ShantanuT01/DACTYL-Pretraining huggingface dataset:
The number of Monotone Triangles with bottom row k1 < k2 < ... < kn is given by a polynomial alpha(n; k1,...,kn) in n variables. The evaluation of this polynomial at weakly decreasing sequences k1 >= k2 >= ... >= kn turns out to be interpretable as signed enumeration of new combinatorial objects called Decreasing Monotone Triangles. There exist surprising connections between the two classes of objects -- in particular it is shown that alpha(n; 1,2,...,n) = alpha(2n; n,n,n-1,n-1,...,1,1). In perfect analogy to the correspondence between Monotone Triangles and Alternating Sign Matrices, the set of Decreasing Monotone Triangles with bottom row (n,n,n-1,n-1,...,1,1) is in one-to-one correspondence with a certain set of ASM-like matrices, which also play an important role in proving the claimed identity algebraically. Finding a bijective proof remains an open problem.
Quantized particle or spin transport upon cyclic parameter variations, determined by topological invariants, is a key signature of Chern insulators in the ground state. While measurable many-body observables exist that preserve the integrity of topological invariants also at finite temperature, quantized transport is generically lost. We here show that a coupling of a one-dimensional Chern insulator at arbitrary finite temperature to an auxiliary lattice can induce quantized transport determined by the finite-temperature invariant. We show for the example of a Rice-Mele model that the spatial distribution of a single particle in the auxiliary chain moves by a quantized number of unit cells in a Thouless cycle when subtracting a spatially homogeneous offset even at a temperature exceeding the band gap.
Let $\Sigma_{2n}$ be the set of all partitions of the even integers from the interval $(4,2n], n>2,$ into two odd prime parts. We show that $\mid\Sigma_{2n}\mid\sim 2n^2/\log^2{n}$ as $n\to\infty$. We also assume that a partition is selected uniformly at random from the set $\Sigma_{2n}$. Let $2X_n\in (4,2n]$ be the size of this partition. We prove a limit theorem which establishes that $X_n/n$ converges weakly to the maximum of two random variables which are independent copies of a uniformly distributed random variable in the interval $(0,1)$. Our method of proof is based on a classical Tauberian theorem due to Hardy, Littlewood and Karamata. We also show that the same asymptotic approach can be applied to partitions of integers into an arbitrary and fixed number of odd prime parts
This letter studies the formation of azimuthal metallicity variations in the disks of spiral galaxies in the absence of initial radial metallicity gradients. Using high-resolution $N$-body simulations, we model composite stellar discs, made of kinematically cold and hot stellar populations, and study their response to spiral arm perturbations. We find that, as expected, disk populations with different kinematics respond differently to a spiral perturbation, with the tendency for dynamically cooler populations to show a larger fractional contribution to spiral arms than dynamically hotter populations. By assuming a relation between kinematics and metallicity, namely the hotter the population, the more metal-poor it is, this differential response to the spiral arm perturbations naturally leads to azimuthal variations in the mean metallicity of stars in the simulated disk. Thus, azimuthal variations in the mean metallicity of stars across a spiral galaxy are not necessarily a consequence of the reshaping, by radial migration, of an initial radial metallicity gradient. They indeed arise naturally also in stellar disks which have initially only a negative vertical metallicity gradient.
Supermassive black hole binaries are likely to accrete interstellar gas through a circumbinary disk. Shortly before merger, the inner portions of this circumbinary disk are subject to general relativistic effects. To study this regime, we approximate the spacetime metric of close orbiting black holes by superimposing two boosted Kerr-Schild terms. After demonstrating the quality of this approximation, we carry out very long-term general relativistic magnetohydrodynamic simulations of the circumbinary disk. We consider black holes with spin dimensionless parameters of magnitude 0.9, in one simulation parallel to the orbital angular momentum of the binary, but in another anti-parallel. These are contrasted with spinless simulations. We find that, for a fixed surface mass density in the inner circumbinary disk, aligned spins of this magnitude approximately reduce the mass accretion rate by 14% and counter-aligned spins increase it by 45%, leaving many other disk properties unchanged.
Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, one should consider a suitable class of SPDEs defined on a graph, corresponding to the stream function of the underlying incompressible flow.
The Majumdar-Papapetrou system is the subset of the Einstein-Maxwell-charged dust matter theory, when the charge of each particle is equal to its mass. Solutions for this system are less difficult to find, in general one does not need even to impose any spatial symmetry a priori. For instance, any number of extreme Reissner-Nordstrom solutions (which in vacuum reduce to extreme Reissner-Nordstrom black holes) located at will is a solution. In matter one can also find solutions with some ease. Here we find an exact solution of the Majumdar-Papapetrou system, a spherically symmetric charged thick shell, with mass m, outer radius r_o, and inner radius r_i. This solution consists of three regions, an inner Minkowski region, a middle region with extreme charged dust matter, and an outer Reissner-Nordstrom region. The matching of the regions, obeying the usual junction conditions for boundary surfaces, is continuous. For vanishing inner radius, one obtains a Bonnor star, whereas for vanishing thickness, one obtains an infinitesimally thin shell. For sufficiently high mass of the thick shell or sufficiently small outer radius, it forms an extreme Reissner-Nordstrom quasi-black hole, i.e., a star whose gravitational properties are virtually indistinguishable from a true extreme black hole. This quasi-black hole has no hair and has a naked horizon, meaning that the Riemann tensor at the horizon on an infalling probe diverges. At the critical value, when the mass is equal to the outer radius, m=r_o, there is no smooth manifold. Above the critical value when m>r_o there is no solution, the shell collapses into a singularity. Systems with m< r_o are neutrally stable. Many of these properties are similar to those of gravitational monopoles.
In this talk we review the consequences of the chiral SU(3) symmetry for strangeness propagation in nuclear matter. Objects of crucial importance are the meson-baryon scattering amplitudes obtained within the chiral coupled-channel effective field theory. Results for antikaon and hyperon-resonance spectral functions in cold nuclear matter are presented and discussed. The importance of the Sigma(1385) resonance for the subthreshold antikaon production in heavy-ion reaction at SIS is pointed out. The in-medium properties of the latter together with an antikaon spectral function based on chiral SU(3) dynamics suggest a significant enhancement of the pi \Lambda -> bar K N reaction in nuclear matter.
For certain K3 surfaces, there are two constructions of mirror symmetry that are very different. The first, known as BHK mirror symmetry, comes from the Landau-Ginzburg model for the K3 surface; the other, known as LPK3 mirror symmetry, is based on a lattice polarization of the K3 surface in the sense of Dolgachev's definition. There is a large class of K3 surfaces for which both versions of mirror symmetry apply. In this class we consider the K3 surfaces admitting a certain purely nonsymplectic automorphism of order 4, 8, or 12, and we complete the proof that these two formulations of mirror symmetry agree for this class of K3 surfaces.
We compute the divisor class group and the Picard group of projective varieties with Hibi rings as homogeneous coordinate rings. These varieties are precisely the toric varieties associated to order polytopes. We use tools from the theory of toric varieties to get a description of the two groups which only depends on combinatorial properties of the underlying poset.
