The bond force constants of graphene and benzene calculated by density functional theory

Stretching (k_r) and bending (k_θ) bond force constants appropriate to describe the bond stiffness of graphene and benzene are calculated using density functional theory. The effect of employing different exchange-correlation functionals for the calculation of k_r and k_θ is discussed using the generalised gradient approximation (GGA) and the local density approximation (LDA). For benzene, k_r = 7.93 mdyn Å^-1 and k_θ = 0.859 mdyn Å rad^-2 using LDA, while k_r = 7.67 mdyn Å^-1 and k_θ = 0.875 mdyn Å rad^-2 using GGA. For graphene, k_r = 7.40 mdyn Å^-1 and k_θ = 0.769 mdyn Å rad^-2 using LDA, while k_r = 6.88 mdyn Å^-1 and k_θ = 0.776 mdyn Å rad^-2 using GGA. This means the difference between the bond force constants for benzene and graphene can be as large as ～12%. The comparison between these two systems allows for elucidation of the effect of periodicity and substitution of carbon atoms by hydrogen in the stiffness of C–C bonds. This effect can be explained by a different redistribution of the charge density when the systems are subjected to strain. The parameters k_r and k_θ computed here can serve as an input to molecular mechanics or finite element codes of larger carbon molecules, which in the past had frequently assumed the same bond force constants for graphene, benzene or carbon nanotubes.     

A family of angle-moments proportional to r-n,n = 1,2,…, in free space

The moments M_n(r) ≡ 1/2 ∝^2π₀ dθ sinⁿ θ I(r,θ) of the intensity I(r, θ) in free space surrounding a spherical object emitting radiation with an arbitrary directional dependence are shown to be exactly proportional to r^-(n+1), n = 0, 1,….     

Synchrotron peak luminosity,black hole mass and Eddington ratio for SDSS flat-spectrum radio quasars

For a sample of 185 flat-spectrum radio quasars (FSRQs) constructed from the SDSS DR3 quasar catalog, we found a significant correlation between the synchrotron peak luminosity and both the black hole mass and Eddington ratio. This implies that the physics of its jet formation is not only tightly related with the black hole mass, but also with the accretion rate. We verify that the synchrotron peak luminosity can be a better indicator of jet emission than 5 GHz luminosity, through comparing the relationships between each of these two parameters and both black hole mass and Eddington ratio. The fundamental plane of black hole activity for our FSRQs is established as L _r ∝ L ^0.80±0.06_x M ^{−0.04±0.09}_bh with a weak dependence on black hole mass, however, the scatter is significant.

     

Validity of rough surface backscattering models

Abstract

A study of the regions of validity for rough surface scattering models is conducted for surfaces with Gaussian and power law power spectra. Models included in the study are physical optics (PO), geometrical optics, small perturbation method and small slope approximation. The range of validity of the PO model is commonly described by a bound on the radius curvature of the surface relative to the electromagnetic wavelength. We show empirically that for backscattering the region of accuracy is more accurately described by a bound on surface slope. For surfaces with a Gaussian power spectrum, the PO model is accurate to within 2 dB for RMS surface slope values less than 0.59 cos³θ. For surfaces with a power law power spectral density, the PO model is accurate for significant slope values (RMS surface height/wavelength of the dominant spectral peak) less than 0.037 cos³θ. These conditions are valid up to approximately 30°. The regions of validity of other models in the study are also shown to be well approximated by bounds on surface slope.     

Theoretical study of stereodynamics for the O（3P） ＋ H2 → OH ＋ H reaction

This paper employs the quasi-classical trajectory calculations to study the influence of collision energy on the title reaction on the potential energy surface of the ground ³A' triplet state developed by Rogers et al. (J. Phys. Chem. A 2000 104 2308). It calculates the product angular distribution of P(θ_r), P(φ_r) and P(θ_r, φ_r) which reflects vector correlation. The distribution P(θ_r) shows that product rotational angular momentum vectors j' of the products are strongly aligned along the relative velocity direction k. The distribution of P(φ_r) implies a preference for left-handed product rotation in planes parallel to the scattering plane. Four different polarisation-dependent cross-sections are also presented in the centre-of-mass frame. Results indicate that OH is sensitively affected by collision energies of H₂.     

