ShantanuT01/DACTYL-Pretraining huggingface dataset:
The forging of strong correlations on decreasing temperature can take place without the arousal of conventional order. If this happens, as in some geometrically frustrated magnets, disorder can be a phenomenon more interesting than order itself. A Coulomb phase, for example, has critical-like pair-spin correlations, leading to neutron scattering \textit{pinch points} and emergent electromagnetism. Here we present a new instance of disorder in an Ising pyrochlore lattice: the \textit{Polarized Monopole Liquid} (PML), a dense monopole fluid with pinch points in the \textit{magnetic charge}-pair correlations. It is a phase of "monopole matter" never considered before which, in principle, can be stabilized in real materials using a magnetic field and uniaxial stress along the [100] direction. To explain how the monopole correlations arise, we show that the PML is a Coulomb phase in which spin fluctuations cannot be assigned either to monopoles or to internal magnetic moments, but necessarily comprehend both degrees of freedom. We develop a simple but nontrivial method to Helmholtz decompose the spin field into a divergenceless and a divergenceful part in magnetic charge disordered pyrochlores that shows the appearance of pinch points associated to the divergenceful component in places where Bragg peaks are observed for the "all-in/all-out" antiferromagnet.
Starting from the two-point covariance function derived in [1], we have developed a toy model to investigate the effect of gluonic fluctuations on the transverse energy profile predicted by MC-KLN Color-Glass Condensate initial conditions. We find that the effect of these fluctuations on the eccentricity harmonics varies strongly with the correlation length and consequently the value of the fixed saturation momentum Qs used in [1]. Using approximate values for the minimum and maximum saturation momenta probed at RHIC in Au-Au collisions, we estimate the increase in the eccentricity coefficients resulting from gluonic fluctuations is as large as 10 to 20 percent in central collisions.
The formalism of photon and dilepton productions in a thermal bath are discussed in the frame work of finite temperature field theory. The emission rate has been expressed in terms of the discontinuities or imaginary part of the photon self energy in the thermal bath. The photon and dilepton emissions have been computed by taking into account the in-medium modifications of the particles appearing in the internal loop of the self energy diagram using a phenomenological effective lagrangian approach. The results has been compared with the photon spectra measured by WA 98 collaboration at CERN SPS energies.
We compute a minimum degree threshold sufficient for 3-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, K\"uhn, Lo, Osthus and Taylor, this leads to bounds for exact decompositions and in particular the completion problem for sparse partial latin squares. Some extensions are considered as well.
The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite's orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity.
We prove that for any fixed $n$, and for most permutation patterns $q$, the number $\textup{Av}_{n,\ell}(q)$ of $q$-avoiding permutations of length $n$ that consist of $\ell$ skew blocks is a monotone decreasing function of $\ell$. We then show that this implies that for most patterns $q$, the generating function $\sum_{n\geq 0} \textup{Av}_n(q)z^n$ of the sequence $\textup{Av}_n(q)$ of the numbers of $q$-avoiding permutations is not rational. Placing our results in a broader context, we show that for rational power series $F(z)$ and $G(z)$ with nonnegative real coefficients, the relation $F(z)=1/(1-G(z))$ is supercritical, while for most permutation patterns $q$, the corresponding relation is not supercritical.
Let $A$ be an abelian variety over $\mathbb{Q}$ of dimension $g$ such that the image of its associated absolute Galois representation $\rho_A$ is open in $\operatorname{GSp}_{2g}(\hat{\mathbb{Z}})$. We investigate the arithmetic of the traces $a_{1, p}$ of the Frobenius at $p$ in $\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ under $\rho_A$, modulo varying primes $p$. In particular, we obtain upper bounds for the counting function $\#\{p \leq x: a_{1, p} = t\}$ and we prove an Erd\"os-Kac type theorem for the number of prime factors of $a_{1, p}$. We also formulate a conjecture about the asymptotic behaviour of $\#\{p \leq x: a_{1, p} = t\}$, which generalizes a well-known conjecture of S. Lang and H. Trotter from 1976 about elliptic curves.
We derive the formulas of the squeezed back-to-back correlation (SBBC) between a boson and antiboson with different in-medium masses in high-energy heavy-ion collisions. The influence of the in-medium mass difference between a boson and antiboson on the SBBC is investigated. We calculate the SBBC functions of $D$-meson pairs for the hydrodynamic sources described by the VISH2+1 code for Au+Au collisions at $\sqrt{s_{NN}} =200$~GeV. Our results indicate that the SBBC strengths of $D^+D^-$ and $D^0{\bar D}^0$ are different if there are charge-dependent in-medium interactions.
