ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the mass-metallicity relation of galactic systems with stellar masses larger than 10^9 Mo in Lambda-CDM scenarios by using chemical hydrodynamical simulations. We find that this relation arises naturally as a consequence of the formation of the structure in a hierarchical scenario. The hierarchical building up of the structure determines a characteristic stellar mass at M_c ~10^10.2 Moh^-1 which exhibits approximately solar metallicities from z ~ 3 to z=0. This characteristic mass separates galactic systems in two groups with massive ones forming most of their stars and metals at high redshift. We find evolution in the zero point and slope of the mass-metallicity relation driven mainly by the low mass systems which exhibit the larger variations in the chemical properties. Although stellar mass and circular velocity are directly related, the correlation between circular velocity and metallicity shows a larger evolution with redshift making this relation more appropriate to confront models and observations. The dispersion found in both relations is a function of the stellar mass and reflects the different dynamical history of evolution of the systems.
Let G be a finite group and \rho: G--> End(E) be a group representation of G on a coherent sheaf over an integral scheme. The purpose of this paper shall give a decomposition theorem of such representations in non-splitting components and apply this results to the studie of Galois covers
We study three instability stratifications of the stack of twisted Higgs bundle of a fixed rank and degree on a smooth complex projective curve. The first is the Harder-Narasimhan (HN) stratification, defined by the instability type of the Higgs bundle. The second is the bundle Harder-Narasimhan (bHN) stratification, defined by the instability type of the underlying bundle. While an unstable HN stratum fibres over the stack parametrising Higgs bundles which are isomorphic to their graded, this is not true for Higgs bundles of unstable bHN type. Obtaining such a fibration requires refining the bHN stratification; this is the third instability stratification. After introducing these three stratifications, we establish comparison results. In particular we obtain explicit criteria for determining semistability of a Higgs bundle of low rank with unstable underlying bundle. Then we show how the HN and bHN stratifications can be used to filter the stack of Higgs bundles by global quotient stacks in two different ways. Finally we use these filtrations to relate the HN and bHN stratifications to GIT instability stratifications, and the refined bHN stratification to a Bialynicki-Birula stratification.
Cyg X-3 is an unusual X-ray binary which shows remarkable correlative behavior between the hard X-ray, soft X-ray, and the radio. We present an analysis of these long term light curves in the context of spectral changes of the system. This analysis will also incorporate a set of pointed RXTE observations made during a period when Cyg X-3 made a transition from a quiescent radio state to a flaring state (including a major flare) and then returned to a quiescent radio state.
We introduce a self-adjoint operator that indicates the direction of time within the framework of standard quantum mechanics. That is, as a function of time its expectation value decreases monotonically for any initial state. This operator can be defined for any system governed by a Hamiltonian with a uniformly finitely degenerate, absolutely continuous and semibounded spectrum. We study some of the operator's properties and illustrate them for a large equivalence class of scattering problems. We also discuss some previous attempts to construct such an operator, and show that the no-go theorems developed in this context are not applicable to our construction.
We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bi-directional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center, followed by power-law long tails at both spectrum edges. The largest eigenvalue \lambda_1 depends on system size N as \lambda_1 \sim N^{1/4} for large N, and the corresponding eigenfunction is strongly localized at the hub, the vertex with largest degree. The component of the normalized eigenfunction at the hub is of order unity. We also find that the mass gap scales as N^{-0.68}.
We have quantified the statistical uncertainties of the low-energy coupling-constants (LECs) of an optimized nucleon-nucleon (NN) interaction from chiral effective field theory ($\chi$EFT) at next-to-next-to-leading order (NNLO). In addition, we have propagated the impact of the uncertainties of the LECs to two-nucleon scattering phase shifts, effective range parameters, and deuteron observables.
A theory of far-from-equilibrium transport in arrays of tunnel junctions is developed. We show that at low temperatures the energy relaxation ensuring tunneling current can become a cascade two-stage process. First, charge carriers lose their energy to a bosonic environment via non-phonon energy exchange. The role of such an environment can be taken by electromagnetic fluctuations or dipole excitations (electron-hole pairs). The environment, in its turn, relaxes the energy to the thermostat by means of phonon irradiation. We derive the current-voltage characteristics for the arrays and demonstrate that opening the energy gap in the spectrum of the environmental excitations completely suppresses the tunneling current. The consequences of the cascade relaxation in various physical systems are discussed.
