ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use diquark-antidiquark currents to investigate the masses and partial decay widths of the recently observed mesons $D_{sJ}^{+}(2317)$, $D_0^{*0}(2308)$ and X(3872), considered as four-quark states, in a QCD sum rule approach. In particular we investigate the coupling constant $g_{D_{sJ}DK}$. We found that the $g_{D_{sJ}DK}$ obtained in this four-quark scenario is smaller than the coupling constant obtained when $D_{sJ}^{+}(2317)$ is considered as a conventional $c\bar{s}$ state.
We apply methods developed by Lovelace, Lipatov and Kirschner to evaluate the leading Regge trajectories \alpha(t) with the quantum numbers of nonexotic quark-antiquark mesons at N_c = infinity and in the limit of t going to minus infinity. In this region renormalization group improved perturbation theory should be valid. We discuss the compatibility of nonlinear trajectories with narrow resonance approximations.
For a graph $G$, the unraveled ball of radius $r$ centered at a vertex $v$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s$-th (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon--Boppana type bound for a class of irregular graphs.
We present sensitive CO (J = 1 - 0) emission line observations of three metal-poor dwarf irregular galaxies Leo P (Z ~ 3% Z_Solar), Sextans A (Z ~ 7.5% Z_Solar), and Sextans B (Z ~ 7.5% Z_Solar), all obtained with the Combined Array for Millimeter-wave Astronomy (CARMA) interferometer. While no CO emission was detected, the proximity of the three systems allows us to place very stringent (4 sigma) upper limits on the CO luminosity (L_CO) in these metal-poor galaxies. We find the CO luminosities to be L_CO < 2900 K km/s pc^2 for Leo P, L_CO < 12400 K km/s pc^2 for Sextans A, and L_CO < 9700 K km/s pc^2 for Sextans B. Comparison of our results with recent observational estimates of the factor for converting between L_CO and the mass of molecular hydrogen, as well as theoretical models, provides further evidence that either the CO-to-H_2 conversion factor increases sharply as metallicity decreases, or that stars are forming in these three galaxies very efficiently, requiring little molecular hydrogen.
We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a realignment of opinions closer towards each other. This mechanism triggers formation of consensus among the individuals. Our main focus is on strong consensus (i.e. global agreement of all individuals) versus weak consensus (i.e. local agreement among neighbors). By extending a known model to a more general opinion space, which lacks a "central" opinion acting as a contraction point, we provide an example of an opinion formation process on the one-dimensional lattice with weak consensus but no strong consensus.
Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements $a_1,...,a_m$ of the cyclic group of order $m$, there is a permutation $\pi$ such that $1a_{\pi(1)}+...+ma_{\pi(m)}=0$.
In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime, steady states satisfy a minimum entropy production principle. The result is applied to master equation systems, opening a new path to a well-known version of the principle regarding invariant states. Moreover, with the aid of a simple example, the principle is shown to conform to Prigogine's original formulation. Finally, we discuss analogies and differences with a recently proposed maximum entropy production principle.
We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when $f = \Lambda$ and $f = \tau$, and provide new results when $f = \tau_r$ with $r \geqslant 3$, breaking the $\frac{1}{2}$-barrier in each case. The functions $f=\mu^2$, $f=2^\omega$ and $f=\omega$ are also investigated.
The paper by M. Baker and S. Norine in 2007 introduced a new parameter on configurations of graphs and gave a new result in the theory of graphs which has an algebraic geometry flavour. This result was called Riemann-Roch formula for graphs since it defines a combinatorial version of divisors and their ranks in terms of configuration on graphs. The so called chip firing game on graphs and the sandpile model in physics play a central role in this theory.   In this paper we give a presentation of the theorem of Baker and Norine in purely combinatorial terms, which is more accessible and shorter than the original one. An algorithm for the determination of the rank of configurations is also given for the complete graph $K_n$. This algorithm has linear arithmetic complexity. The analysis of number of iterations in a less optimized version of this algorithm leads to an apparently new parameter which we call the prerank. This parameter and the classical area parameter provide an alternative description to some well known $q,t$-Catalan numbers. Restricted to a natural subset of configurations, the two natural statistics degree and rank in Riemann-Roch formula lead to a distribution which is described by a generating function which, up to a change of variables, is a symmetric fraction involving two copies of Carlitz q-analogue of the Catalan numbers.
We consider the Cauchy problem for the nonlinear Schr\"odinger equation with double nonlinearities with opposite sign, with one term is mass-critical and the other term is mass-supercritical and energy-subcritical, which includes the famous two-dimensional cubic-quintic nonlinear Schr\"odinger equaton. We prove global wellposedness and scattering in $H^1(\mathbb{R}^d)$ below the threshold for non-radial data when $1 \le d \le 4$.
