Complete Set Of Coefficients Research Articles

Scattering by a Multilayered Infinite Cylinder Arbitrarily Illuminated With a Shaped Beam

A method of calculating the scattered electromagnetic fields of a multilayered infinite cylinder, for arbitrary incidence of a shaped beam, is presented. A complete set of coefficients, which describes the electromagnetic fields within the different regions of a multilayered infinite cylinder, is determined by solving a system of linear equations derived from the boundary conditions. As an example, for a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis of a two-layered and three-layered infinite cylinder, the three-dimensional (3D) nature of the scattering problem, greatly different from the case of an incident plane wave, is described in detail, and numerical results of the normalized differential scattering cross section are evaluated.

A two-time-scale turbulence model for compressible flows: Turbulence dominated by mean deformation interaction

The multiple-time-scale concept is applied to develop a turbulence model for compressible flows. Transport equations for the turbulent kinetic energies and the energy transfer rates are linked to each domain of the turbulent spectrum. The model coefficients are calibrated, with respect to simple flows, by using a new method which takes advantage of the spectral character of the model. One innovation of this method is to use, as a component, the CG model [V. M. Canuto and I. Goldman, Phys. Rev. Lett. 54, 430 (1985)] which gives the large scale spectrum as a function of the instability-generating turbulence. Then, the two-time-scale model, with its complete set of coefficients, has been successfully applied to the simulation of plane mixing layers and homogeneous shear flows. A significant issue of this work is the study of the behavior of the two-time-scale model when a shock wave interacts with a homogeneous turbulence. We first compare model results with experimental data for a 2.8 Mach number interaction [D. Alem, Ph.D. thesis, Université de Poitiers, 1995]. The decrease of the integral length scale, predicted by the linear analysis, is reproduced with the two-time-scale model, which, moreover, recovered the rate of reduction measured by Alem. The amplification of the turbulence level through the shock wave is also consistent with the measurements. Then, we confront our results with a direct numerical simulation of the shock–turbulence interaction at M=1.2 [S. Lee et al., J. Fluid Mech. 251, 533 (1993)]. The spectrum of the turbulence injected in the inflow region of the direct numerical simulation appeared to be far from the freely decaying state. The two-time-scale model, which accounts for the spectral nonequilibrium effects, is able to recover the spatial decrease of turbulence in the inflow region whereas a single-time-scale model fails. Moreover, the profiles for the turbulent kinetic energy and its dissipation rate over all the calculation domain are much better reproduced with the two-time-scale model than with the primary k–ε model.

Scattering coefficients for a multilayered sphere: analytic expressions and algorithms

A calculational procedure for obtaining the complete set of scattering coefficients for a multilayered sphere is proposed. The procedure is based on the utilization of a prescription which relates the coefficients for an r-layered sphere to those for an (r − 1)-layered sphere. The prescription is derived directly from the determinantal form of the scattering amplitudes for a multilayered sphere. The complete set of coefficients considered includes the coefficients required to describe the fields within the various regions of the multilayered sphere.

The General Solution Method of Power Network Analysis

The general solution method of power network analysis grew from the systematic investigation of the effects of changes in a power system being analyzed by mathematical methods. The investigation led to an improved method of computing load-flow studies by which successive approximations converging upon precise answers could be carried through without the solving of simultaneous equations, a method so flexible that changes in loads, ratios, phase shifts, or even the circuit offer no difficulties. The general solution, by taking advantage of a previously computed solution when computing a new solution, is particularly adapted to the computation of a family of solutions for a particular network. Investigation of the effects of changes indicated that the effect of a change in loading, transformer ratio, or phase shift upon any particular network answer could be closely approximated by multiplying the change by a coefficient. Similarly, the effect of a change in value of a circuit element, or the effect of a new circuit element added, upon any particular network answer could be approximated by multiplying a constant by a coefficient. This paper is concerned with the computation of the complete set of coefficients describing the effects of any loading, transformer ratio, phase shift, or circuit change upon any flow, voltage, or phase angle. The complete set of coefficients is termed in this paper the ``general solution'' to the network.