We here re-examine the validity of the constant-index power-law relation between the fireshell Lorentz gamma factor and its radial coordinate, usually adopted in the current Gamma-Ray Burst (GRB) literature on the grounds of an "ultrarelativistic" approximation. Such expressions are found to be mathematically correct but only approximately valid in a very limited range of the physical and astrophysical parameters and in an asymptotic regime which is reached only for a very short time, if any.
We study a nonlinear integro-differential equation arising in population dynamics. It has been already proved by Rybka, Tang and Waxman that it has a unique local in time solution. Here, after deriving appropriate a priori estimates we show that the dynamics is global in time.
We investigate physical properties of an Anderson impurity embedded in the bulk of a topological insulator. The slave-boson mean-field approximation is used to account for the strong electron correlation at the impurity. Different from the results of a quantum impurity on the surface of a topological insulator, we find for the band-inverted case, a Kondo resonant peak and in-gap bound states can be produced simultaneously. However, only one type of them appears for the normal case. It is shown that the mixed-valence regime is much broader in the band-inverted case, while it shrinks to a very narrow regime in the normal case. Furthermore, a self-screening of the Kondo effect may appear when the interaction between the bound-state spin and impurity spin is taken into account.
The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e.existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as $10^{23}$ degrees of freedom systems, {\it i.e.} for simple as well as very complex systems, and reflecting the Hamiltonian nature of the microscopic motion. In Nonequilibrium Thermodynamics theorems of comparable generality do not seem to be available. Yet it is possible to find general, model independent, properties valid even for simple chaotic systems ({\it i.e.} the hyperbolic ones), which acquire special interest for large systems: the Chaotic Hypothesis leads to the Fluctuation Theorem which provides general properties of certain very large fluctuations and reflects the time-reversal symmetry. Implications on Fluids and Quantum systems are briefly hinted. The physical meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation Theorem is discussed in the context of their interpretation and relevance in terms of Coarse Grained Partitions of phase space. This review is written taking some care that each section and appendix is readable either independently of the rest or with only few cross references.
This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Dr\"{u}hl in 1982. The experimental results demonstrated the possibility of simultaneously observing both particle-like and wave-like behavior of a quantum via quantum entanglement. The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum.
This paper has been withdrawn as it has been superseded by 0808.2697
We report on observations of the active K2 dwarf $\epsilon$ Eridani based on contemporaneous SPIRou, NARVAL, and TESS data obtained over two months in late 2018, when the activity of the star was reported to be in a non-cyclic phase. We first recover the fundamental parameters of the target from both visible and nIR spectral fitting. The large-scale magnetic field is investigated from polarimetric data. From unpolarized spectra, we estimate the total magnetic flux through Zeeman broadening of magnetically sensitive nIR lines and the chromospheric emission using the CaII H & K lines. The TESS photometric monitoring is modeled with pseudo-periodic Gaussian Process Regression. Fundamental parameters of $\epsilon$ Eridani derived from visible and near-infrared wavelengths provide us with consistent results, also in agreement with published values. We report a progressive increase of macroturbulence towards larger nIR wavelengths. Zeeman broadening of individual lines highlights an unsigned surface magnetic field $B_{\rm mono} = 1.90 \pm 0.13$ kG, with a filling factor $f = 12.5 \pm 1.7$% (unsigned magnetic flux $Bf = 237 \pm 36$ G). The large-scale magnetic field geometry, chromospheric emission, and broadband photometry display clear signs of non-rotational evolution over the course of data collection. Characteristic decay times deduced from the light curve and longitudinal field measurements fall in the range 30-40 d, while the characteristic timescale of surface differential rotation, as derived through the evolution of the magnetic geometry, is equal to $57 \pm 5$ d. The large-scale magnetic field exhibits a combination of properties not observed previously for $\epsilon$ Eridani, with a surface field among the weakest previously reported, but also mostly axisymmetric, and dominated by a toroidal component.
A systematic review of main physical effects generated by ion exchange in silicate glasses is presented. Ion concentration distributions, residual stress profiles, and refractive index effects are discussed with particular attention on the physical and mathematical underpinnings of the ion exchange process. The study has the purpose of presenting a scientific foundation to enable future developments in the field. In this respect, the objective of this article is more educational than to present new research results. Appendixes are included to consider the detail of some specific topics without disrupting the continuity of the overall discussion. Despite the review approach of this study, some original topics are included, such as the concentration distribution with variable boundary conditions and residual stress profile with anomalies due to different relaxation mechanisms, viz., either isochoric and non-isochoric and stress driven or free energy driven. The time scale of the different relaxation mechanisms results, for some specific glass chemical compositions, in the appearance of a subsurface compression maximum progressively moving apart from glass surface and eventually turning in a reversal from compression into tensile state upon prolonged ion exchange processes. Finally, a broad discussion on optical effects induced by ion exchange is presented, paying particular attention to the possibility of experimental determination of residual stress profile.
