横向各向同性均匀介质中格林张量的近似解

利用球座标系下的三重博里叶逆变换导出了均匀各向异性介质中具有横向各向同性性质一类介质的格林张量近似解,为研究属于这类介质的单向纤维增强复合材料和奥氏体钢等材料中声波的散射问题提供了理论基础。将所得的近似解与各向同性介质的情况作了比较,并进行了简单讨论。     

Explanation for Malischewsky's approximate expression for the Rayleigh wave velocity

An approach for obtaining approximations of the Rayleigh wave velocity created by the principle of least squares is introduced. In view of this approach, Malischewsky's approximation of the Rayleigh wave velocity for Poisson ratios v in the set of [-1, 0.5] proposed quite recently is explained. It is shown that Malischewsky's approximation obtained by trial and error is (almost) identical with the one established by this approach.     

An approximate analytical expression for the energies of the tight-bound states of the Zeeman effect in hydrogen

A simple approximate analytical expression for the energies of the tight-bound states of the Zeeman effect in hydrogen is developed that incorporates both the perturbation series in powers of the field strength and the asymptotic logarithmic expansion for the superstrong-field case. Results for the lowest tight-bound states are compared with very accurate non-perturbative calculations.     

An approximate formula for the diffusion coefficient for the periodic Lorentz gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.     

An image-processing toolset for diffusion tensor tractography

Diffusion tensor imaging (DTI)-based fiber tractography holds great promise in delineating neuronal fiber tracts and, hence, providing connectivity maps of the neural networks in the human brain. An array of image-processing techniques has to be developed to turn DTI tractography into a practically useful tool. To this end, we have developed a suite of image-processing tools for fiber tractography with improved reliability. This article summarizes the main technical developments we have made to date, which include anisotropic smoothing, anisotropic interpolation, Bayesian fiber tracking and automatic fiber bundling. A primary focus of these techniques is the robustness to noise and partial volume averaging, the two major hurdles to reliable fiber tractography. Performance of these techniques has been comprehensively examined with simulated and in vivo DTI data, demonstrating improvements in the robustness and reliability of DTI tractography.     

An approximate solution scheme for the algebraic random eigenvalue problem

A reduced basis formulation is presented for the efficient solution of large-scale algebraic random eigenvalue problems. This formulation aims to improve the accuracy of the first order perturbation method, and also allow the efficient computation of higher order statistical moments of the eigenparameters. In the present method, the two terms of the first order perturbation approximation for the eigenvector are used as basis vectors for Ritz analysis of the governing random eigenvalue problem. This leads to a sequence of reduced order random eigenvalue problems to be solved for each eigenmode of interest. Since, only two basis vectors are used to represent each eigenvector, explicit expressions for the random eigenvalues and eigenvectors can readily be derived. This enables the statistics of the random eigenparameters and the forced response to be efficiently computed. Numerical studies are presented for free and forced vibration analysis of a linear stochastic structural system. It is demonstrated that the reduced basis method gives better results as compared to the first order perturbation method.     

An approximate inertial manifold for computing Burgers'' equation

We present a numerical scheme for the approximation of nonlinear evolution equations over large time intervals. Our algorithm is motivated from the dynamical systems point of view. In particular, we adapt the methodology of approximate inertial manifolds to a finite difference scheme. This leads to a differential treatment in which the higher (i.e. unresolved) modes are expressed in terms of the lower modes. As a particular example we derive an approximate inertial manifold for Burgers' equation and develop a numerical algorithm suitable for computing. We perform a parameter study in which we compare the accuracy of a standard scheme with our modified scheme. For all values of the parameters (which are the coefficient of viscosity and the cell size), we obtain a decrease in the numerical error by at least a factor of 2.0 with the modified scheme. The decrease in error is substantially greater over large regions of the parameters space.     

The applicability of an approximate expression for radiative heating

An analysis considering small departures from radiative equilibrium within a gas, for which radiative heating is approximately formulated in terms of a radiative response time, is compared with an exact solution. It is shown that the approximate formulation does not properly describe local departures from radiative equilibrium, although it is useful in a spatially averaged context.     

An approximate Lorentz-invariant Hamilton-Jacobi equation

The transformation properties of the nonrelativistic and quasirelativistic Hamilton-Jacobi equations (HJE) are investigated as far as approximate Lorentz invariance is concerned. It is pointed out that these properties depend on whether or not the potential rest energy is included in the particle energy. An approximate Lorentz invariance of the many-particle nonrelativistic HJE is established by means of the multiple time Dirac-Fock-Podolsky formalism.     

Modified expression for permeability tensor in partially magnetised ferrites

Green and Sandy's experimental results [IEEE Trans Microwave Theory Tech.MTT-22 641 (1974)] for μ', the permeability tensor element of the partially magnetised ferrites, show systematic discrepancies with the values computed by them from their formula for large values of the normalised average magnetisation. It has been shown that a good agreement is possible if Schlömann's expression for μ'₀ occuring in this formula is replaced by another expression originally given by Sandy provided the average demagnetisation factor N of the domains is taken as a linear function of the magnetisation. This modification is also able to interpret the author's experimental results on Magneto-Microwave Kerr Effect successfully, which are not at all explained by the original Green and Sandy formula.     

An approximate formulation for the characteristic impedance of noncoplanar fin antennas

This paper describes an approximation for the characteristic impedance of noncoplanar fin antennas. The formulation is simple and enough accurate for practical applications. The error made by the approximation is less than ±2%, it has been proved to be effective by stripline theory. The numerical results are good agreement to the experimental results given by literature. The expression is useful for the design of wideband antennas.     

An approximate multi-property empirical isotropic interatomic pair potential for the krypton dimer

An approximate empirical isotropic interatomic potential for krypton interaction is developed by simultaneously fitting the Morse-Morse-Morse-Spline-van der Waals potential form to the pressure second virial coefficient, viscosity, thermal conductivity and depolarized interaction-induced light scattering data. Absolute zeroth and second moments of the two-and three-body spectra, the pressure third virial coefficient and isotopic thermal diffusion factor have been measured and compared with theoretical calculations using various models for the interatomic potential. The results show that it is the most accurate potential yet reported for this system. The use of the new potential in lattice sum calculations yields good results for several properties of solid krypton.     

An approximate theory for the sound radiated from a periodic line-supported plate

An approximate method is presented for estimating the sound power radiated by an infinite plate, supported elastically along parallel, equi-spaced lines and subjected to a simple pressure field convecting uniformly over the plate in a direction perpendicular to the supports. Suitable complex modes are assumed for the induced plate flexural wave motion, and an energy method is used to estimate the plate response and the radiated sound power. The effect on the plate response of the acoustic loading is taken into account. The influence of the convection velocity (which may be subsonic) and of certain plate parameters is investigated.     

An approximate formula for the intermolecular Pauli repulsion between closed shell molecules

The exchange repulsion formula proposed by Murrell and co-workers (Proc. Roy. Soc. (Lond.) 1965, A284, 566; J. chem. Phys., 1967, 47, 4916) is considered in detail. Potentially important terms missing in the formalism of Murrell and co-workers are identified and evaluated for the water dimer using several basis sets. Insights into the contributing terms are obtained by using localized molecular orbitals. The results point towards a relatively simple expression for intermolecular exchange repulsion, based on the isolated wavefunctions of the two overlapping species.