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes of the route. Since several classes of connections going through the nodes of the network are considered, an original mean-field result in a multi-class context is established. It is shown that, as the number of connections goes to infinity, the behavior of the different classes of connections can be represented by the solution of an unusual nonlinear stochastic differential equation depending not only on the sample paths of the process, but also on its distribution. Existence and uniqueness results for the solutions of these equations are derived. Properties of their invariant distributions are investigated and it is shown that, under some natural assumptions, they are determined by the solutions of a fixed-point equation in a finite-dimensional space.
The total mass M_GCS in the globular cluster (GC) system of a galaxy is empirically a near-constant fraction of the total mass M_h = M_bary + M_dark of the galaxy, across a range of 10^5 in galaxy mass. This trend is radically unlike the strongly nonlinear behavior of total stellar mass M_star versus M_h. We discuss extensions of this trend to two more extreme situations: (a) entire clusters of galaxies, and (b) the Ultra-Diffuse Galaxies (UDGs) recently discovered in Coma and elsewhere. Our calibration of the ratio \eta_M = M_GCS / M_h from normal galaxies, accounting for new revisions in the adopted mass-to-light ratio for GCs, now gives \eta_M = 2.9 \times 10^{-5} as the mean absolute mass fraction. We find that the same ratio appears valid for galaxy clusters and UDGs. Estimates of \eta_M in the four clusters we examine tend to be slightly higher than for individual galaxies, butmore data and better constraints on the mean GC mass in such systems are needed to determine if this difference is significant. We use the constancy of \eta_M to estimate total masses for several individual cases; for example, the total mass of the Milky Way is calculated to be M_h = 1.1 \times 10^{12} M_sun. Physical explanations for the uniformity of \eta_M are still descriptive, but point to a picture in which massive, dense star clusters in their formation stages were relatively immune to the feedback that more strongly influenced lower-density regions where most stars form.
Self-organized criticality in the Hwa-Kardar model of "running sandpile" [Phys. Rev. A 45, 7002 (1992)] with a turbulent motion of the environment taken into account is studied with the field theoretic renormalization group (RG). The turbulent flow is modelled by the synthetic $d$-dimensional anisotropic velocity ensemble introduced by Avellaneda and Majda [Commun. Math. Phys.131: 381 (1990)] with finite correlation time. The Hwa-Kardar model with time-independent (spatially quenched) random noise is considered alongside the original model with the white noise. The aim of the present paper is to explore fixed points of RG equations which determine the possible types of universality classes (regimes of critical behavior of the system) and critical dimensions of the measurable quantities. Our calculations demonstrate that influence of the type of the random noise is extremely large: in contrast to the case of the white noise where the system possess three fixed points, the case of the spatially quenched noise involves four fixed points with overlapping stability regions. This means that in the latter case the critical behavior of the system depends not only on the global parameters of the system which is the usual case, but also on the initial values of the charges (coupling constants) of the system. These initial conditions determine the specific fixed point which will be reached by RG flow. Since now the critical properties of the system are not defined strictly by its parameters the situation may be interpreted as universality violation. Such systems are not forbidden but they are very rare. It is especially interesting that the same model without turbulent motion of the environment does not predict this nonuniversal behavior and demonstrates the "usual" one with prescribed universality classes instead [J.~Stat. Phys. 178, 392 (2020)].
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
We give the full classification of smooth toric Legendrian subvarieties in projective space. We also prove that under some minor assumptions the group of linear automorphisms preserving given Legendrian subvariety preserves the contact structure of the ambient projective space.
We present theoretical aspects of spin polarized two dimensional electron gas (SP2DEG) which can be achieved in doped semimagnetic quantum wells. This original model system has been recently studied by magneto Raman scattering experiments has given a new access to spin resolved excitations and spectrum of the SP2DEG. Starting from the Diluted Magnetic Semiconductor (DMS) Hamiltonian in presence of the Coulomb interaction between conduction electrons, we define the conditions to reach such a SP2DEG. The equilibrium state is studied at low temperature; in particular a theory for the degree of spin polarization is derived. Dynamical spin susceptibilities are further calculated in the framework of a spin density functional formalism already developed in the past. We then derive spin conserving and spin flip excitations dispersions using a recent determination of the SP2DEG correlation energy corrected from the thickness of the well. The SP2DEG presents two key features: the spin flip wave, which existence is a direct consequence of the Coulomb interaction between the spin polarized electrons, with a dispersion and energy range typical to the SP2DEG obtained in DMS, the spin density fluctuations exhibiting a specific collective behaviour when the spin polarization is increased. The dissipation spectrum through these excitations is studied in detail. Particular attention is given to the spectrum determined by resonant Raman scattering. We show, indeed, that the latter gives unique access to the spin-fluctuations spectrum of the SP2DEG.
