ShantanuT01/DACTYL-Pretraining huggingface dataset:
Recent observations have revealed an amazing diversity of extremely luminous supernovae, seemingly increasing in radiant energy without bound. We consider here the physical limits of what existing models can provide for the peak luminosity and total radiated energy for non-relativistic, isotropic stellar explosions. The brightest possible supernova is a Type I explosion powered by a sub-millisecond magnetar. Such models can reach a peak luminosity of $\rm 2\times10^{46}\ erg\ s^{-1}$ and radiate a total energy of $\rm 4 \times10^{52}\ erg$. Other less luminous models are also explored, including prompt hyper-energetic explosions in red supergiants, pulsational-pair instability supernovae, and pair-instability supernovae. Approximate analytic expressions and limits are given for each case. Excluding magnetars, the peak luminosity is near $\rm 1\times10^{44}\ erg\ s^{-1}$ for the brightest models. The corresponding limits on total radiated power are $\rm3 \times 10^{51}\ erg$ (Type I) and $\rm1 \times 10^{51}\ erg$ (Type II). A magnetar-based model for the recent transient event, ASASSN-15lh is presented that strains, but does not exceed the limits of what the model can provide.
We give two combinatorial proofs of Goulden and Jackson's formula for the number of minimal transitive factorizations of a permutation when the permutation has two cycles. We use the recent result of Goulden, Nica, and Oancea on the number of maximal chains of annular noncrossing partitions of type $B$.
In an earlier work we used a path integral analysis to propose a higher genus generalization of the elliptic genus. We found a cobordism invariant parametrized by Teichmuller space. Here we simplify the formula and study the behavior of our invariant under the action of the mapping class group of the Riemann surface. We find that our invariant is a modular function with multiplier just as in genus one.
We have carried out high-resolution near-infrared spectroscopic observations toward 16 Galactic supernova remnants (SNRs) showing strong H$_{2}$ emission features. A dozen bright H$_{2}$ emission lines are clearly detected for individual SNRs, and we have measured their central velocities, line widths, and fluxes. For all SNRs except one (G9.9$-$0.8), the H$_{2}$ line ratios are well consistent with that of thermal excitation at $T\sim2000$ K, indicating that the H$_{2}$ emission lines are most likely from shock-excited gas and therefore that they are physically associated with the remnants. The kinematic distances to the 15 SNRs are derived from the central velocities of the H$_{2}$ lines using a Galactic rotation model. We derive for the first time the kinematic distances to four SNRs: G13.5$+$0.2, G16.0$-$0.5, G32.1$-$0.9, and G33.2$-$0.6. Among the remaining 11 SNRs, the central velocities of the H$_{2}$ emission lines for six SNRs are well consistent ($\pm5$ km s$^{-1}$) with those obtained in previous radio observations, while for the other five SNRs (G18.1$-$0.1, G18.9$-$1.1, Kes 69, 3C 396, W49B) they are significantly different. We discuss the velocity discrepancies in these five SNRs. In G9.9$-$0.8, the H$_{2}$ emission shows nonthermal line ratios and narrow line width ($\sim 4$ km s$^{-1}$), and we discuss its origin.
We prove a conjecture by DiVincenzo, which in the terminology of Preskill et al. [quant-ph/0102043] states that ``semicausal operations are semilocalizable''. That is, we show that any operation on the combined system of Alice and Bob, which does not allow Bob to send messages to Alice, can be represented as an operation by Alice, transmitting a quantum particle to Bob, and a local operation by Bob. The proof is based on the uniqueness of the Stinespring representation for a completely positive map. We sketch some of the problems in transferring these concepts to the context of relativistic quantum field theory.
Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix variate generalization of the chi-squared distribution. Since Wishart processes are defined as a solution to a stochastic differential equation, the existence and uniqueness of strong solutions will be discussed comprehensively. It is also shown that some solutions of the stochastic differential equation can be expressed as squares of matrix variate Ornstein-Uhlenbeck processes. Wishart processes have the property of being symmetric positive definite and are therefore heavily used for modeling interest rates or the covariance matrix in stochastic volatility models.
In this work, we present an expression for the near-field thermal radiative transfer between two spheres with an arbitrary numbers of coatings. We numerically demonstrate that the spectrum of heat transfer between layered spheres exhibits novel features due to the newly introduced interfaces between coatings and cores. These features include broad super-Planckian peaks at non-resonant frequencies and near-field selective emission between metallic spheres with polar material coatings. Spheres with cores and coatings of two different polar materials are also shown to exceed the total conductance of homogeneous spheres in some cases.
