ShantanuT01/DACTYL-Pretraining huggingface dataset:
A collection $\mathcal{C}$ of $k$-element subsets of $\{1,2,\ldots,m\}$ is weakly separated if for each $I, J \in \mathcal{C}$, when the integers $1,2,\ldots,m$ are arranged around in a circle, there is a chord separating $I \backslash J$ from $J \backslash I$. Oh, Postnikov and Speyer constructed a correspondence between weakly separated collections which are maximal by inclusion and reduced plabic graphs, a class of networks defined by Postnikov which give coordinate charts on the Grassmannian of $k$-planes in m-space. As a corollary, they proved Scott's Purity Conjecture, which states that a weakly separated collection is maximal by inclusion if and only if it is maximal by size. In this note, we describe maximal weakly separated collections corresponding to symmetric plabic graphs, which give coordinate charts on the Lagrangian Grassmannian, and prove a symmetric version of the Purity Conjecture.
We investigate the evolution of supermassive black holes in the `Evolution and Assembly of GaLaxies and their Environments' (EAGLE) cosmological hydrodynamic simulations. The largest of the EAGLE volumes covers a $(100 \,\rm cMpc)^3$ and includes state-of-the-art physical models for star formation and black hole growth that depend only on local gas properties. We focus on the black hole mass function, Eddington ratio distribution and the implied duty cycle of nuclear activity. The simulation is broadly consistent with observational constraints on these quantities. In order to make a more direct comparison with observational data, we calculate the soft and hard X-ray luminosity functions of the active galactic nuclei (AGN). Between redshifts $0$ and $1$, the simulation is in agreement with data. At higher redshifts, the simulation tends to underpredict the luminosities of the brightest observed AGN. This may be due to the limited volume of the simulation, or a fundamental deficiency of the underlying model. It seems unlikely that additional unresolved variability can account for this difference. The simulation shows a similar `downsizing' of the AGN population as seen in observational surveys.
There is overwhelming evidence that the Milky Way has formed its stars at a rel- atively constant rate throughout the Hubble time. This implies that its stock of cold gas was not in place since the beginning but it has been acquired slowly through gas accretion. The gas accretion must have been at low metallicity in order to reconcile the metallicities observed in the disc with the predictions of chemical evolution models. But how does this gas accretion take place? I review the current evidence of gas accretion into the Milky Way and similar galaxies through the infall of cold gas clouds and satellites. The conclusion from these studies is that the infalling gas at high column densities observed in HI emission is a least one order of magnitude below the value required to sustain star formation, thus accretion must come from a different channel. The likely reservoir for gas accretion is the cosmological corona of virial-temperature gas in which every galaxy must be embedded. At the interface between the disc and the corona the cold high-metallicity disc gas and the hot coronal medium must mix efficiently and this mix- ing causes the cooling and accretion of the lower corona. I show how this mechanism reproduces the kinematics of the neutral extraplanar gas in the Milky Way and other nearby galaxies and the ionised high-velocity clouds observed in HST spectra. I conclude with the speculation that the loss in efficiency of the disc-corona interaction is the ultimate cause for the evolution of disc galaxies towards the red sequence.
Extreme mass ratio inspirals (EMRIs) (capture and inspiral of a compact stellar mass object into a Massive Black Hole (MBH)) are among the most interesting objects for the gravitational wave astronomy. It is a very challenging task to detect those sources with the accurate estimation parameters of binaries primarily due to a large number of the secondary maxima on the likelihood surface. Search algorithms based on the matched filtering require computation of the gravitational waveform hundreds of thousands of times, which is currently not feasible with the most accurate (faithful) models of EMRIs. Here we propose to use a phenomenological template family which covers a large range of EMRIs parameter space. We use these phenomenological templates to detect the signal in the simulated data and then, assuming a particular EMRI model, estimate the physical parameters of the binary. We have separated the detection problem, which is done in a model-independent way, from the parameter estimation. For the latter one, we need to adopt the model for inspiral in order to map phenomenological parameters onto the physical parameter characterizing EMRIs.