(Abridged) In this paper we present photometric redshift estimates for a sample of X-ray selected sources detected in the wide field (~2 deg^2), bright [f_{X} (0.5-8 keV)~10^{-14} cgs] XMM-Newton/2dF survey. Unlike deeper X-ray samples comprising a large fraction of sources with colours dominated by the host galaxy, our bright survey primarily probes the QSO X-ray population. Therefore photometric redshift methods employing both galaxy and QSO templates need to be used. We employ the photometric redshift technique of Hatziminaoglou, Mathez & Pello (2000) using 5-band photometry from the SDSS. We separate our X-ray sources according to their optical profile to point-like and extended. We apply QSO and galaxy templates to the point-like and extended sources respectively. X-ray sources associated with Galactic stars are identified and discarded from our point-like sample on the basis of their low X-ray--to--optical flux ratio and their broad band colours that are best fit by stellar templates. Comparison of our results with spectroscopic redshifts available, allows calibration of our method and estimation of the photometric redshift accuracy. For ~70 per cent of the point-like sources photometric redshifts are correct within dz <= 0.3 (or ~75 per cent have dz/(1+z) <= 0.2), and the rms scatter is estimated to be sigma_z = 0.30. For the optically extended objects the photometric redshifts work only in the case of red (g - r > 0.5 mag) sources yielding dz <= 0.15 and dz/(1+z) <= 0.2 for 73 and 93 per cent respectively. However, we find that the above photometric redshift technique does not work in the case of extended sources with blue colours (g - r < 0.5): such sources cannot be fit successfully by QSO or galaxy templates, or any linear combination of the two.
We present numerical models of the gas dynamics in the inner parsec of the Galactic centre. We follow the gas from its origin as stellar winds of several observed young massive stars, until it is either captured by the central black hole, or leaves the system. Unlike our previous models, we include an outflow from the inner accretion flow. Two different kinds of outflows are modelled: (i) an instantaneous-response feedback mode, in which the outflow rate is directly proportional to the current black hole gas capture rate; and (ii) an outburst mode, which is stronger but lasts for a limited time. The latter situation may be particularly relevant to Sgr A*, since there is evidence that Sgr A* was much brighter in the recent past. We find that both types of outflow perturb the gas dynamics near the Bondi radius and the black hole capture rate significantly. The effects persist longer than the outflow itself. We also compare the effects of spherically symmetric and collimated outflows, and find that the latter are far less efficient in transferring its energy to the surrounding gas near the capture radius. Our results imply that accretion feedback is important for non-radiative accretion flows not only within but also outside the capture radius. Steady-state Bondi accretion rate estimates that do not account for feedback outflows over-predict not only the accretion rate onto the black hole but also the capture rate at the Bondi radius itself. Finally, the steady-state assumption under which non-radiative flows have been routinely studied in the literature may have to be abandoned if accretion feedback is bursty in nature.
Initial-state and final-state interactions, which are conventionally neglected in the parton model, have a profound effect in QCD hard-scattering reactions. These effects, which arise from gluon exchange between the active and spectator quarks, cause leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, and the breakdown of the Lam-Tung relation in Drell-Yan reactions. Diffractive deep inelastic scattering also leads to nuclear shadowing and non-universal antishadowing of nuclear structure functions through multiple scattering reactions in the nuclear target. Factorization-breaking effects are particularly important for hard hadron interactions since both initial-state and final-state interactions appear. Related factorization breaking effects can also appear in exclusive electroproduction reactions and in deeply virtual Compton scattering. None of the effects of initial-state and final-state interactions are incorporated in the light-front wavefunctions of the target hadron computed in isolation.
