.7mum emission line fluxes from a wide range of sources in the rich Spitzer and ISO archives, and compared the [NeIII]/[NeII], [SIV]/[SIII], and [SIV]/[NeII] ratios. We find a strong correlation between the [SIV]/[NeII] and [\neiii]/[\neii] ratio, with a linear fit of log([NeIII]/[NeII]) = 0.81log([SIV]/[NeII])+0.36, accurate to a factor of ~2 over four orders of magnitude in the line ratios. This demonstrates clearly the ability of ground-based infrared spectrographs to do ionization studies of nebulae.
We explore the connections between the constraints on the precision of quantum logical operations that arise from a conservation law, and those arising from quantum field fluctuations. We show that the conservation-law based constraints apply in a number of situations of experimental interest, such as Raman excitations, and atoms in free space interacting with the multimode vacuum. We also show that for these systems, and for states with a sufficiently large photon number, the conservation-law based constraint represents an ultimate limit closely related to the fluctuations in the quantum field phase.
Neighborhood-prime labeling is a variation of prime labeling. A labeling $f:V(G) \to [|V(G)|]$ is a neighborhood-prime labeling if for each vertex $v\in V(G)$ with degree greater than $1$, the greatest common divisor of the set of labels in the neighborhood of $v$ is $1$. In this paper, we introduce techniques for finding neighborhood-prime labelings based on the Hamiltonicity of the graph, by using conditions on possible degrees of vertices, and by examining a neighborhood graph. In particular, classes of graphs shown to be neighborhood-prime include all generalized Petersen graphs, grid graphs of any size, and lobsters given restrictions on the degree of the vertices. In addition, we show that almost all graphs and almost all regular graphs have are neighborhood-prime, and we find all graphs of order $10$ or less that have a neighborhood-prime labeling. We give several conjectures for future work in this area.
We study the properties of a completely integrable deformation of the CGHS dilaton gravity model in two dimensions. The solution is shown to represent a singularity free black hole that at large distances asymptoticaly joins to the CGHS solution.
We present a python package to calculate interaction rates of light dark matter in dielectric materials, including screening effects. The full response of the material is parametrized in the terms of the energy loss function (ELF) of material, which darkELF converts into differential scattering rates for both direct dark matter electron scattering and through the Migdal effect. In addition, darkELF can calculate the rate to produce phonons from sub-MeV dark matter scattering via the dark photon mediator, as well as the absorption rate for dark matter comprised of dark photons. The package includes precomputed ELFs for Al, $\mathrm{Al}_2\mathrm{O}_3$, GaAs, GaN, Ge, Si, $\mathrm{SiO}_2$, and ZnS, and allows the user to easily add their own ELF extractions for arbitrary materials.
If a primordial magnetic field in the universe has non-zero helicity, the violation of parity symmetry results in non-zero correlations between cosmic microwave background temperature and B-mode polarization. In this paper we derive approximations to the relevant microwave background power spectra arising from a helical magnetic field. Using the cross-power spectrum between temperature and B-mode polarization from the WMAP nine-year data, we set a 95\% confidence level upper limit on the helicity amplitude to be 10 nG$^2$ Gpc for helicity spectral index $n_H = -1.9$, for a cosmological magnetic field with effective field strength of 3 nG and a power-law index $n_B = -2.9$ near the scale-invariant value. Future microwave background polarization maps with greater sensitivity will be able to detect the helicity of an inflationary magnetic field well below the maximum value allowed by microwave background constraints on the magnetic field amplitude.
In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a widely-known class of non-convex bodies, the so-called p-convex bodies, and construct a counter-example for this class.
We studied the interlayer coupling in the quadrilayer consisting of IrMn/CoFe (bottom layer)/NiFeOx/ CoFe (top layer). The in-plane perpendicular interlayer coupling is observed between CoFe layers at room temperature. An anisotropy transition from uniaxial to unidirectional in the perpendicular direction is observed around Tt = 55 K. The nano-oxide layer NiFeOx shows no distinguishable ferromagnetic signal in the high-temperature (uniaxial) phase, while a strong signal appeared in the low-temperature (unidirectional) phase. A possible two-component scenario, that the nano-oxide layer may contain both amorphous short-range antiferromagnetic domains and superparamagneitc clusters, is proposed to explain the phase transition.
