ShantanuT01/DACTYL-Pretraining huggingface dataset:
Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.
Given a closed, convex cone $K\subseteq \mathbb{R}^n$, a multivariate polynomial $f\in\mathbb{C}[\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the non-negative orthant, $K$-stability specializes to the usual notion of stability of polynomials.   We develop generalizations of preservation operations and of combinatorial criteria from usual stability towards conic stability. A particular focus is on the cone of positive semidefinite matrices (psd-stability). In particular, we prove the preservation of psd-stability under a natural generalization of the inversion operator. Moreover, we give conditions on the support of psd-stable polynomials and characterize the support of special families of psd-stable polynomials.
The adjoint 2-dimensional $QCD$ with the gauge group $SU(N)/Z_N$ admits topologically nontrivial gauge field configurations associated with nontrivial $\pi_1[SU(N)/Z_N] = Z_N$. The topological sectors are labelled by an integer $k=0,\ldots, N-1$. However, in contrast to $QED_2$ and $QCD_4$, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply.   The mod. 2 argument suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of $k(N-k)$ zero mode doublets in the topological sector $k$. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the mod. 2 conjecture.   The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.
The inertial effects of magnetic solitons play a crucial role in their dynamics and stability. Yet governing their inertial effects is a challenge for their use in real devices. Here, we show how to control the inertial effects of magnetic droplet solitons. Magnetic droplets are strongly nonlinear and localized autosolitons than can form in current-driven nanocontacts. Droplets can be considered as dynamical particles with an effective mass. We show that the dynamical droplet bears a second excitation under its own inertia. These excitations comprise a chiral profile, and appear when the droplet resists the force induced by the Oersted field of the current injected into the nanocontact. We reveal the role of the spin torque on the excitation of these chiral modes and we show how to control these modes using the current and the field.
A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant theory of such models. We use it to explain how we found our algorithm for computing the invariants [12] and to extend our method in [14] for computing equations for visible elements of order 5 in the Tate-Shafarevich group of an elliptic curve. As a special case of the latter we find a formula for the family of elliptic curves 5-congruent to a given elliptic curve in the case the 5-congruence does not respect the Weil pairing. We also give an algorithm for doubling elements in the 5-Selmer group of an elliptic curve, and make a conjecture about the matrices representing the invariant differential on a genus one normal curve of arbitrary degree.
Let $P(M)$ be the matroid base polytope of a matroid $M$. A {\em matroid base polytope decomposition} of $P(M)$ is a decomposition of the form $P(M) = \bigcup\limits_{i=1}^t P(M_{i})$ where each $P(M_i)$ is also a matroid base polytope for some matroid $M_i$, and for each $1\le i \neq j\le t$, the intersection $P(M_{i}) \cap P(M_{j})$ is a face of both $P(M_i)$ and $P(M_j)$. In this paper, we investigate {\em hyperplane splits}, that is, polytope decompositions when $t=2$. We give sufficient conditions for $M$ so $P(M)$ has a hyperplane split and characterize when $P(M_1 \oplus M_2)$ has a hyperplane split where $M_1 \oplus M_2$ denote the {\em direct sum} of matroids $M_1$ and $M_2$. We also prove that $P(M)$ has not a hyperplane split if $M$ is binary. Finally, we show that $P(M)$ has not a decomposition if its 1-skeleton is the {\em hypercube}.
We demonstrate that all rigidly rotating strings with center of mass at the origin of the $dS_3$ static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser's algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin $<$ 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.
We present results from full general relativistic three-dimensional hydrodynamics simulations of stellar core collapse of a 70 M$_\odot$ star with spectral neutrino transport. To investigate the impact of rotation on non-axisymmetric instabilities, we compute three models by parametrically changing the initial strength of rotation. The most rapidly rotating model exhibits a transient development of the low-$T/|W|$ instability with one-armed spiral flow at the early postbounce phase. Subsequently, the two-armed spiral flow appears, which persists during the simulation time. The moderately rotating model also shows the growth of the low-$T/|W|$ instability, but only with the two-armed spiral flow. In the nonrotating model, a vigorous activity of the standing accretion-shock instability (SASI) is only observed. The SASI is first dominated by the sloshing mode, which is followed by the spiral SASI until the black hole formation. We present a spectrogram analysis of the gravitational waves (GWs) and neutrinos, focusing on the time correlation. Our results show that characteristic time modulations in the GW and neutrino signals can be linked to the growth of the non-axisymmetric instabilities. We find that the degree of the protoneutron star (PNS) deformation, depending upon which modes of the non-axisymmetric instabilities develop, predominantly affects the characteristic frequencies of the correlated GW and neutrino signals. We point out that these signals would be simultaneously detectable by the current-generation detectors up to $\sim10$ kpc. Our findings suggest that the joint observation of GWs and neutrinos is indispensable for extracting information on the PNS evolution preceding the black hole formation.
Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang-Mills theory is considered as the main particular example.
SN 2002es is a peculiar subluminous Type Ia supernova (SN Ia) with a combination of observed characteristics never before seen in a SN Ia. At maximum light, SN 2002es shares spectroscopic properties with the underluminous SN 1991bg subclass of SNe Ia, but with substantially lower expansion velocities (~6000 km/s) more typical of the SN 2002cx subclass. Photometrically, SN 2002es differs from both SN 1991bg-like and SN 2002cx-like supernovae. Although at maximum light it is subluminous (M_B=-17.78 mag), SN 2002es has a relatively broad light curve (Dm15(B)=1.28 +/- 0.04 mag), making it a significant outlier in the light-curve width vs. luminosity relationship. We estimate a 56Ni mass of 0.17 +/- 0.05 M_sun synthesized in the explosion, relatively low for a SN Ia. One month after maximum light, we find an unexpected plummet in the bolometric luminosity. The late-time decay of the light curves is inconsistent with our estimated 56Ni mass, indicating that either the light curve was not completely powered by 56Ni decay or the ejecta became optically thin to gamma-rays within a month after maximum light. The host galaxy is classified as an S0 galaxy with little to no star formation, indicating the progenitor of SN 2002es is likely from an old stellar population. We also present a less extensive dataset for SN 1999bh, an object which shares similar observed properties. Both objects were found as part of the Lick Observatory Supernova Search, allowing us to estimate that these objects should account for ~2.5% of SNe Ia within a fixed volume. We find that current theoretical models are unable to explain the observed of characteristics of SN 2002es.
We study the Coulomb interaction effects on the tunneling conductance of a contact constructed of two parallel quantum wires. The following contacts are considered: two clean identical quantum wires, two disordered identical quantum wires, and asymmetric contact of one clean and another disordered quantum wires. We show that the low-voltage anomaly of the tunneling conductance is less singular than the low-energy anomaly of the one-particle density of states.
The current realization of the International Celestial Reference Frame (ICRF) comprises a total of 717 extragalactic radio sources distributed over the entire sky. An observing program has been developed to densify the ICRF in the northern sky using the European VLBI network (EVN) and other radio telescopes in Spitsbergen, Canada and USA. Altogether, 150 new sources selected from the Jodrell Bank-VLA Astrometric Survey were observed during three such EVN+ experiments conducted in 2000, 2002 and 2003. The sources were selected on the basis of their sky location in order to fill the "empty" regions of the frame. A secondary criterion was based on source compactness to limit structural effects in the astrometric measurements. All 150 new sources have been successfully detected and the precision of the estimated coordinates in right ascension and declination is better than 1 milliarcsecond (mas) for most of them. A comparison with the astrometric positions from the Very Long baseline Array Calibrator Survey for 129 common sources indicates agreement within 2 mas for 80% of the sources.
We present stellar kinematics of 22 nearby early-type galaxies (ETGs), based on two-dimensional (2D) absorption line stellar spectroscopy out to ~2-4 R_e (effective radii), as part of the ongoing SLUGGS Survey. The galaxies span a factor of 20 in intrinsic luminosity, as well as a full range of environment and ETG morphology. Our data consist of good velocity resolution (sigma_inst ~ 25 km/s) integrated stellar-light spectra extracted from the individual slitlets of custom made Keck/DEIMOS slitmasks. We extract stellar kinematics measurements (V, sigma, h_3, and h_4) for each galaxy. Combining with literature values from smaller radii, we present 2D spatially resolved maps of the large-scale kinematic structure in each galaxy. We find that the kinematic homogeneity found inside 1 R_e often breaks down at larger radii, where a variety of kinematic behaviors are observed. While central slow rotators remain slowly rotating in their halos, central fast rotators show more diversity, ranging from rapidly increasing to rapidly declining specific angular momentum profiles in the outer regions. There are indications that the outer trends depend on morphological type, raising questions about the proposed unification of the elliptical and lenticular (S0) galaxy families in the ATLAS^3D survey. Several galaxies in our sample show multiple lines of evidence for distinct disk components embedded in more slowly rotating spheroids, and we suggest a joint photometric-kinematic approach for robust bulge-disk decomposition. Our observational results appear generally consistent with a picture of two-phase (in-situ plus accretion) galaxy formation.
