Effects of element order and interface reconstruction in FEM/volume‐of‐fluid incompressible flow simulation

In previous studies, the moment‐of‐fluid interface reconstruction method showed dramatic accuracy improvements in static and pure advection tests over existing methods, but this did not translate into an equivalent improvement in volume‐tracked multimaterial incompressible flow simulation using low‐order finite elements. In this work, the combined effects of the spatial discretization and interface reconstruction in flow simulation are examined. The mixed finite element pairs, Q₁Q₀ (with pressure stabilization) and Q₂P _{? 1} are compared. Material order‐dependent and material order‐independent first and second‐order accurate interface reconstruction methods are used. The Q₂P _{? 1} elements show significant improvements in computed flow solution accuracy for single material flows but show reduced convergence using element‐average piecewise constant density and viscosity in volume‐tracked simulations. In general, a refined Q₁Q₀ grid, with better material interface resolution, provided an accuracy similar to the Q₂P _{? 1} element grid with a comparable number of degrees of freedom. Moment‐of‐fluid shows more benefit from the higher‐order accurate flow simulation than the LVIRA, Youngs', and power diagram interface reconstruction methods, especially on unstructured grids, but does not recover the dramatic accuracy improvements it has shown in advection tests. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Implicit meanflow–multigrid algorithms for Reynolds stress model computation of 3‐D anisotropy‐driven and compressible flows

The present paper investigates the multigrid (MG) acceleration of compressible Reynolds‐averaged Navier–Stokes computations using Reynolds‐stress model 7‐equation turbulence closures, as well as lower‐level 2‐equation models. The basic single‐grid SG algorithm combines upwind‐biased discretization with a subiterative local‐dual‐time‐stepping time‐integration procedure. MG acceleration, using characteristic MG restriction and prolongation operators, is applied on meanflow variables only (MF–MG), turbulence variables being simply injected onto coarser grids. A previously developed non‐time‐consistent (for steady flows) full‐approximation‐multigrid (s–MG) is assessed for 3‐D anisotropy‐driven and/or separated flows, which are dominated by the convergence of turbulence variables. Even for these difficult test cases CPU‐speed‐ups r_CPUSUP∈[3, 5] are obtained. Alternative, potentially time‐consistent approaches (unsteady u–MG), where MG acceleration is applied at each subiteration, are also examined, using different subiterative strategies, MG cycles, and turbulence models. For 2‐D shock wave/turbulent boundary layer interaction, the fastest s–MG approach, with a V(2, 0) sawtooth cycle, systematically yields CPU‐speed‐ups of 5±½, quasi‐independent of the particular turbulence closure used. Copyright © 2008 John Wiley & Sons, Ltd.     

关于有消失矩的函数的Hilbert变换的加权范数不等式

为刻划一类权函数W,使具有N阶消失矩的函数f的Hilbert变换f满足带权L~P强型不等式Adams给出了一个充要条件。利用A_P权的性质,本文进一步完善了这个结果。     

New studies of X-ray diffraction line profiles from aggregates of distorted crystallites I

The fourth central moment of an X-ray diffraction profile from an aggregate of distorted crystallites has been expressed by Mitra (1964a) as a function of the crystallite size, strain and strain gradients in the specimen. While the usual methods of line profile analysis yield information regarding either the apparent strain or the rms strain, the present study provides additional information regarding strain distribution in the form of strain derivatives and rms displacements of atoms over a given distancet in the direction of study. The strain parameters like 〈ee′〉, 〈ee″〉 have been obtained from fourth moment of the strain profile against range plots. The strain parameters thus obtained have subsequently been used to determine the rms displacements of the atoms. Alloys of copper and zinc at different stages of cold working and annealing have been studied by this method. The results have been discussed in the light of dislocation distribution, polygonisation and grain growth as well as distortion waves in the distorted crystals.     

A higher‐order accuracy lattice Boltzmann model for the wave equation

A lattice Boltzmann model with higher‐order accuracy for the wave motion is proposed. The new model is based on the technique of the higher‐order moment of equilibrium distribution functions and a series of lattice Boltzmann equations in different time scales. The forms of moments are derived from the binary wave equation by designing the higher‐order dissipation and dispersion terms. The numerical results agree well with classical ones. Copyright © 2008 John Wiley & Sons, Ltd.     

On the moment of inertia of a proto neutron star

The influences of σ* and Φ mesons,temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star(PNS) are examined in the framework of relativistic mean field theory for the baryon octet {n,p,Λ,Σ+,Σ0,Σ+,Ξ-,Ξ0} system.It is found that,compared with that without considering σ* and Φ mesons,the moment of inertia decreases.It is also found that the higher the temperature,the larger the incompressibility and symmetry energy coeficient,and the larger the moment of inertia of a PNS.The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ* and Φ mesons.     

Third-order extensions of Lo’s semiparametric bound for European call options

Computing semiparametric bounds for option prices is a widely studied pricing technique. In contrast to parametric pricing techniques, such as Monte-Carlo simulations, semiparametric pricing techniques do not require strong assumptions about the underlying asset price distribution. We extend classical results in this area. Specifically, we derive closed-form semiparametric bounds for the payoff of a European call option, given up to third-order moment (i.e., mean, variance, and skewness) information on the underlying asset price. We analyze how these bounds tighten the corresponding bounds, when only second-order moment (i.e., mean and variance) information is provided. We describe applications of these results in the context of option pricing; as well as in other areas such as inventory management, and actuarial science.     

Pricing American Asian options with higher moments in the underlying distribution

We develop a modified Edgeworth binomial model with higher moment consideration for pricing American Asian options. With lognormal underlying distribution for benchmark comparison, our algorithm is as precise as that of Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85–105] if the number of the time steps increases. If the underlying distribution displays negative skewness and leptokurtosis as often observed for stock index returns, our estimates can work better than those in Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85–105] and are very similar to the benchmarks in Hull and White [J. Hull, A. White, Efficient procedures for valuing European and American path-dependent options, J. Derivatives 1 (Fall) (1993) 21–31]. The numerical analysis shows that our modified Edgeworth binomial model can value American Asian options with greater accuracy and speed given higher moments in their underlying distribution.     

Propagation characteristics of TM Gaussian beam

The propagation characteristics of TM polarized Gaussian beam, which is the rigorous solution of an eigenfunction problem for a confocal resonator, have been investigated using the nonparaxial vectorial moment theory of light beam propagation. The analytical expressions of the beam propagation factors are given by means of Fourier transform. Both the transversal second-order moment beam widths follow a simple hyperbolic variational law. For nonparaxial case, however, beam has different propagating features in the two transversal directions. As to paraxial case, its propagation approximately reduces to that of scalar Gaussian beam TEM₀₀ mode.