We investigate the asymptotic behavior of the a large class of reversible chemical reaction-diffusion equations with the same diffusion. In particular we prove the optimal rate in two cases : when there is no diffusion and in the classical "two-by-two" case.
We introduce a valence-bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. The calculated tunneling and photoemission spectra are consistent with the phenomenology of the normal state of cuprates. We derive a low-energy description of these effects using a generalization of the slave-boson method.
We present an update of the One-Meson-Exchange (OME) results for the weak decay of s- and p-shell hypernuclei (Ref. Phys. Rev. C {\bf 56}, 339 (1997)), paying special attention to the role played by final state interactions between the emitted nucleons. The present study also corrects for a mistake in the inclusion of the $K$ and $K^*$ exchange mechanisms, which substantially increases the ratio of neutron-induced to proton-induced transitions, $\Gamma_n/\Gamma_p$. With the most up-to-date model ingredients, we find that the OME approach is able to describe very satisfactorily most of the measured observables, including the ratio $\Gamma_n/\Gamma_p$.
Early-type galaxies obey a narrow relation traced by their stellar content between the mass and size (Mass- Radius relation). The wealth of recently acquired observational data essentially confirms the classical relations found by Burstein, Bender, Faber, and Nolthenius, i.e. log(R_1/2) \propto log(Ms)\simeq 0.54 for high mass galaxies and log(R_1/2) \propto log(Ms) \simeq 0.3 for dwarf systems (shallower slope), where R_1/2 and Ms are the half-light radius and total mass in stars, respectively. Why do galaxies follow these characteristic trends? What can they tell us about the process of galaxy formation? We investigate the mechanisms which concur to shape the Mass-Radius relation, in order to cast light on the physical origin of its slope, its tightness, and its zero point. We perform a theoretical analysis, and couple it with the results of numerical hydrodynamical (NB-TSPH) simulations of galaxy formation, and with a simulation of the Mass-Radius plane itself. We propose a novel interpretation of the Mass-Radius relation, which we claim to be the result of two complementary mechanisms: on one hand, the result of local physical processes, which fixes the ratio between masses and radii of individual objects; on the other hand, the action of cosmological global, statistical principles, which shape the distribution of objects in the plane. We reproduce the Mass-Radius relation with a simple numerical technique based on this view.
I study A-infinity enhancements of algebraic Calabi-Yau triangulated categories admitting a (triangle) generator, showing that the Serre pairing on such categories determines and is determined by a cyclic pairing on an enhancement of the generator. Using this result, I construct a formal topological string field action inducing an extended D-brane superpotential for such categories. I also give a procedure for lifting certain 2d boundary topological field theories to open topological string theories generated by a single D-brane.
Applying a variational multiparticle-multihole configuration mixing method whose purpose is to include correlations beyond the mean field in a unified way without particle number and Pauli principle violations, we investigate pairing-like correlations in the ground states of $ ^{116}$Sn,$ ^{106}$Sn and $ ^{100}$Sn. The same effective nucleon-nucleon interaction namely, the D1S parameterization of the Gogny force is used to derive both the mean field and correlation components of nuclear wave functions. Calculations are performed using an axially symetric representation. The structure of correlated wave functions, their convergence with respect to the number of particle-hole excitations and the influence of correlations on single-particle level spectra and occupation probabilities are analyzed and compared with results obtained with the same two-body effective interaction from BCS, Hartree-Fock-Bogoliubov and particle number projected after variation BCS approaches. Calculations of nuclear radii and the first theoretical excited $0^+$ states are compared with experimental data.