Ideal hydrodynamics outside and inside a black hole: Hamiltonian description in Painlevé-Gullstrand coordinates

We show that when the Painlevé-Gullstrand coordinates are used in their Cartesian version, the Hamiltonian of relativistic ideal hydrodynamics in the vicinity of a nonrotating black hole differs by only one simple term from the corresponding Hamiltonian in a flat spacetime. The interior region of the black hole is also described in a unified way, because there is no singularity on the event horizon in Painlevé-Gullstrand coordinates. We present the exact solution describing the steady accretion of extremely hard matter (? ∝ n ²) onto a moving black hole up to the central singularity. In the local induction approximation, we derive the equation of motion for a thin vortex filament against the background of such an accretion flow. We explicitly calculate the Hamiltonian for a fluid with an ultrarelativistic equation of state, ? ∝ n ^4/3, and solve the problem of a centrally symmetric steady flow of such matter.     

Statistics of long-wavelength fluctuations and the expansion rate of Richtmyer-Meshkov turbulence zone

The important problem of Richtmyer-Meshkov turbulence (RMT) is solved. Much work has been devoted to the experimental, numerical (direct numerical simulation), and semiphenomenological (turbulent diffusion and bubble envelope models) analysis of RMT.All of them were of approximate character. They considered the evolution of a mixing layer, and its average thickness h(t) was found. Then, the approximate value of the most important exponent θ (h ∝ t ^θ) was judged from the slope of the h(t) curve in the lnt-lnh coordinates. In this work, the theoretical approach for the exact determination of θ is developed.     

New insights into AGNs with low-mass black holes and high accretion rates: the case of narrow-line Seyfert 1 galaxies

Narrow-line Seyfert 1 (NLS1) galaxies are believed to harbor low-mass black holes accreting at high rates, and they are therefore important targets when studying the nature of black hole growth, galaxy evolution, and accretion physics. We have rigorously studied the physical properties of a sample of NLS1 galaxies. We briefly review previous findings and present new results, including: (1) The locus of NLS1 galaxies on the M _BH-σ plane, which we find to follow the relation of non-active galaxies after removing objects obviously dominated by outflows. (2) The presence of “blue outliers” which hint at extreme outflows as they would be predicted from merger models. (3) More subtle evidence for winds and outflows across the whole NLS1 population. (4) New correlations and trends which link black hole mass, Eddington ratio and physical parameters of the emission-line region. A new element is added to the eigenvector 1 space based on a principal component analysis, which aims at identifying the main drivers of AGN correlation properties.

     

Theoretical study of stereodynamics for the reaction O(3P) +D2 (v=0, j=0) to OD+D and isotope effect

Quasi-classical trajectory (QCT) calculations have been performed to study the product polarization behaviours in the reaction O(³P) + D₂ (v= 0, j= 0)→OD + D. By running trajectories on the ³A′ and ³A″ potential energy surfaces (PESs), vector correlations such as the distributions of the polarization-dependent differential cross sections (PDDCSs), the angular distributions of P(θ_r) and P(ø_r) are presented. Isotope effect is discussed in this work by a comprehensive comparison with the reaction O(³P) + H₂ (v= 0, j= 0) → H + H. Common characteristics as well as differences are discussed in product alignment and orientation for the two reactions. The isotope mass effect differs on the two potential energy surfaces: the isotope mass effect has stronger influence on P(θ_r) and PDDCSs of the ³A′ PES while the opposite on P(ø_r) of the ³A″ potential energy surface.     