We present an analysis of the sky distribution of neutral hydrogen (HI) deficiency and spectral asymmetry for galaxies detected by the HI Parkes All-Sky Survey (HIPASS) as a function of projected environment density. Previous studies of galaxy HI deficiency using HIPASS were sensitive to galaxies that are extremely HI rich or poor. We use an updated binning statistic for measuring the global sky distribution of HI deficiency that is sensitive to the average deficiencies. Our analysis confirms the result from previous studies that galaxies residing in denser environments, such as Virgo, are on average more HI deficient than galaxies at lower densities. However, many other individual groups and clusters are not found to be on average significantly HI poor, in contradiction to previous work. In terms of HI spectral asymmetries, we do not recover any significant trend of increasing asymmetry with environment density as found for other galaxy samples. We also investigate the correlation between HI asymmetry and deficiency, but find no variation in the mean asymmetry of galaxies that are HI rich, normal or poor. This indicates that there is either no dependence of asymmetry on HI deficiency, or a galaxy's HI deficiency only has a small influence on the measured HI asymmetry that we are unable to observe using only integrated spectra.
When a finite volume of an etching solution comes in contact with a disordered solid, a complex dynamics of the solid-solution interface develops. Since only the weak parts are corroded, the solid surface hardens progressively. If the etchant is consumed in the chemical reaction, the corrosion dynamics slows down and stops spontaneously leaving a fractal solid surface, which reveals the latent percolation criticality hidden in any random system. Here we introduce and study, both analytically and numerically, a simple model for this phenomenon. In this way we obtain a detailed description of the process in terms of percolation theory. In particular we explain the mechanism of hardening of the surface and connect it to Gradient Percolation.
We construct a simple theoretical model to investigate how entrainment gradually erodes high-speed FR II jets. This process is described by embedding a mixing-layer model developed originally to describe FR I objects in a self-similar model for the lobe structure of classical FR II sources. Following the classical FR II models, we assume that the lobe is dominated by the particles injected from the central jet. The entrainment produces a boundary shear layer which acts at the interface between the dense central jet and the less denser surrounding lobe, and the associated erosion of the jet places interesting limits on the maximum size of FR II sources. The model shows that this limit depends mainly on the initial bulk velocity of the relativistic jet triggered. The bulk velocities of FR IIs suggested by our model are in good agreement with that obtained from direct pc-scale observations on ordinary radio galaxies and quasars. Finally, we discuss how FR IIs may evolve into FR Is upon reaching their maximum, entrainment-limited sizes.
The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+\-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c_s \geq 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r_D \geq 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the 4-point function in the local model tauNL < 2800 (95% CL). These constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.
In this paper, we study entanglement distillation of multipartite continuous-variable Gaussian entangled states. Following Opatrn\'{y} \emph{et al.}'s photon subtraction (PS) scheme, the probability of successful distillation decreases exponentially with the number of parties $N$. However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with $N$. Our protocol employs several local squeezers, but it requires only a single PS operation. Using the logarithmic negativity as a measure of entanglement, we find that both the success probability and the distilled entanglement can be improved at the same time. Moreover, an $N$-mode transfer theorem (transferring states from phase space to Hilbert space) is presented.
We introduce the notion of combinatorial type of varieties $X$ which generalizes the concept of the dual complex of SNC divisors. It is a unique, up to homotopy, finite simplicial complex $\Sigma(X)$ which is functorial with respect to morphisms of varieties. Its cohomology $H^i(\Sigma(X),Q)$ for complex projective varieties coincide with weight zero part of the Deligne filtration $W_0(H^i(X,Q))$. The notion can be understood as a topological measure of the singularities of algebaric schemes of finite type. We also prove that any variety in characteristic zero admits the Hironaka desingularization with all fibers having SNC. Moreover the dual complexes of the fibers are isomorphic on strata. Also for any morphism $f:X\to Y$ there exists a similar desingularization $\tilde{X}\to X$ for which the induce morphism $\tilde{X}\to Y$ has SNC fibers. One of the consequence is that for any projective morphism $f:X\to Y$ the combinatorial type of the fiber is a constructible function. In particular $\dim(W_0H^i(f^{-1}(y))$ is constructible.
In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3. When n=3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.