SN 2010jl was an extremely bright, Type IIn SNe which showed a significant IR excess no later than 90 days after explosion. We have obtained Spitzer 3.6 and 4.5 \mum and JHK observations of SN 2010jl \sim90 days post explosion. Little to no reddening in the host galaxy indicated that the circumstellar material lost from the progenitor must lie in a torus inclined out of the plane of the sky. The likely cause of the high mid-IR flux is the reprocessing of the initial flash of the SN by pre-existing circumstellar dust. Using a 3D Monte Carlo Radiative Transfer code, we have estimated that between 0.03-0.35 Msun of dust exists in a circumstellar torus around the SN located 6 \times 10 ^17 cm away from the SN and inclined between 60-80\cdot to the plane of the sky. On day 90, we are only seeing the illumination of approximately 5% of this torus, and expect to see an elevated IR flux from this material up until day \sim 450. It is likely this dust was created in an LBV-like mass loss event of more than 3 Msun, which is large but consistent with other LBV progenitors such as {\eta} Carinae.
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of vacancy particles are considered. In one set all vacancies are of one-cell size. In the other set the sizes of vacancy particles match the separation between atoms. Explicit expressions are obtained for the Gibbs free energy and the distribution of spaces between atoms at thermal equilibrium. Applications to various types of interaction potentials are discussed, including long-range potentials that give rise to phase transitions. Extensions to hard rod systems are straightforward and are shown to agree with existing results for lattice models and their continuum limits.
Three lines of evidence indicate that in the most common type of core collapse supernovae, the energy deposited in the ejecta by the exploding core is approximately proportional to the progenitor mass cubed. This results stems from an observed uniformity of light curve plateau duration, a correlation between mass and ejecta velocity, and the known correlation between luminosity and velocity. This result ties in analytical and numerical models together with observations, providing us with clues as to the mechanism via which the explosion of the core deposits a small fraction of its energy into the hurled envelope.
We present the first auxiliary field Monte Carlo calculations for a rare earth nucleus, Dy-170. A pairing plus quadrupole Hamiltonian is used to demonstrate the physical properties that can be studied in this region. We calculate various static observables for both uncranked and cranked systems and show how the shape distribution evolves with temperature. We also introduce a discretization of the path integral that allows a more efficient Monte Carlo sampling.
Folsom, Kent, and Ono used the theory of modular forms modulo $\ell$ to establish remarkable ``self-similarity'' properties of the partition function and give an overarching explanation of many partition congruences. We generalize their work to analyze powers $p_r$ of the partition function as well as Andrews's spt-function. By showing that certain generating functions reside in a small space made up of reductions of modular forms, we set up a general framework for congruences for $p_r$ and spt on arithmetic progressions of the form $\ell^mn+\delta$ modulo powers of $\ell$. Our work gives a conceptual explanation of the exceptional congruences of $p_r$ observed by Boylan, as well as striking congruences of spt modulo 5, 7, and 13 recently discovered by Andrews and Garvan.
We prove the unpolarized Shafarevich conjecture for K3 surfaces: the set of isomorphism classes of K3 surfaces over a fixed number field with good reduction away from a fixed and finite set of places is finite. Our proof is based on the theorems of Faltings and Andr\'e, as well as the Kuga-Satake construction.
We show that large gaps between smooth numbers are infrequent. The key new tool is a novel mean value bound for a special type of Dirichlet polynomial.
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage Mechanics, is reformulated as a mixed form of two different types of doubly nonlinear evolution equations. Global (in time) solutions to some approximate problems are constructed by performing a time discretization argument and by taking advantage of energy techniques based on specific structures of the equation. Moreover, a variational comparison principle for (possibly non-unique) approximate solutions is established and it also enables us to obtain a local solution as a limit of approximate ones.