Comprehensive muon spin rotation/relaxation (muSR) and neutron powder diffraction (NPD) studies supported via bulk measurements have been performed on the ordered double perovskite Sr2YbRuO6 to investigate the nature of the magnetic ground state. Two sharp transitions at TN1 ~ 42 K and TN2 ~ 36 K have been observed in the static and dynamic magnetization measurements, coinciding with the heat capacity data. In order to confirm the origin of the observed phase transitions and the magnetic ground state, microscopic evidences are presented here. An initial indication of long-range magnetic ordering comes from a sharp drop in the muon initial asymmetry and a peak in the relaxation rate near TN1. NPD confirms that the magnetic ground state of Sr2YbRuO6 consists of an antiferromagnetic (AFM) structure with interpenetrating lattices of parallel Yb3+ and Ru5+ moments lying in the ab-plane and adopting a A-type AFM structure. Intriguingly, a small but remarkable change is observed in the long-range ordering parameters at TN2 confirming the presence of a weak spin reorientation (i.e. change in spin configuration) transition of Ru and Yb moments, as well as a change in the magnetic moment evolution of the Yb3+ spins at TN2. The temperature dependent behaviour of the Yb3+ and Ru5+ moments suggests that the 4d-electrons of Ru5+ play a dominating role in stabilizing the long range ordered magnetic ground state in the double perovskite Sr2YbRuO6 whereas only the Yb3+ moments show an arrest at TN2. The observed magnetic structure and the presence of a ferromagnetic interaction between Ru- and Yb- ions are explained with use of the Goodenough-Kanamori-Anderson (GKA) rules. Possible reasons for the presence of the second magnetic phase transition and of a compensation point in the magnetization data are linked to competing mechanisms of magnetic anisotropy.
X-ray observations of hot gas in galaxy groups indicate higher entropies than can be achieved in the accretion shocks as it fell into the dark halos. It has been proposed that this entropy excess results from some universal external heating process in the early universe - AGN, population III stars, etc. - that occurred before most of the gas entered the dark halos. Alternatively, the hot gas in groups may be heated internally by Type II supernovae when the galactic stars formed. We investigate here the gas-dynamical consequences of various amounts of external, high redshift heating and compare with internal supernova heating. Radiative losses and distributed mass dropout are included. We find that externally heated flows are unsatisfactory; when the heating is high enough to bring the X-ray luminosities into agreement with observations, the gas entropy is too high. Flows internally heated by Type II supernovae are preferred. Our results are insensitive to the epoch and spatial distribution of the supernova heating process. However, with a Salpeter IMF a large fraction of the energy produced by supernovae must heat the hot gas. Alternatively, only about 20 percent of the Type II supernova energy would be required to heat the gas if the initial mass function is flatter than Salpeter, as suggested by stellar mass to light ratios.
Two ways of possibly solving the angular momentum problem plaguing cold dark matter (CDM) ab initio simulations of disk galaxy formation are discussed: 1) Stellar feedback processes and 2) Warm dark matter (WDM) rather than CDM.   In relation to the chemical evolution of disk galaxies our simulations indicate that in case 1) the first generation of disk stars formed in disk galaxies like the Milky Way should have an abundance about two dex below solar, in fairly good agreement with the lowest observed abundance of the metal-weak tail of the Galactic thick disk. For the second case no such statements can be made without further assumptions about the star-formation history of the galaxies.   We find that the I-band Tully-Fisher relation can be matched by WDM disk galaxy formation simulations provided (M/L_I) is about 0.8 for disk galaxies, which Sommer-Larsen & Dolgov (1999) argue is a reasonable value.   Finally it is discussed how the magnetic field strengths observed in galactic disks can be obtained through disk galaxy formation, as an alternative to the conventional dynamo hypothesis.