We analyze the high temperature spin dynamics of compass models using a moment expansion. We point out that the evaluation of moments maps to the enumeration of paths in a branching process on the lattice. This mapping to a statistical mechanics combinatorics problem provides an elegant visualization of the analysis. We present results for the time dependent spin correlation function (which is of relevance to NMR experiments) for two compass models: the Kitaev honeycomb model and two-dimensional compass model.
We use the complete, X-ray flux-limited ROSAT Bright Survey (RBS) to measure the space density of magnetic cataclysmic variables (mCVs). The survey provides complete optical identification of all sources with count rate >0.2/s over half the sky ($|b|>30^\circ$), and detected 6 intermediate polars (IPs) and 24 polars. If we assume that the 30 mCVs included in the RBS are representative of the intrinsic population, the space density of mCVs is $8^{+4}_{-2} \times 10^{-7}\,{\rmpc^{-3}}$. Considering polars and IPs separately, we find $\rho_{polar}=5^{+3}_{-2} \times 10^{-7}\,{\rm pc^{-3}}$ and $\rho_{IP}=3^{+2}_{-1} \times 10^{-7}\,{\rm pc^{-3}}$. Allowing for a 50% high-state duty cycle for polars (and assuming that these systems are below the RBS detection limit during their low states) doubles our estimate of $\rho_{polar}$ and brings the total space density of mCVs to $1.3^{+0.6}_{-0.4} \times 10^{-6}\,{\rm pc^{-3}}$. We also place upper limits on the sizes of faint (but persistent) mCV populations that might have escaped detection in the RBS. Although the large uncertainties in the $\rho$ estimates prevent us from drawing strong conclusions, we discuss the implications of our results for the evolutionary relationship between IPs and polars, the fraction of CVs with strongly magnetic white dwarfs (WDs), and for the contribution of mCVs to Galactic populations of hard X-ray sources at $L_X \ga 10^{31} {\rm erg/s}$. Our space density estimates are consistent with the very simple model where long-period IPs evolve into polars and account for the whole short-period polar population. We find that the fraction of WDs that are strongly magnetic is not significantly higher for CV primaries than for isolated WDs. Finally, the space density of IPs is sufficiently high to explain the bright, hard X-ray source population in the Galactic Centre.
The radio luminosity function (RLF) of radio galaxies and radio-loud quasars is often modelled as a broken power-law. The break luminosity is close to the dividing line between the two Fanaroff-Riley (FR) morphological classes for the large-scale radio structure of these objects. We use an analytical model for the luminosity and size evolution of FRII-type objects together with a simple prescription for FRI-type sources to construct the RLF. We postulate that all sources start out with an FRII-type morphology. Weaker jets subsequently disrupt within the quasi-constant density cores of their host galaxies and develop turbulent lobes of type FRI. With this model we recover the slopes of the power laws and the break luminosity of the RLF determined from observations. The rate at which AGN with jets of jet power $Q$ appear in the universe is found to be proportional to $Q^{-1.6}$. The model also roughly predicts the distribution of the radio lobe sizes for FRII-type objects, if the radio luminosity of the turbulent jets drops significantly at the point of disruption. We show that our model is consistent with recent ideas of two distinct accretion modes in jet-producing AGN, if radiative efficiency of the accretion process is correlated with jet power.
Abundances of light nuclei formed during primordial nucleosynthesis are predicted by Standard Big Bang Model. The latest data from WMAP, with precision's higher than ever before, provides a motivation to determine theoretical higher order corrections to change in helium abundance and the related parameters. Here we evaluate the QED corrections to the change in these parameters during primordial nucleosynthesis using finite temperature effects at the two loop level. Relative variations in neutron decay rate, total energy density of the universe, relative change in neutrino temperature etc., with two loop corrections to electron mass, at the timescale when QED corrections were relevant, have been estimated.
3D MHD global solar simulations coupling the turbulent convective zone and the radiative zone have been carried out. Essential features of the Sun such as differential rotation, meridional circulation and internal waves excitation are recovered. These realistic models are used to test the possibility of having the solar tachocline confined by a primordial inner magnetic field. We find that the initially confined magnetic fields we consider open into the convective envelope. Angular momentum is transported across the two zones by magnetic torques and stresses, establishing the so-called Ferarro's law of isorotation. In the parameter space studied, the confinement of the magnetic field by meridional circulation penetration fails, also implying the failure of the tachocline confinement by the magnetic field. Three-dimensional convective motions are proven responsible for the lack of magnetic field confinement. Those results are robust for the different magnetic field topologies considered, i.e. aligned or oblique dipole.