碰撞能及反应物振动激发对Ar+H_2~+→ArH~++H反应立体动力学性质的影响

基于我们最近所构建的Ar+H+2→ArH++H(12A′)反应的新势能面,采用准经典轨线法研究了碰撞能分别为0.48,0.77,1.24 eV以及能量为0.48 eV时反应物不同振动态下Ar+H+2→ArH++H反应的立体动力学性质.结果显示在给定的碰撞能情况下,以及当反应物振动量子数由0变到2时计算的积分反应截面与实验值符合得较好.通过比较发现,碰撞能对此反应k-j′关联函数P(θr)分布的影响大于其受振动激发的影响,并且关于k-k′-j′三矢量相关的函数P(?r)分布以及极化微分反应截面对碰撞能较敏感,同时发现振动激发对P(?r)分布和极化微分反应截面也有较大的影响.     

Fractal Inspired Models of quark and gluon distributions and longitudinal structure function FL (x, Q2) at small x

In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F _L (x, Q ²) within this approach. We make predictions using the Quantum Chromodynamics (QCD) based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible with the QCD expectation.     

Experimental measurements and modelling of the structure of the radial electric field in RFX

The experimental determination of the radial electric fieldE _r and the associatedE ×B drift velocity at the edge of RFX is presented and possible mechanisms responsible for its generation are discussed.E _r measurements by means of an array of Langmuir probes and those deduced from Doppler spectroscopy of impurity lines agree fairly well. In particular the rotation velocity of the plasma edge has been determined from the Doppler shift of a C III emission line. The observation of other ions characterised by different radial positions, such as B IV and C V, has allowed an estimate of the velocity shear. Typical values of plasma rotation at the edge are around 10 km/s while the velocity shear is of the order of (10⁵−10⁶)s⁻¹ in the spontaneous layer, a few cm thick, usually observed in standard discharges. Plasma rotation has been artificially modified by both positive and negative edge biasing and the associated increase or decrease of the fluid velocity is well in agreement with the radial electric field change. The modification ofE _r during edge biasing and Pulsed Poloidal Current Drive (PPCD) are also reported and interpreted within a momentum balance model. Analytical and self-consistent Monte Carlo models at the plasma edge suggest that impurities have a relevant role in the generation of the radial electric field, due to their relatively large Larmor radius. Presented at the Workshop on Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June 2000.     

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

On the tangent bundle TS^N-1 of the unit sphere S^N-1, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel--Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.     

The Coevolution of Galaxies and Supermassive Black Holes in the Near Universe

A fundamental role is attributed to supermassive black holes (SMBH), and the feedback they generate, in the evolution of galaxies. But theoretical models trying to reproduce the M_SMBH vs. sigma relation (between the SMBH mass and stellar velocity dispersion of the galaxy bulge) make broad assumptions about the physical processes involved. These assumptions are needed due to the scarcity of observational constraints on the relevant physical processes which occur when the SMBH is being fed via mass accretion in active galactic nuclei (AGN). In search for these constraints, our group—AGN integral field spectroscopy (AGNIFS)—has been mapping the gas kinematics as well as the stellar population properties of the inner few hundred parsecs of a sample of nearby AGN hosts. In this contribution, I report on results obtained so far which show gas inflows along nuclear spirals and compact disks in the inner tens to hundreds of pc in nearby AGN hosts which seem to be the sources of fuel to the AGN. As the inflow rates are much larger than the AGN accretion rate, the excess gas must be depleted via formation of new stars in the bulge. Indeed, in many cases, we find ～100 pc circumnuclear rings of recent star formation (ages ～10–500 Myr) that can be interpreted as a signature of coevolution of the host galaxy and its AGN. I also report on the mapping of outflows in ionized gas, which are ubiquitous in Seyfert galaxies, and discuss mass outflow rates and powers.     

Power series expansions of quantum-mechanical potential surfaces

Power series expansions of quantum-mechanical potential surfaces for H₂O and LiH₂ are generated using conventional valence displacement coordinates and alternative distance [(r-r _e)/r] and angle [(sin (θ/2) — sin (θ_e/2))/sin (θ_e/2)] variables. Power series in the new variables are demonstrated to be superior in terms of the quality of the fit to the energygeometry data, predicted equilibrium geometry and energy, and stability of expansion coefficients.     