We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the order one - that we evaluate and compare at two different scales - and are specifically tailored for studying the Gaussian fluctuations of sequences of geometric functionals displaying a form of weak stabilization - see Penrose and Yukich (2001) and Penrose (2005). Our main bounds extend the estimates recently exploited by Chatterjee and Sen (2017) in the proof of a quantitative version of the central limit theorem (CLT) for the length of the Poisson-based Euclidean minimal spanning tree (MST). We develop in full detail three applications of our bounds, namely: (i) to a quantitative multidimensional spatial CLT for functionals of the on-line nearest neighbor graph, (ii) to a quantitative multidimensional CLT involving functionals of the empirical measure associated with the edge-length of the Euclidean MST, and (iii) to a collection of multidimensional CLTs for geometric functionals of the excursion set of heavy-tailed shot noise random fields. Application (i) is based on a collection of general probabilistic approximations for strongly stabilizing functionals, that is of independent interest.
We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.
Recent advances in non-critical string theory allow a unique continuation of critical Polyakov string amplitudes to off-shell momenta, while preserving conformal invariance. These continuations possess unusual, apparently stringy, characteristics, as we illustrate with our results for three-point functions. (Talk by R.C.M. at Strings '93)
The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins. The method is based on path factorization of the evolution operator and requires no prior knowledge of the underlying energy landscape. The efficiency of the new method is demonstrated in simulations of anomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetic trapping.
Scaling relations between supermassive black hole mass, M_BH, and host galaxy properties are a powerful instrument for studying their coevolution. A complete picture involving all of the black hole scaling relations, in which each relation is consistent with the others, is necessary to fully understand the black hole-galaxy connection. The relation between M_BH and the central light concentration of the surrounding bulge, quantified by the S\'ersic index n, may be one of the simplest and strongest such relations, requiring only uncalibrated galaxy images. We have conducted a census of literature S\'ersic index measurements for a sample of 54 local galaxies with directly measured M_BH values. We find a clear M_BH - n relation, despite an appreciable level of scatter due to the heterogeneity of the data. Given the current M_BH - L_sph and the L_sph - n relations, we have additionally derived the expected M_BH - n relations, which are marginally consistent at the 2 sigma level with the observed relations. Elliptical galaxies and the bulges of disc galaxies are each expected to follow two distinct bent M_BH - n relations due to the S\'ersic/core-S\'ersic divide. For the same central light concentration, we predict that M_BH in the S\'ersic bulges of disc galaxies are an order magnitude higher than in S\'ersic elliptical galaxies if they follow the same M_BH - L_sph relation.
In general relativity, the causal structure of space-time may sometimes be depicted by conformal Carter-Penrose diagrams or a recent extension of these - the projection diagrams. The introduction of conformal diagrams in the sixties was one of the progenitors of the golden age of relativity. They are the key ingredient of many scientific papers. Unfortunately, drawing them in the form suitable for LaTeX documents is time-consuming and not easy. We present below a library that allows one to draw an arbitrary conformal diagram in a few simple steps.
The X-ray background (XRB) is due to the aggregate of active galactic nuclei (AGN), which peak in activity at z~1 and is often modeled as the sum of different proportions of unabsorbed, moderately- and heavily-absorbed AGN. We present the summed spectrum of a complete sample of local AGN (the Northern Galactic Cap of the 58-month Swift/BAT catalog, z<0.2) using 0.4-200keV data and directly determine the different proportions of unabsorbed, moderately and heavily-absorbed AGN that make up the summed spectrum. This stacked low redshift AGN spectrum is remarkably similar in shape to the XRB spectrum (when shifted to z~1), but the observed proportions of different absorption populations differ from most XRB synthesis models. AGN with Compton-thick absorption account for only ~12% of the sample, but produce a significant contribution to the overall spectrum. We confirm that Compton reflection is more prominent in moderately-absorbed AGN and that the photon index differs intrinsically between unabsorbed and absorbed AGN. The AGN in our sample account for only ~1% of the XRB intensity. The reproduction of the XRB spectral shape suggests that strong evolution in individual AGN properties is not required between z~0 and 1.