Consider a spectrally positive L\'evy process $Z$ with log-Laplace exponent $\Psi$ and a positive continuous function $R$ on $(0,\infty)$. We investigate the entrance from $\infty$ of the process $X$ obtained by changing time in $Z$ with the inverse of the additive functional $\eta(t)=\int_{0}^{t}\frac{{\rm d} s}{R(Z_s)}$. We provide a necessary and sufficient condition for infinity to be an entrance boundary of the process $X$. Under this condition, the process can start from infinity and we study its speed of coming down from infinity. When the L\'evy process has a negative drift $\delta:=-\gamma<0$, sufficient conditions over $R$ and $\Psi$ are found for the process to come down from infinity along the deterministic function $(x_t,t\geq 0)$ solution to ${\rm d} x_t=-\gamma R(x_t) {\rm d} t$, with $x_0=\infty$.   When $\Psi(\lambda)\sim c\lambda^{\alpha}$, with $\lambda \rightarrow 0$, $\alpha\in (1,2]$, $c>0$ and $R$ is regularly varying at $\infty$ with index $\theta>\alpha$, the process comes down from infinity and we find a renormalisation in law of its running infimum at small times.
Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.
Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been found so far. In this paper we provide the first bijective proof of the operator formula for monotone triangles, which has been the main tool for several non-combinatorial proofs of such equivalences. In this proof, signed sets and sijections (signed bijections) play a fundamental role.
The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-$\beta$ decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-$\beta$ decay matrix elements on the like-nucleon pairing, particle-particle T=0 and T=1, and particle-hole proton-neutron interactions is obtained. It is found that double-$\beta$ decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-$\beta$ decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further, energy-weighted Fermi and Gamow-Teller sum rules connecting Delta Z = 2 nuclei are discussed. It is proposed that these sum rules can be used to study the residual interactions of the nuclear Hamiltonian, which are relevant for charge-changing nuclear transitions.
We trace the evolution of the theory of stochastic partial differential equations from the foundation to its development, until the recent solution of long-standing problems on well-posedness of the KPZ equation and the stochastic quantization in dimension three.
Mean field calculations, based on the D1S, D1N and D1M parametrizations of the Gogny energy density functional, have been carried out to obtain the potential energy surfaces relevant to fission in several Ra isotopes with the neutron number 144 $\le$ N $\le$ 176. Inner and outer barrier heights as well as first and second isomer excitation energies are given. The existence of a well developed third minimum along the fission paths of Ra nuclei, is analyzed in terms of the energetics of the "fragments" defining such elongated configuration. The masses and charges of the fission fragments are studied as functions of the neutron number in the parent Ra isotope. The comparison between fission and $\alpha$-decay half-lives, reveals that the former becomes faster for increasing neutron numbers. Though there exists a strong variance of the results with respect to the parameters used in the computation of the spontaneous fission rate, a change in tendency is observed at N=164 with a steady increase that makes heavier neutron-rich Ra isotopes stable against fission, diminishing the importance of fission recycling in the r-process.
Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\leq \kappa^g(G)\leq n-2g-2$ for $0\leq g\leq \left\{\Delta(G),\left\lfloor \frac{n-3}{2}\right\rfloor\right\}$, and graphs with $\kappa^g(G)=1,2$ and trees with $\kappa^g(T_n)=n-t$ for $4\leq t\leq \frac{n+2}{2}$ are characterized, respectively. In the end, we get the three extremal results for the $g$-good-neighbor connectivity.
We give brief ideas on building gauge models in superstring theory, especially the four-dimensional models obtained from the compactification of F-theory. According to Vafa, we discuss the construction of F-theory to approach non-perturbative aspects of type IIB superstring. Then, we present local models of F-theory, which can generate new four-dimensional gauge models with applications to phenomenology.
We have used the Cosmic Origins Spectrograph (COS) to obtain far-UV spectra of three closely-spaced QSO sight lines that probe the circumgalactic medium (CGM) of an edge-on spiral galaxy, ESO 157-49, at impact parameters of 74 and 93 kpc near its major axis and 172 kpc along its minor axis. H I Ly\alpha\ absorption is detected at the galaxy redshift in the spectra of all three QSOs, and metal lines of Si III, Si IV, and C IV are detected along the two major-axis sight lines. Photoionization models of these clouds suggest metallicities close to the galaxy metallicity, cloud sizes of ~1 kpc, and gas masses of ~10^4 solar masses. Given the high covering factor of these clouds, ESO 157-49 could harbor ~2x10^9 solar masses of warm CGM gas. We detect no metals in the sight line that probes the galaxy along its minor axis, but gas at the galaxy metallicity would not have detectable metal absorption with ionization conditions similar to the major-axis clouds. The kinematics of the major-axis clouds favor these being portions of a "galactic fountain" of recycled gas, while two of the three minor-axis clouds are constrained geometrically to be outflowing gas.   In addition, one of our QSO sight lines probes a second more distant spiral, ESO 157-50, along its major axis at an impact parameter of 88 kpc. Strong H I Ly\alpha\ and C IV absorption only are detected in the QSO spectrum at the redshift of ESO 157-50.