Quasi-Stable Configurations of Torus Vortex Knots and Links

The dynamics of torus vortex configurations V_{n, p, q} in a superfluid liquid at zero temperature (n is the number of quantum vortices, p is the number of turns of each filament around the symmetry axis of the torus, and q is the number of turns of the filament around its central circle; radii R₀ and r₀ of the torus at the initial instant are much larger than vortex core width ξ) has been simulated numerically based on the regularized Biot–Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter B₀ = r₀/R₀ for various values of parameter Λ = ln(R₀/ξ). It turns out that for certain values of n, p, and q, there exist quasi-stability regions in the plane of parameters (B₀, Λ), in which the vortices remain almost invariable during dozens and even hundreds of characteristic lengths.

     

Overview on neutrinos and the Daya Bay experiment

Neutrinos are elementary particles in the Standard Model. Neutrino oscillation is a quantum mechanical phenomenon beyond the Standard Model. Neutrino oscillation can be described by two independent mass-squared differences Δm ₂₁ ² , Δm ₃₁ ² (or Δm ₃₂ ² ) and a 3 × 3 unitary matrix, containing three mixing angles θ ₁₂, θ ₂₃, θ ₁₃, and one charge-parity (CP) phase. θ ₁₂ is about 34° and determined by solar neutrino experiments and the reactor neutrino experiment KamLAND. θ ₂₃ is about 45° and determined by atmospheric neutrino experiments and accelerator neutrino experiments. θ ₁₃ can be measured by either accelerator or reactor neutrino experiments. On Mar. 8, 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero θ ₁₃ with 5.2 standard deviations. In June, with 2.5× previous data, Daya Bay improved the measurement of sin²2θ ₁₃ = 0.089 ± 0.010(stat) ± 0.005(syst).     

X-ray emission from non-Keplerian magnetically dominated accretion disks

Summary Most accretion disk models do assume Keplerian rotation as the ?natural? one. This is not so obvious and is somewhat aprioristic, as shown by some attempts to follow different approaches. In the present work we suggest a new approach to the problem, pointing out that the disk structure is deeply related to the balance between the magnetic energy produced by dynamo action and the rotational energy associated with the accreting flow. This balance, together with the conservation laws, allows us to derive analytically the angular-velocity field, the radial velocity field and the magnetic-energy distribution inside the disk. As far as the disk X-ray emission is concerned, we adopt the point of view that the buoyancy and emergence at the disk surface of the azimuthal magnetic field generated by differential rotation gives rise to looplike structures in a hot magnetically confined corona, which is not merely overimposed, as in other models, but ?naturally? fits to the disk structure. The magnetic-energy dissipation into the coronal medium, which sustains the X-ray luminosity, is due to twisting of the magnetic loops. we give an exact analytical expression for the integrated luminosityL _x in terms of the mass of the compact object, the accretion rate, the disk size and rotational velocity, and show that in the limitr _i≪r _e (wherer _i andr _e are the inner and the outer radius of the accretion disk, respectively) it agrees fairly well with the characteristic observed values of both galactic and extragalactic strong compact sources, within the reasonable range commonly accepted for the relevant parameters. Paper presented at the 2° Convegno Nazionale di Fisica Cosmica, held at L'Aquila, 29 May–2 June 1984.     

Photodisintegration of the deuteron in the few GeV region using asymptotic amplitudes

Exclusive photodisintegration of the deuteron in the 1–4 GeV range is described in terms of a simple covariant and gauge invariant approach using an effective counting rule as the hard part of the d–np vertex. At a scattering angle of θ_cm=90° a prescaling behavior of the differential cross section ∝s⁻⁽ⁿ⁻²⁾ with n≈12 is obtained; going away from 90° the value of n decreases slowly, in qualitative agreement with the recent data.