Topological insulators exhibit gapless edge or surface states that are topologically protected by time-reversal symmetry. However, several promising candidates for topologically insulating materials (such as Bi$_2$Se$_3$ and HgTe) contain spinful nuclei or other types of magnetic impurities that break time-reversal symmetry. We investigate the consequences of such impurities coupled to electronic edge states in a topological insulator quantum ring threaded by a magnetic flux. We use spin conservation and additional symmetry arguments to derive a universal formula for the spectrum of propagating edge modes in terms of the amplitude of transmission through the impurity. Our results apply for impurities of arbitrary spin. We show that there exists an energy regime in which the spectrum becomes nearly independent of the flux and significant spectral gaps form. We further analyze the electron-impurity entanglement entropy, finding that maximal entanglement occurs near the gaps in the spectrum. Our predictions can be investigated with quantum ring transport interference experiments or through spin-resolved STM measurements, providing a new approach to understand the role of impurities in topological insulator edge transport.
There is now convincing evidence that the intensity of HCN molecular line emission is enhanced around active galactic nuclei. In this paper we examine the specific case of the Seyfert galaxy NGC3227, for which there are subarcsecond resolution data for the HCN (1-0) 88 GHz and CO (2-1) 230 GHz rotational lines, enabling us to spatially separate a circumnuclear ring at a radius of 140pc and an inner nuclear region within 40pc of the AGN. The HCN(1-0)/CO(2-1) flux ratio differs by more than an order of magnitude between these two regions. We carry out large velocity gradient (LVG) computations to determine the range of parameters (gas temperature and density, HCN/CO abundance ratio, column densities and velocity gradients) that yield physically plausible solutions for the observed flux ratio in the central 100pc. The observed HCN/CO intensity ratio in the nucleus is consistent with very optically thick thermalized emission in very dense (>=10^5cm^{-3}) gas, in which case the HCN/CO abundance ratio there is unconstrained. Alternatively, the HCN/CO intensity ratio could be due to optically thinner emissions but with very high (~10^{-2}) HCN/CO abundance ratios. This possibility is more consistent with the CO and HCN emissions seen in the nuclei of the Seyfert galaxies NGC1068 and NGC6951. It would imply the velocity gradients are large and the clouds may be gravitationally unbound. We estimate that the X-ray ionisation rate at radii less than 20pc in the centre of NGC3227 exceeds 10^{-13}s^{-1}. X-ray ionisation and heating may lead to high HCN/CO ratios in warm gas in a high-ionisation molecular phase near the AGN.
Let $G$ be a simple graph with $n$ vertices and let $\mu_1 \geqslant \mu_2 \geqslant...\geqslant \mu_{n - 1} \geqslant \mu_n = 0$ be the eigenvalues of its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as $LEE (G) = \sum\limits_{i = 1}^n e^{\mu_i}$. Using the recent connection between Estrada index of a line graph and Laplacian Estrada index, we prove that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among trees on $n$ vertices. In addition, we find the unique tree with the second maximal Laplacian Estrada index.
We consider the first-hitting time of a tempered $\beta$-stable subordinator, also called inverse tempered stable (ITS) subordinator. The density function of the ITS subordinator is obtained, for the index of stability $\beta \in (0,1)$. The series representation of the ITS density is also obtained, which could be helpful for computational purposes. The asymptotic behaviors of the $q$-th order moments of the ITS subordinator are investigated. In particular, the limiting behaviors of the mean of the ITS subordinator is given. The limiting form of the ITS density, as the space variable $x\rightarrow 0$, and its $k$-th order derivatives are obtained. The governing PDE for the ITS density is also obtained. The corresponding known results for inverse stable subordinator follow as special cases.
Spatially homogeneous models in quantum supergravity with a nonvanishing cosmological constant are studied. A class of exact nontrivial solutions of the supersymmetry and Lorentz constraints is obtained in terms of the Chern-Simons action on the spatially homogeneous 3-manifold, both in Ashketar variables where the solution is explicit up to reality conditions, and, more concretely, in the tetrad-representation, where the solutions are given as integral representations differing only by the contours of integration. In the limit of a vanishing cosmological constant earlier exact solutions for Bianchi type IX models in the tetrad-representation are recovered and additional asymmetric solutions are found.