We use the Robinson-Schensted correspondence, followed by symbol-crunching, in order to derive explicit expressions for the quantities mentioned in the title. We follow it by number crunching, in order to compute the first terms of these sequences. As an encore, we cleverly implement Ira Gessel's celebrated determinant formula for the generating functions of these sequences, to crank out many terms.   This modest tribute is dedicated to one of the greatest enumerators alive today (and definitely the most modest one!), Ira Martin Gessel, who is turning 64 years-old today
We present a determination of the distributions of photon spectral index and gamma-ray flux - the so called LogN-LogS relation - for the 352 blazars detected with a greater than approximately seven sigma detection threshold and located above +/- 20 degrees Galactic latitude by the Large Area Telescope of the Fermi Gamma-ray Space Telescope in its first year catalog. Because the flux detection threshold depends on the photon index, the observed raw distributions do not provide the true LogN-LogS counts or the true distribution of the photon index. We use the non-parametric methods developed by Efron and Petrosian to reconstruct the intrinsic distributions from the observed ones which account for the data truncations introduced by observational bias and includes the effects of the possible correlation between the two variables. We demonstrate the robustness of our procedures using a simulated data set of blazars and then apply these to the real data and find that for the population as a whole the intrinsic flux distribution can be represented by a broken power law with high and low indexes of -2.37 +/- 0.13 and -1.70 +/- 0.26, respectively, and the intrinsic photon index distribution can be represented by a Gaussian with mean of 2.41 +/- 0.13 and width of 0.25 +/- 0.03. We also find the intrinsic distributions for the sub-populations of BL Lac and FSRQs type blazars separately. We then calculate the contribution of Fermi blazars to the diffuse extragalactic gamma-ray background radiation. Under the assumption that the flux distribution of blazars continues to arbitrarily low fluxes, we calculate the best fit contribution of all blazars to the total extragalactic gamma-ray output to be 60%, with a large uncertainty.
We analyze the continuous measurement of two non-commuting observables for a qubit, and investigate whether the simultaneously observed noisy signals are consistent with the evolution of an equivalent classical system. Following the approach outlined by Leggett and Garg, we show that the readouts violate macrorealistic inequalities for arbitrarily short temporal correlations. Moreover, the derived inequalities are manifestly violated even in the absence of Hamiltonian evolution, unlike for Leggett-Garg inequalities that use a single continuous measurement. Such a violation should indicate the failure of at least one postulate of macrorealism: either physical quantities do not have well defined values at all times, or the measurement process itself disturbs what is being measured. For measurements of equal strength we are able to construct a classical stochastic model for a spin that perfectly emulates both the qubit evolution and the observed noisy signals, thus emulating the violations; interestingly, this model also requires an unphysical noise to emulate the readouts, which effectively restricts the ability of an observer to learn information about the spin.
For nuclear level densities, a modification of an enhanced generalized superfluid model with different collective state enhancement factors is studied. An effect of collective states on forming the temperature is taken into account. The ready-to-use tables for the asymptotic value of $a$-parameter of level density as well as for addition shift to excitation energy are prepared using the chi-square fit of the theoretical values of neutron resonance spacing and cumulative number of low-energy levels to experimental values. The systematics of these parameters as a function of mass number and neutron excess are obtained. The collective state effect on gamma-ray spectra and excitation functions of neutron-induced nuclear reactions is investigated by the use of EMPIRE 3.1 code with modified enhanced generalized superfluid model for nuclear level density.
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.
We present an analysis of the level of polarized dust and synchrotron emission using the WMAP9 and Planck data. The primary goal of this study is to inform the assessment of foreground contamination in the cosmic microwave background (CMB) measurements below $\ell\sim200$ from 23 to 353 GHz. We compute angular power spectra as a function of sky cut based on the Planck 353 GHz polarization maps. Our primary findings are the following. (1) There is a spatial correlation between the dust emission as measured by Planck at 353 GHz and the synchrotron emission as measured by WMAP at 23 GHz with $\rho\approx0.4$ or greater for $\ell<20$ and $f_{\mathrm{sky}}\geq0.5$, dropping to $\rho\approx0.2$ for $30<\ell<200$. (2) A simple foreground model with dust, synchrotron, and their correlation fits well to all possible cross spectra formed with the WMAP and Planck 353 GHz data given the current uncertainties. (3) In the 50$\%$ cleanest region of the polarized dust map, the ratio of synchrotron to dust amplitudes at 90 GHz for 50 $\leq \ell \leq$110 is $0.3_{-0.2}^{+0.3}$. Smaller regions of sky can be cleaner although the uncertainties in our knowledge of synchrotron emission are larger. A high-sensitivity measurement of synchrotron below 90 GHz will be important for understanding all the components of foreground emission near 90 GHz.