We present constraints on the parameters of the $\Lambda$CDM cosmological model in the presence of massive neutrinos, using the one-dimensional Ly$\alpha$ forest power spectrum obtained with the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS) by Palanque-Delabrouille et al. (2013), complemented by additional cosmological probes. The interpretation of the measured Ly$\alpha$ spectrum is done using a second-order Taylor expansion of the simulated power spectrum. BOSS   Ly$\alpha$ data alone provide better bounds than previous Ly$\alpha$ results, but are still poorly constraining, especially for the sum of neutrino masses $\sum m_\nu$, for which we obtain an upper bound of 1.1~eV (95\% CL), including systematics for both data and simulations. Ly$\alpha$ constraints on $\Lambda$CDM parameters and neutrino masses are compatible with CMB bounds from the Planck collaboration. Interestingly, the combination of Ly$\alpha$ with CMB data reduces the uncertainties significantly, due to very different directions of degeneracy in parameter space, leading to the strongest cosmological bound to date on the total neutrino mass, $\sum m_\nu < 0.15$~eV at 95\% CL (with a best-fit in zero). Adding recent BAO results further tightens this constraint to $\sum m_\nu < 0.14$~eV at 95\% CL. This bound is nearly independent of the statistical approach used, and of the different combinations of CMB and BAO data sets considered in this paper in addition to Ly$\alpha$. Given the measured values of the two squared mass differences $\Delta m^2$, this result tends to favor the normal hierarchy scenario against the inverted hierarchy scenario for the masses of the active neutrino species.
We study nuclear shadowing at small Bjorken x < 0.01 in the color dipole approach. Such a light-cone quantum-chromodynamics formalism based on the Green function technique incorporates naturally color transparency and coherence length effects. The nuclear shadowing for the barq-q Fock component of the photon is calculated using exact numerical solution of the evolution equation for the Green function. At x < 0.01 we demonstrate that a contribution of higher Fock states containing gluons to overall nuclear shadowing becomes effective. Numerical results for nuclear shadowing are compared with available data from the E665 and NMC collaborations. Model calculations are finally tested with the results obtained from other models.
Using finite temperature diagonalization techniques it is shown that the quarter-filled t-J-V model on a trellis lattice structure provides a quantitative explanation of the highly anisotropic optical conductivity of the $\alpha'-NaV_{2}O_{5}$ compound. The combined effects of the short-range Coulomb interaction and valence fluctuations of V-ions determine the main absorption and the fundamental gap. Inter-ladder hopping is necessary for the explanation of the anomalous in-gap absorption and generation of spectral weight at high energy. The role of valence fluctuations is explained in terms of the domain wall excitations of an anisotropic 2D Ising model in a transverse field close to criticality.
We explore the scenarios where the only accessible new states at the electroweak scale consist of a pair of color-singlet electroweak particles, whose masses are degenerate at the tree level and split only by electroweak symmetry breaking at the loop level. For the sake of illustration, we consider a supersymmetric model and study the following three representative cases with the lower-lying states as (a) two spin-1/2 Higgsino SU(2)$_L$ doublets, (b) a spin-1/2 wino SU(2)$_L$ triplet and (c) a spin-0 left-handed slepton SU(2)$_L$ doublet. Due to the mass-degeneracy, those lower-lying electroweak states are difficult to observe at the LHC and rather challenging to detect at the $e^+ e^-$ collider as well. We exploit the pair production in association with a hard photon radiation in high energy $e^+ e^-$ collisions. If kinematically accessible, such single-photon processes at $e^+e^-$ colliders with polarized beams enable us to characterize each scenario by measuring the energy and scattering angle of the associated hard photon, and to determine the spin of the nearly invisible particles unambiguously through the threshold behavior in the photon energy distribution.
We investigate the effect of the p-type top contact on the optoelectronic characteristics of light emitting diodes (LEDs) based on (In,Ga)N/GaN nanowire (NW) ensembles grown by molecular beam epitaxy on Si substrates. We compare devices fabricated with either Ni/Au or indium tin oxide (ITO) top contact. The NW-LEDs with ITO exhibit a number density of NWs emitting electroluminescence about ten times higher, significantly lower turn-on voltage and series resistance, and a relative external quantum efficiency more than one order of magnitude higher than the sample with Ni/Au. These results show that limitations in the performance of such devices reported so far can be overcome by improving the p-type top-contact.
The objective of this paper is to study the thermodynamics and thermodynamic geometry of charged de-Sitter and charged anti de-Sitter black hole solutions in massive gravity. We study the effect of curvature parameter as well as the mass of graviton in the thermodynamics of the black hole system. We further extend our studies to different topology of the space time and its effects on phase transition and thermodynamics. In addition, the phase transition structure of the black hole and its interactions are reproduced using geometrothermodynamics.