Aims. We study the dust content of a large optical input sample of 910 early-type galaxies (ETG) in the Virgo cluster, extending also to the dwarf ETG, and examine the results in relation with those on the other cold ISM components. Methods. We searched for far-infrared emission in all galaxies of the input sample using the 250 micron image of the Herschel Virgo Cluster Survey (HeViCS). This image covers a large fraction of the cluster. For the detected ETG we measured fluxes in 5 bands from 100 to 500 micron, and estimated the dust mass and temperature with modified black-body fits. Results. Dust is detected above the completeness limit of 25.4 mJy at 250 micron in 46 ETG, 43 of which are in the optically complete part of the input sample. In addition dust is present at fainter levels in another 6 ETG. We detect dust in the 4 ETG with synchrotron emission, including M 87. Dust appears to be much more concentrated than stars and more luminous ETG have higher dust temperatures. Dust detection rates down to the 25.4 mJy limit are 17% for ellipticals, about 40% for lenticulars (S0 + S0a) and around 3% for dwarf ETG. Dust mass does not correlate clearly with stellar mass and is often much more than that expected for a passive galaxy in a closed-box model. The dust-to-stars mass ratio anticorrelates with galaxy luminosity, and for some dwarf ETG reaches values as high as for dusty late-type galaxies. In the Virgo cluster slow rotators appear more likely to contain dust than fast ones. Comparing the dust results with those on HI from ALFALFA, there are only 8 ETG detected both in dust and in HI in the HeViCS area; 39 have dust but only an upper limit on HI, and 8 have HI but only an upper limit on dust. The locations of these galaxies in the cluster are different, with the dusty ETG concentrated in the densest regions, while the HI rich ETG are at the periphery.
The n-type doping of Ge is a self-limiting process due to the formation of vacancy-donor complexes (DnV with n <= 4) that deactivate the donors. This work unambiguously demonstrates that the dissolution of the dominating P4V clusters in heavily phosphorus-doped Ge epilayers can be achieved by millisecond-flash lamp annealing at about 1050 K. The P4V cluster dissolution increases the carrier concentration by more than three-fold together with a suppression of phosphorus diffusion. Electrochemical capacitance-voltage measurements in conjunction with secondary ion mass spectrometry, positron annihilation lifetime spectroscopy and theoretical calculations enabled us to address and understand a fundamental problem that has hindered so far the full integration of Ge with complementary-metal-oxide-semiconductor technology.
We analyze relativistic effects in transverse momentum using Quantum Molecular Dynamics [QMD] and its covariant extension Relativistic Quantum Molecular Dynamics [RQMD]. The strength of the relativistic effects is found to increase with the bombarding energy and with an averaged impact parameter. The variation in the intensity of the relativistic effects with variation in the mass of the colliding nuclei is not systematic. Furthermore, the hard EOS is affected drastically by the relativistic effects whereas the soft EOS is affected less. Our analysis shows that up to the bombarding energy of 1 GeV/nucl., the influence of relativistic effects is small. Whereas at higher energies, relativistic effects become naturally very important.
We prove a conjecture of Pixton, namely that his proposed formula for the double ramification cycle on Mbar_{g,n} vanishes in codimension beyond g. This yields a collection of tautological relations in the Chow ring of Mbar_{g,n}. We describe, furthermore, how these relations can be obtained from Pixton's 3-spin relations via localization on the moduli space of stable maps to an orbifold projective line.
A Survey of Ionized Gas in the Galaxy, made with the Arecibo telescope (SIGGMA) uses the Arecibo L-band Feed Array (ALFA) to fully sample the Galactic plane (30 < l < 75 and -2 < b < 2; 175 < l < 207 and -2 < b < 1) observable with the telescope in radio recombination lines (RRLs). Processed data sets are being produced in the form of data cubes of 2 degree (along l) x 4 degree (along b) x 151 (number of channels), archived and made public. The 151 channels cover a velocity range of 600 km/s and the velocity resolution of the survey changes from 4.2 km/s to 5.1 km/s from the lowest frequency channel to the highest frequency channel, respectively.RRL maps with 3.4 arcmin resolution and line flux density sensitivity of 0.5 mJy will enable us to identify new HII regions, measure their electron temperatures, study the physics of photodissociation regions (PDRs) with carbon RRLs, and investigate the origin of the extended low density medium (ELDM). Twelve Hn{\alpha} lines fall within the 300 MHz bandpass of ALFA; they are resampled to a common velocity resolution to improve the signal-to-noise ratio (SN) by a factor of 3 or more and preserve the line width. SIGGMA will produce the most sensitive fully sampled RRL survey to date. Here we discuss the observing and data reduction techniques in detail. A test observation toward the HII region complex S255/S257 has detected Hn{\alpha} and Cn{\alpha} lines with SN>10.