Cosmic Rays escaping the Galaxy exert a force on the interstellar medium directed away from the Galactic disk. If this force is larger than the gravitational pull due to the mass embedded in the Galaxy, then galactic winds may be launched. Such outflows may have important implications for the history of star formation of the host galaxy, and in turn affect in a crucial way the transport of cosmic rays, both due to advection with the wind and to the excitation of waves by the same cosmic rays, through streaming instability. The possibility to launch cosmic ray induced winds and the properties of such winds depend on environmental conditions, such as the density and temperature of the plasma at the base of the wind and the gravitational potential, especially the one contributed by the dark matter halo. In this paper we make a critical assessment of the possibility to launch cosmic ray induced winds for a Milky-Way-like galaxy and how the properties of the wind depend upon the conditions at the base of the wind. Special attention is devoted to the implications of different conditions for wind launching on the spectrum of cosmic rays observed at different locations in the disc of the galaxy. We also comment on how cosmic ray induced winds compare with recent observations of Oxygen absorption lines in quasar spectra and emission lines from blank-sky, as measured by XMM-Newton/EPIC-MOS.
In this paper, we give the integer parts of reciprocals of tails of the alternating Riemann zeta function at $s=1,2,3,4$ by using several new inequalities and elementary method.
We present an exact derivation of the isobaric partition function of lattice hard rods with arbitrary nearest neighbor interactions. Free energy and all thermodynamics functions are derived accordingly and they written in a form that is a suitable for numerical implementation. As an application, we have considered lattice rods with pure hard core interactions, rods with long range gravitational attraction and finally a charged hard rods with charged boundaries (Bose gas), a model that is relevant for studying several phenomena such as charge regulation, ionic liquids near charged interfaces, and an array of charged smectic layers or lipid multilayers. In all cases, thermodynamic analysis have been done numerically using the Broyden algorithm.
We can survey an Ellis wormhole which is the simplest Morris-Thorne wormhole in our galaxy with microlensing. The light curve of a point source microlensed by the Ellis wormhole shows approximately $4\%$ demagnification while the total magnification of images lensed by a Schwarzschild lens is always larger than unity. We investigate an extended source effect on the light curves microlensed by the Ellis wormhole. We show that the depth of the gutter of the light curves of an extended source is smaller than the one of a point source since the magnified part of the extended source cancels the demagnified part out. We can, however, distinguish between the light curves of the extended source microlensed by the Ellis wormhole and the ones by the Schwarzschild lens in their shapes even if the size of the source is a few times larger than the size of an Einstein ring on a source plane. If the relative velocity of a star with the radius of $10^6$ km at $8$ kpc in the bulge of our galaxy against an observer-lens system is smaller than $10$ km/s on a source plane, we can detect microlensing of the star lensed by the Ellis wormhole with the throat radius of $1$ km at $4$ kpc.
The {\it profile} of a relational structure $R$ is the function $\phi_R$ which counts for every integer $n$ the number of its $n$-element substructures up to an isomorphism. Many counting functions are profiles. Interesting examples come from permutation groups. Some salient facts about the behavior of the profile are presented. Techniques from ordered sets and combinatorics (notably the notion of well-quasi-order, the related notions of ordered algebras, Ramsey theorem) are illustrated. Ongoing resarch suggests to view the profile of a relational structure $R$ as the Hilbert function of some graded algebra associated with $R$. A hint at the solution of a conjecture of P.J.Cameron on the integrity of the ring of the orbit algebra is given. Recent progress made with Y.Boudabbous and N.Thi\'ery on the conjecture that the profile is a quasi-polynomial if its growth is polynomial (and the structure has a finite kernel) are presented.