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$ this relation corresponds to the Boltzmann-Gibbs entropy, but for other values of $q$ it is claimed that it leads to a formalism which is consistent with the laws of thermodynamics. However, it is shown here that the joint entropy for systems having {\it different} values of $q$ is not defined in this formalism, and consequently fundamental thermodynamic concepts such as temperature and heat exchange cannot be considered for such systems. Moreover, for $q\ne 1$ the probability distribution for weakly interacting systems does not factor into the product of the probability distribution for the separate systems, leading to spurious correlations and other unphysical consequences, e.g. non-extensive energy, that have been ignored in various applications given in the literature.
S. Lang conjectured in 1974 that a hyperbolic algebraic variety defined over a number field has only finitely many rational points, and its analogue over function fields. We discuss the Nevanlinna-Cartan theory over function fields of arbitrary dimension and apply it for Diophantine property of hyperbolic projective hypersurfaces (homogeneous Diophantine equations) constructed by Masuda-Noguchi. We also deal with the finiteness property of $S$-units points of those Diophantine equations over number fields.
In this article we consider the growth of seed black holes immersed in dark matter halos. We first investigate the adiabatic growth in various initial distribution functions (isothermal, power law, and NFW) and find the resulting density, radial velocity, and anisotropy profiles. In addition we estimate the growth rate for a given black hole mass in the corresponding adiabatically modified dark matter distribution function. Only in the isothermal case is there a convincing black hole mass-age relation. By calculating the line of sight velocity dispersion for the various cases as a function of the black hole mass, we find the predicted adiabatic $M_{bh}-\sigma$ relation; this never approaches the recently observed power law. We conclude by abandoning adiabaticity, suggesting that the black hole grows proportionally to the dark matter halo itself on a dynamic time scale. This allows us to relate the observed $M_{bh}-\sigma$ relation to the cosmological power spectrum on galactic scales by using dimensional scaling arguments.
Helium implantation in surfaces is of interest for plasma facing materials and other nuclear applications. Vanadium as both a representative bcc material and a material relevant for fusion applications is implanted using a Helium ion beam microscope, and the resulting swelling and nanomechanical properties are quantified. These values are put in correlation to data obtained from micro residual stress measurements using a focused ion beam based ring-core technique. We found that the swelling measured is similar to literature values. Further we are able to measure the surface stress caused by the implantation and find it approaches the yield strength of the material at blistering doses. The simple calculations performed in the present work, along with several geometrical considerations deduced from experimental results confirm the driving force for blister formation comes from bulging resulting mainly from gas pressure buildup, rather than solely stress induced buckling.
The nanoflare-heating theory predicts steady hot plasma emission in the non-flaring active regions. It is hard to find this emission with conventional non-monochromatic imagers (such as Atmospheric Imaging Assembly or X-Ray Telescope), because their images contain a cool temperature background. In this work, we search for hot plasma in non-flaring active regions using the Mg XII spectroheliograph onboard Complex Orbital Observations Near-Earth of Activity on the Sun (CORONAS)-F/SPectroheliographIc X-ray Imaging Telescope (SPIRIT). This instrument acquired monochromatic images of the solar corona in the Mg XII 8.42 \AA line, which emits only at temperatures higher than 4 MK. The Mg XII images contain the signal only from hot plasma without any low-temperature background. We studied the hot plasma in active regions using the SPIRIT data from 18-28 February 2002. During this period, the Mg XII spectroheliograph worked with a 105-second cadence almost without data gaps. The hot plasma was observed only in the flaring active regions. We do not observe any hot plasma in non-flaring active regions. The hot plasma column emission measure in the non-flaring active region should not exceed $3 \times 10^{24}$ cm$^{-5}$. The hot Differential Emission Measure (DEM) is less than 0.01 % of the DEM of the main temperature component. Absence of Mg XII emission in the non-flaring active regions can be explained by weak and frequent nanoflares (delay less than 500 seconds) or by very short and intense nanoflares that lead to non-equilibrium ionization.
We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to PDEs and is not based on either integration by parts or on the maximum principle. Instead, our starting point builds on the probabilistic representation of derivatives via limits of difference quotients in the Young measures over a toric compactification of the space of jets. After developing some basic theory, as a first application we consider the Dirichlet problem and we prove existence-uniqueness-partial regularity of solutions to fully nonlinear degenerate elliptic 2nd order systems and also existence of solutions to the $\infty$-Laplace system of vectorial Calculus of Variations in $L^\infty$.