We analyse the wave function collapse as seem by two distinct observers (with identical detectors) in relative motion. Imposing that the measurement process demands information transfer from the system to the detectors, we note that although different observers will acquire different amount of information from their measurements due to correlations between spin and momentum variables, all of them will agree about the orthogonality of the outcomes, as defined by their own reference frame. So, in this sense, such a quantum mechanical postulate is observer invariant, however the effective efficiency of the measurement process differs for each observer.
Using pulsewidth data for 872 isolated radio pulsars we test the hypothesis that pulsars evolve through a progressive narrowing of the emission cone combined with progressive alignment of the spin and magnetic axes. The new data provide strong evidence for the alignment over a time-scale of about 1 Myr with a log standard deviation of around 0.8 across the observed population. This time-scale is shorter than the time-scale of about 10 Myr found by previous authors, but the log standard deviation is larger. The results are inconsistent with models based on magnetic field decay alone or monotonic counter-alignment to orthogonal rotation. The best fits are obtained for a braking index parameter n_gamma approximately equal to 2.3, consistent the mean of the six measured values, but based on a much larger sample of young pulsars. The least-squares fitted models are used to predict the mean inclination angle between the spin and magnetic axes as a function of log characteristic age. Comparing these predictions to existing estimates it is found that the model in which pulsars are born with a random angle of inclination gives the best fit to the data. Plots of the mean beaming fraction as a function of characteristic age are presented using the best-fitting model parameters.
Let $F$ be a field of characteristic $p>2$ and $A\subset F$ have sufficiently small cardinality in terms of $p$. We improve the state of the art of a variety of sum-product type inequalities. In particular, we prove that $$ |AA|^2|A+A|^3 \gg |A|^6,\qquad |A(A+A)|\gg |A|^{3/2}. $$ We also prove several two-variable extractor estimates: ${\displaystyle |A(A+1)| \gg|A|^{9/8},}$ $$ |A+A^2|\gg |A|^{11/10},\; |A+A^3|\gg |A|^{29/28}, \; |A+1/A|\gg |A|^{31/30}.$$   Besides, we address questions of cardinalities $|A+A|$ vs $|f(A)+f(A)|$, for a polynomial $f$, where we establish the inequalities $$ \max(|A+A|,\, |A^2+A^2|)\gg |A|^{8/7}, \;\; \max(|A-A|,\, |A^3+A^3|)\gg |A|^{17/16}. $$ Szemer\'edi-Trotter type implications of the arithmetic estimates in question are that a Cartesian product point set $P=A\times B$ in $F^2$, of $n$ elements, with $|B|\leq |A|< p^{2/3}$ makes $O(n^{3/4}m^{2/3} + m + n)$ incidences with any set of $m$ lines. In particular, when $|A|=|B|$, there are $\ll n^{9/4}$ collinear triples of points in $P$, $\gg n^{3/2}$ distinct lines between pairs of its points, in $\gg n^{3/4}$ distinct directions.   Besides, $P=A\times A$ determines $\gg n^{9/16}$ distinct pair-wise distances.   These estimates are obtained on the basis of a new plane geometry interpretation of the incidence theorem between points and planes in three dimensions, which we call collisions of images.
We present results from the final six months of a survey to search for pulsations in white dwarfs and hot subdwarf stars with the Kepler spacecraft. Spectroscopic observations are used to separate the objects into accurate classes, and we explore the physical parameters of the subdwarf B (sdB) stars and white dwarfs in the sample. From the Kepler photometry and our spectroscopic data, we find that the sample contains 5 new pulsators of the V1093 Her type, one AM CVn type cataclysmic variable, and a number of other binary systems. This completes the survey for compact pulsators with Kepler. No V361 Hya type of short-period pulsating sdB stars were found in this half, leaving us with a total of one single multiperiodic V361 Hya and 13 V1093 Her pulsators for the full survey. Except for the sdB pulsators, no other clearly pulsating hot subdwarfs or white dwarfs were found, although a few low-amplitude candidates still remain. The most interesting targets discovered in this survey will be observed throughout the remainder of the Kepler Mission, providing the most long-term photometric datasets ever made on such compact, evolved stars. Asteroseismic investigations of these datasets will be invaluable in revealing the interior structure of these stars, and will boost our understanding of their evolutionary history.
We study a basic plasma physics model--the one-fluid Euler--Poisson system on the square torus, in which a compressible electron fluid flows under its own electrostatic field. In this paper we prove long-term regularity of periodic solutions of this system in 2 spatial dimensions.   Our main conclusion is that on a square torus of side length $R$, if the initial data is sufficiently close to a constant solution, then the solution is wellposed for a time at least $R/\epsilon^2(\log R)^{O(1)}$, where $\epsilon$ is the size of the initial data.