Numerical simulation of viscous three-dimensional flow over aerospace vehicles using Euler/boundary-layer zonal approach

This paper presents a viscous three-dimensional simulations coupling Euler and boundary layer codes for calculating flows over arbitrary surfaces. The governing equations are written in a general non orthogonal coordinate system. The Levy-Lees transformation generalized to three-dimensional flows is utilized. The inviscid properties are obtained from the Euler equations using the Beam and Warming implicit approximate factorization scheme. The resulting equations are discretized and approximated by a two-point fmitedifference numerical scheme. The code developed is validated and applied to the simulation of the flowfield over aerospace vehicle configurations. The results present good correlation with the available data.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Nonmodal energetics of resistive drift waves

The modal and nonmodal linear properties of the Hasegawa-Wakatani system are examined. This linear model for plasma drift waves is nonnormal in the sense of not having a complete set of orthogonal eigenvectors. A consequence of nonnormality is that finite-time nonmodal growth rates can be larger than modal growth rates. In this system, the nonmodal time-dependent behavior depends strongly on the adiabatic parameter and the time scale of interest. For small values of the adiabatic parameter and short time scales, the nonmodal growth rates, wave number, and phase shifts (between the density and potential fluctuations) are time dependent and differ from those obtained by normal mode analysis. On a given time scale, when the adiabatic parameter is less than a critical value, the drift waves are dominated by nonmodal effects while for values of the adiabatic parameter greater than the critical value, the behavior is that given by normal mode analysis. The critical adiabatic parameter decreases with time and modal behavior eventually dominates. The nonmodal linear properties of the Hasegawa-Wakatani system may help to explain features of the full system previously attributed to nonlinearity.

Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Discrete generator coordinate: Symmetry restoration in finite-dimensional spaces

Group theoretical-based techniques and fundamental results from number theory are used in order to allow for the construction of exact projectors in finite-dimensional spaces. These operators are shown to make use only of discrete variables, which play the role of discrete generator coordinates, and their application in the number symmetry restoration is carried out in a nuclear BCS wave function which explicitly violates that symmetry. © 1999 Published by Elsevier Science B.V. All rights reserved.

Crystal structures and magnetic properties of CuX2(pdmp)2 complexes (X = Br, Cl)

We report the synthesis and the structural and magnetic characterization of two new compounds: dibromobis-(pdmp)copper(II), CuBr2C22H24N4 (1), and dichlorobis(pdmp)copper(II), CuCl2C22H24N4 (2), where pdmp = 1-phenyl-3,5-dimethylpyrazole. The structures were refined by full-matrix least-squares techniques to R1 = 0.0620 and 0.0777, respectively. Compound 1 belongs to the space group P21/n with a = 8.165(5) Å, b = 10.432(3) Å, c = 13.385(4) Å, β = 100.12(4)̊, and Z = 2. Compound 2 belongs to the space group P21/c with a = 8.379(2) Å, b = 22.630(2) Å, c = 12.256(2) Å, β= 98.43(3)°, and Z = 4. It has the same molecular formula as a compound reported previously but a different crystal structure. Detailed single-crystal EPR measurements were performed for single-crystal samples of 1 and 2 at 9 and 35 GHz and at room temperature. The positions and line widths of the EPR lines were measured as a function of the magnetic field orientation in three orthogonal planes. The data were used to study the electronic properties of the copper ions and to evaluate the exchange interactions between them. Our results are discussed in terms of the electronic pathways for superexchange between copper ions, which are provided by the stacking of pyrazole and phenyl rings of neighboring molecules and by hydrogen-halogen bonds. © 1999 American Chemical Society.

Inversely symmetric interpolatory quadrature rules

We consider interpolatory quadrature rules with nodes and weights satisfying symmetric properties in terms of the division operator. Information concerning these quadrature rules is obtained using a transformation that exists between these rules and classical symmetric interpolatory quadrature rules. In particular, we study those interpolatory quadrature rules with two fixed nodes. We obtain specific examples of such quadrature rules.

Nonmodal energetics of electromagnetic drift waves

The linear properties of an electromagnetic drift-wave model are examined. The linear system is non-normal in that its eigenvectors are not orthogonal with respect to the energy inner product. The non-normality of the linear evolution operator can lead to enhanced finite-time growth rates compared to modal growth rates. Previous work with an electrostatic drift-wave model found that nonmodal behavior is important in the hydrodynamic limit. Here, similar behavior is seen in the hydrodynamic regime even with the addition of magnetic fluctuations. However, unlike the results for the electrostatic drift-wave model, nonmodal behavior is also important in the adiabatic regime with moderate to strong magnetic fluctuations. © 2000 American Institute of Physics.

Electronic correlations in a two-level dimer

The exact solution for the full electronic Hamiltonian for a two-level dimer is obtained. The parameter constellation (roughly 20) is reparametrized via orthogonal Gaussian atomic orbitals, yielding a five-parameter model. With the dimer embedded in a thermal bath, the specific heat and several temperature-dependent dynamical susceptibilities are computed. © 2001 Elsevier Science B.V. All rights reserved.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polyno-mial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high. © 2001 American Society of Animal Science. All rights reserved.

double-struck D signn-forced symmetry breaking of double-struck O sign (2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problems f(z, λ, μ) = f1 (z, λ) + μf2(z, λ, μ) = 0, where f1 is double-struck O sign (2)-equivariant and f2 is double-struck D sign n-equivariant with the orthogonal group actions on z ∈ ℝ2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

Thermally developing forced convection of non-Newtonian fluids inside elliptical ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.