CONTEXT. The GOSSS spectral classifications and Gaia data have significantly improved our ability to measure distances and determine memberships of stellar groups with OB stars. AIMS. We have started a program to identify, measure distances, and determine the membership of Galactic stellar groups with OB stars. We start with the identification and distance determinations of groups with O stars. In this paper we concentrate on groups that contain stars with the earliest spectral subtypes. METHODS. We use GOSSS to select Galactic stellar groups with O2-O3.5 stars and a method that combines Gaia DR2 photometry, positions, proper motions, and parallaxes to assign robust memberships and measure distances. We also include the two clusters in that paper to generate our first list of 16 O-type Galactic stellar groups. RESULTS. We derive distances, determine the membership, and analyze the structure of sixteen Galactic stellar groups with O stars, Villafranca O-001 to O-016, including the 14 groups with the earliest-O-type optically-accessible stars known in the Milky Way. We compare our distance with previous results and establish that the best consistency is with VLBI parallaxes and the worst is with kinematic distances. Our results indicate that massive stars can form in relatively low-mass clusters or even in near-isolation, as is the case for the Bajamar star in the North America nebula. This lends support to the hierarchical scenario of star formation, where some stars are born in well-defined bound clusters but others are born in associations that are unbound from the beginning: groups of newborn stars come in many shapes and sizes. We propose that HD 64 568 and HD 64 315 AB could have been ejected simultaneously from Villafranca O-012 S. Our results are consistent with a difference of approx. 20 microas in the Gaia DR2 parallax zero point between bright and faint stars. (ABRIDGED)
It is discussed a recently proposed connection among U(1)$_{\rm em}$ electromagnetic gauge invariance and the nature of the neutrino mass terms in the framework of $\mbox {SU(3)}_C\otimes G_W \otimes {\mbox U(1)}_N$, $G_W$ = SU(3)$_L$, extensions of the Standard Model. The impossibility of that connection, also in the extended case $G_W $ = SU(4)$_L$, is demonstrated.
Geometric frustration leads to complex phases of matter with exotic properties. Antiferromagnets on triangular lattices and square ice are two simple models of geometrical frustration. We map their highly degenerated ground-state phase spaces as discrete networks such that network analysis tools can be introduced to phase-space studies. The resulting phase spaces establish a novel class of complex networks with Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic except under periodic boundary conditions. We elucidate the boundary effects by mapping the two models as stacks of cubes and spheres in higher dimensions. Sphere stacking in various containers, i.e. square ice under various boundary conditions, reveals challenging combinatorial questions. This network approach can be generalized to phase spaces of some other complex systems.
There have been conflicting points of view concerning the Riemann--Lanczos problem in 3 and 4 dimensions. Using direct differentiation on the defining partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar (in dimensions n > 2) have argued that there are effective constraints so that not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of integrability of ideals of differential forms Bampi and Caviglia have argued that there are no such constraints in dimensions n < 5, and that, in these dimensions, all Riemann tensors can have Lanczos potentials. In this paper we give a simple direct derivation of a constraint equation, confirm explicitly that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue that the Bampi and Caviglia conclusion must therefore be flawed. In support of this, we refer to the recent work of Dolan and Gerber on the three dimensional problem; by a method closely related to that of Bampi and Caviglia, they have found an 'internal identity' which we demonstrate is precisely the three dimensional version of the effective constraint originally found by Massa and Pagani, and Edgar.
Intersections where vehicles are permitted to turn and interact with vulnerable road users (VRUs) like pedestrians and cyclists are among some of the most challenging locations for automated and accurate recognition of road users' behavior. In this paper, we propose a deep conditional generative model for interaction detection at such locations. It aims to automatically analyze massive video data about the continuity of road users' behavior. This task is essential for many intelligent transportation systems such as traffic safety control and self-driving cars that depend on the understanding of road users' locomotion. A Conditional Variational Auto-Encoder based model with Gaussian latent variables is trained to encode road users' behavior and perform probabilistic and diverse predictions of interactions. The model takes as input the information of road users' type, position and motion automatically extracted by a deep learning object detector and optical flow from videos, and generates frame-wise probabilities that represent the dynamics of interactions between a turning vehicle and any VRUs involved. The model's efficacy was validated by testing on real--world datasets acquired from two different intersections. It achieved an F1-score above 0.96 at a right--turn intersection in Germany and 0.89 at a left--turn intersection in Japan, both with very busy traffic flows.
An atomistic method of calculating the spin-lattice relaxation times ($T_1$) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of $T_1$ with the number of donors and electrons, as well as donor locations. Without any adjustable parameters, the relaxation rates in a magnetic field for both systems are found to vary as $B^5$ in excellent quantitative agreement with experimental measurements. The results also show that by engineering electronic wavefunctions in nanostructures, $T_1$ times can be varied by orders of magnitude.