The zero-temperature limit of the backgammon model under resetting is studied. The model is a balls-in-boxes model whose relaxation dynamics is governed by the density of boxes containing just one particle. As these boxes become rare at large times, the model presents an entropy barrier. As a preliminary step, a related model with faster relaxation, known to be mapped to a symmetric random walk, is studied by mapping recent results on diffusion with resetting onto the balls-in-boxes problem. Diffusion with an absorbing target at the origin (and diffusion constant equal to one), stochastically reset to the unit position, is a continuum approximation to the dynamics of the balls-in-boxes model, with resetting to a configuration maximising the number of boxes containing just one ball. In the limit of a large system, the relaxation time of the balls-in-boxes model under resetting is finite. The backgammon model subject to a constant resetting rate is then studied using an adiabatic approximation.
An ideal 1H phase monolayer MoS$_2$ has the mirror reflection symmetry but this symmetry is broken in common experimental situations, where the monolayer is placed on a substrate. By using the k$\cdot$p perturbation theory, we investigate the effect of the mirror symmetry breaking on the Berry curvature of the material. We find that the symmetry breaking may modify the Berry curvature considerably and the spin/valley Hall effect due to the modified Berry curvature is in qualitative agreement with a recent experimental result [Science $\bf 344$, 1489 (2014)], which cannot be explained by previous theories that ignore the mirror symmetry breaking.
A constant-dimension code (CDC) is a set of subspaces of constant dimension in a common vector space with upper bounded pairwise intersection. We improve and generalize two constructions for CDCs, the improved linkage construction and the parallel linkage construction, to the generalized linkage construction which in turn yields many improved lower bounds for the cardinalities of CDCs; a quantity not known in general.
A P\'olya urn process is a Markov chain that models the evolution of an urn containing some coloured balls, the set of possible colours being $\{1,\ldots,d\}$ for $d\in \mathbb{N}$. At each time step, a random ball is chosen uniformly in the urn. It is replaced in the urn and, if its colour is $c$, $R_{c,j}$ balls of colour $j$ are also added (for all $1\leq j\leq d$). We introduce a model of measure-valued processes that generalises this construction. This generalisation includes the case when the space of colours is a (possibly infinite) Polish space $\mathcal P$.   We see the urn composition at any time step $n$ as a measure ${\mathcal M}_n$ -- possibly non atomic -- on $\mathcal P$. In this generalisation, we choose a random colour $c$ according to the probability distribution proportional to ${\mathcal M}_n$, and add a measure ${\mathcal R}_c$ in the urn, where the quantity ${\mathcal R}_c(B)$ of a Borel set $B$ models the added weight of "balls" with colour in $B$.   We study the asymptotic behaviour of these measure-valued P\'olya urn processes, and give some conditions on the replacements measures $({\mathcal R}_c, c\in \mathcal P)$ for the sequence of measures $({\mathcal M}_n, n\geq 0)$ to converge in distribution, possibly after rescaling. For certain models, related to branching random walks, $({\mathcal M}_n, n\geq 0)$ is shown to converge almost surely under some moment hypothesis; a particular case of this last result gives the almost sure convergence of the (renormalised) profile of the random recursive tree to a standard Gaussian.
This work reports the results of EPR and NMR study of the Ce3+ incorporation in LaAlO3 single crystals grown by the micro-pulling-down method in the range of the Ce concentrations from x=0.1 at.% up to 100 at.%. From EPR measurements, Ce3+ g tensor parameters were obtained as function of Ce concentration. The g tensor has orthorhombic symmetry even in the trigonal phase (x < 10 at.%) suggesting that the incorporation of Ce at La site lowers lattice symmetry near this ion. The local properties of the La1-xCexAlO3 crystals were further studied by 27Al and 139La high-resolution NMR measurements. It was found that 139La chemical shift has the Fermi contact interaction origin. It linearly increases with Ce concentration up to 165 ppm at x = 0.5. Due to this strong Fermi contact interaction, separated peaks corresponding to different Ce-O-La spin transfer passways are resolved in the 139La NMR spectra. On the other hand, no Fermi contact interaction is visible in 27Al NMR spectra. However, these spectra contain satellite peak which intensity linearly increases with increase of Ce concentration leaving position of this peak unchanged. This was interpreted as manifestation of crystal structure modification in vicinity of Ce ions in agreement with EPR data. Thus, optical properties of Ce3+ in LaAlO3 will be namely determined by the local crystal structure near this ion.