The most direct way to confront observed galaxies with those formed in numerical simulations is to forward-model simulated galaxies into synthetic observations. Provided that synthetic galaxy observations include similar constraints and limitations as real observations, they can be used to (1) carry out even-handed comparisons of observation and theory and (2) map the observable characteristics of simulated galaxies to their a priori known origins. In particular, integral field spectroscopy (IFS) expands the scope of such comparisons and mappings to an exceptionally broad set of physical properties. We therefore present RealSim-IFS: a tool for forward-modelling galaxies from hydrodynamical simulations into synthetic IFS observations. The core components of RealSim-IFS model the detailed spatial sampling mechanics of any fibre-bundle, image slicer, or lenslet array IFU and corresponding observing strategy, real or imagined, and support the corresponding propagation of noise adopted by the user. The code is highly generalized and can produce cubes in any light- or mass-weighted quantity (e.g. specific intensity, gas/stellar line-of-sight velocity, stellar age/metallicity, etc.). We show that RealSim-IFS exactly reproduces the spatial reconstruction of specific intensity and variance cubes produced by the MaNGA survey Data Reduction Pipeline using the calibrated fibre spectra as input. We then apply RealSim-IFS by producing a public synthetic MaNGA stellar kinematic survey of 893 galaxies with $\log M_{\star}/M_{\odot}>10$ from the TNG50 cosmological hydrodynamical simulation.
We use the model of ballistic deposition as a simple way to establish cooperation among the columns of a growing surface, \emph{the single individual of the same society}. We show that cooperation generates memory properties and at same time non-Poisson renewal events. The variable generating memory can be regarded as the velocity of a particle driven by a bath with the same time scale, and the variable generating renewal processes is the corresponding diffusional coordinate.
Neutron star mergers can form a hypermassive neutron star (HMNS) remnant, which may be the engine of a short gamma ray burst (SGRB) before it collapses to a black hole, possibly several hundred milliseconds after the merger. During the lifetime of a HMNS, numerical relativity simulations indicate that it will undergo strong oscillations and emit GWs with frequencies of a few kilohertz, which are unfortunately too high for detection to be probable with Advanced LIGO. Here we discuss the current and future prospects for detecting these oscillations as modulation of the SGRB. The understanding of the physical mechanism responsible for the HMNS oscillations will provide information on the equation of state of the hot HMNS, and the observation of these frequencies in the SGRB data would give us insight into the emission mechanism of the SGRB.
We prove that every stability two unit disk graph has chromatic number at most 3/2 times its clique number.
Publications in astrophysics are nowadays mainly published and read in digitized formats. Astrophysical publications in both research and in popular outreach often use colorful representations of stars to indicate various stellar types, that is, different spectral types or effective temperatures. Computer generated and computer displayed imagery has become an integral part of stellar astrophysics communication. There is, however, no astrophysically motivated standard color palette for illustrative representations of stars and some stars are actually represented in misleading colors. We use pre-computed PHOENIX and TLUSTY stellar model spectra and convolve them with the three standard color matching functions for human color perception between 360$\,$nm and 830$\,$nm. The color matching functions represent the three sets of receptors in the eye that respond to red, green, and blue light. For a grid of main sequence stars with effective temperatures between 2300$\,$K and 55,000$\,$K of different metallicities we present the red-blue-green and hexadecimal color codes that can be used for digitized color representations of stars as if seen from space. We find significant deviations between the color codes of stars computed from stellar spectra and from a black body radiator of the same effective temperature. We illustrate the main sequence in the color wheel and demonstrate that there are no yellow, green, cyan, or purple stars. Red dwarf stars (spectral types M0V - M9V) actually look orange to the human eye. Old white dwarfs such as WD$\,$1856$+$534, host to a newly discovered transiting giant planet candidate, occur pale orange to the human eye, not white. Our freely available software can be used to generate color codes for any input spectrum such as those from planets, galaxies, quasars etc.
We define Eisenstein series twisted by modular symbols on the group SL(n), generalizing a construction of the first author. We show that, in the case of series attached to the minimal parabolic subgroup, our series converges for all points in a suitable cone. We conclude with examples for SL(2) and SL(3).
The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the BKT insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debye-H\"uckel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of `underscreening' and `pinch point' scattering that are relevant to experiments on ionic liquids and artificial spin ice respectively.