This article shows a Bessel bridge representation for the transition density of Brownian motion on the Poincare space. This transition density is also referred to as the heat kernel on the hyperbolic space in differential geometry literature. The representation recovers the well-known closed form expression for the heat kernel on hyperbolic space in dimension three. However, the newly derived bridge representation is different from the McKean kernel in dimension two and from the Gruet's formula in higher dimensions. The methodology is also applicable to the derivation of an analogous Bessel bridge representations for heat kernel on a Cartan-Hadamard radially symmetric space and for the transition density of hyperbolic Bessel process.
We investigate the properties of both the prompt and X-ray afterglows of gamma-ray bursts (GRBs) in the burst frame with a sample of 33 Swift GRBs. Assuming that the steep decay segment in the canonical X-ray afterglow lightcurves is due to the curvature effect, we fit the lightcurves with a broken power-law to derive the zero time of the last emission epoch of the prompt emission (t1) and the beginning as well as the end time of the shallow decay segment (t2 and t3).We show that both the isotropic peak gamma-ray luminosity and gamma-ray energy are correlated with the isotropic X-ray energy of the shallow decay phase and the isotropic X-ray luminosity at t2. We infer the properties of the progenitor stars based on a model proposed by Kumar et al. who suggested that both the prompt gamma-rays and the X-ray afterglows are due to the accretions of different layers of materials of the GRB progenitor star by a central black hole (BH). We find that most of the derived masses of the core layers are 0.1-5 solar mass with a radius of 10^8-10^10 cm. The rotation parameter is correlated with the burst duration, being consistent with the expectation of collapsar models. The estimated radii and the masses of the fall-back materials for the envelope layers are 10^10-10^12 cm and 10^-3~1 solar mass, respectively. The average accretion rates in the shallow decay phase are correlated with those in the prompt gamma-ray phase, but they are much lower. The derived radii of the envelope are smaller than the photospheric radii of Wolf-Rayet (WR) stars. It is interesting that the assembled mass density profile for the bursts in our sample is also well consistent with the simulation for a pre-supernova star with 25 solar mass.
In this paper we focus on the TP-AGB evolution of intermediate-mass stars experiencing envelope burning (M=4-5Mo). The approach we have adopted is a semi-analytical one as it combines analytical relationships derived from complete models of TP-AGB stars with sole envelope models in which the physical structure is calculated from the photosphere down to the core. Our efforts are directed to analyse the effects produced by envelope burning, such as: i) the energy contribution which may drive significant deviations from the standard core mass-luminosity relationship; and ii) the changes in the surface chemical composition due to nuclear burning via the CNO cycle. Evolutionary models for stars with initial mass of 4.0, 4.5, 5.0 Mo and two choices of the initial chemical composition ([Y=0.28,Z=0.02] and [Y=0.25,Z=0.008]) are calculated from the first thermal pulse till the complete ejection of the envelope. We find that massive TP-AGB stars can rapidly reach high luminosities (-6>Mbol>-7), without exceeding, however, the classical limit to the AGB luminosity of Mbol~-7.1 corresponding to the Chandrasekhar value of the core mass. No carbon stars brighter than Mbol~-6.5 are predicted to form (the alternative of a possible transition from M-star to C-star during the final pulses is also explored), in agreement with observations which indicate that most of the very luminous AGB stars are oxygen-rich. Finally, new chemical yields from stars in the mass range 4-5 Mo are presented, so as to extend the sets of stellar yields from low-mass stars already calculated by Marigo et al. (1996). For each CNO element we give both the secondary and the primary components.