The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame (RF) to an uniformly accelerated RF is given. The explicit form of the conformal deformation of time is established. The expression defining the location cosmological distance in the form of simple function on the red shift is obtained. By coupling it with the well known relativistic formula defining the relative velocity of the mutually moving apart source and receiver of the signal, the explicit analytic expression for the Hubble law is obtained. The connection between acceleration and the Hubble constant follows therefrom immediately. The expression for the conformal time deformation in the small time limit leads to the quadratic time nonlinearity. Being applied to describe the location-type experiments, this predicts the existence of the uniformly changing blue-shifted frequency drift. Phenomenon of the Pioneer Anomaly (PA) is treated as the first of such a kind of effects discovered experimentally. The obtained formulae reproduce the PA experimental data. The expression generalizing the conventional Hubble law reproduces the experimentally observed phenomenon which in the frame of the conventional cosmological paradigm is treated as the transition from the decelerated expansion of the Universe to the accelerated one.
Inspired by the geometry and shape of the classical radio-frequency radiator, the Hertzian dipole, here we analyze the design of a plasmonic optical dimer nanoantenna. We show how it may be possible to operate a pair of closely spaced spherical nanoparticles as an efficient optical nanoradiator, and how its tuning and matching properties may be tailored with great degree of freedom by designing suitable nanoloads placed at the dimer's gap. In this sense, we successfully apply nanocircuit concepts to model the loading nanoparticles. High levels of optical radiation efficiency are achieved, even considering the realistic absorption of optical metals, thanks to this specific geometry and design.
We study the limits of accuracy for weak lensing maps of dark matter using diffuse 21-cm radiation from the pre-reionization epoch using simulations. We improve on previous "optimal" quadratic lensing estimators by using shear and convergence instead of deflection angles. We find that non-Gaussianity provides a limit to the accuracy of weak lensing reconstruction, even if instrumental noise is reduced to zero. The best reconstruction result is equivalent to Gaussian sources with effectively independent cell of side length 2.0/h Mpc. Using a source full map from z=10-20, this limiting sensitivity allows mapping of dark matter at a Signal-to-Noise ratio (S/N) greater than 1 out to l < 6000, which is better than any other proposed technique for large area weak lensing mapping.
We consider in this work some class of strongly perturbed for the semilinear wave equation with conformal power nonlinearity. We obtain an optimal estimate for a radial blow-up solution and we have also obtained two less stronger estimates. These results are achieved in three-steps argument by the construction of a Lyapunov functional in similarity variables and the Pohozaev identity.
Classical transport properties of an electron, moving in plain, in an array of magnetic antidot has been calculated. The homogeneous magnetic field in z-direction fills the whole space except of cylinders of radius r_0. The magnetoresistance shows additional peak and minimum according to pinned orbits at antidots and to propagating orbits in transport direction, respectively.
In this paper we study the spin transport in frustrated antiferromagnetic FCC films by Monte Carlo simulation. In the case of Ising spin model, we show that the spin resistivity versus temperature exhibits a discontinuity at the phase transition temperature: an upward jump or a downward fall, depending on how many parallel and antiparallel localized spins interacting with a given itinerant spin. The surface effects as well as the difference of two degenerate states on the resistivity are analyzed. Comparison with non frustrated antiferromagnets is shown to highlight the frustration effect. We also show and discuss the results of the Heisenberg spin model on the same lattice.
We investigate supergravity solutions describing D5 branes wrapped on a two cycle which are dual to N=2 super Yang Mills theory. Brane probing these solutions allows the moduli space of the field theory to be identified. There are a unique set of coordinates in which the field theory on the probe takes an N=2 form and in these coordinates the running coupling of the gauge theory may be identified. We show that the geometry, when restricted to the moduli space, takes a very simple form involving only two functions. One is the running gauge coupling whilst the other parametrizes the scalar operators of the field theory. The D5 brane distributions, for the full set of solutions in the literature,can be determined by assuming the field theory's form for the running coupling as a function of scalar vevs. We show that the resulting distributions also correctly reproduce the scalar operators parametrized elsewhere providing the first non-trivial consistency check on the duality.