Improved Perturbation Method Research Articles

Lessons pertaining to the finite element method for stochastic problems, learned from simplest example

The simplest structure – uniform bar with stochastic modulus of elasticity, but other properties and the excitation being deterministic is studied in the view to extract some useful lessons for the finite element method in stochastic setting. Closed-form solutions as well as various approximations are derived for the probabilistic characteristics of the tip displacement. Improved perturbation method is confronted on one hand, with classical perturbation method, and, on the other, with polynomial chaos expansion in conjunction with the Galerkin's method.

Improved perturbation method for scattering from a fluid cylinder

The scattering of sound from a fluid cylinder having strong compressibility contrast is considered. For such a problem, direct application of the Neumann solution results in a divergent series for the pressure. The divergence of the aforementioned series is shown to be the result of an inadequate choice of gauge functions for the expansion. Asymptotic representations equivalent to the Neumann series are obtained using the method of Padé approximants. The method of Padé approximants is shown to extend the range of contrast as well as accelerate the convergence of the Neumann series. Optimal truncation of the Neumann series is shown to yield low-order approximations for the pressure at moderate values of contrast and wavelength. Numerical results using the method of Padé approximants are shown to agree favorably with analytical solutions for scattered pressure from a fluid cylinder.

Brewster angle effect on the performance of omni-directional circular dielectric grating antenna-improved perturbation analysis

The radiation characteristics of the omni-directional periodic leaky wave antenna operating in TMol mode is investigated by the improved perturbation method with a particular attention directed to the Brewster angle effect on the performance of the antenna, and some interesting results are given.

Improved perturbation analysis of millimeter-wave omni-directional periodic dielectric rod antenna

The characteristics of the omni-directional periodic circular dielectric rod leaky-wave antenna is analyzed by the improved perturbation method. The electromagnetic fields are described in terms of a radial transmission-line network, which brings considerable physical insight into the overall behavior of the periodic antenna. The analysis yields expression for the leakage constant in a closed form, and the design procedure of the antenna is tremendously simplified. Comparisons between the approximate and rigorous results, as well as the experiment data, are made. It is found that accuracy obtainable from the perturbation analysis is adequate for practical design purposes.

Shallow surface impurity states of isotropic and anisotropic semiconductors

The surface impurity states of the isotropic semiconductors InP, InAs, InSb and the anisotropic semiconductors Ge, Si, GaP are studied using three different approximation methods, namely the fast convergent method, the principle of minimal sensitivity, and the improved perturbation method. Our treatment is based on (i) a parabolic one-band model, (ii) an infinite-barrier model for electronic states, and (iii) the effective mass approximation method. The hydrogenic wavefunctions are used to calculate the effective charges, effective Bohr radii, and the binding energies for the lower lying states. It is found that the results obtained by the principle of minimal sensitivity are better than the other two approximation methods.

Double dielectric grating leaky-wave antenna-improved perturbation analysis

The radiation characteristics of the double dielectric grating leaky-wave antenna are analyzed by the improved perturbation method. The results indicate that under the condition of the same radiation intensity, the double dielectric grating antenna has relatively smaller dimensions than that of the single one. It is undoubtly of great importance in the case that the limitation of the weight and volume of system is strictly required. The results obtained from this paper are compared with the exact solution based on the mode matching method. It is justified that the present perturbation procedure yields as highly results as the rigorous approach with extremely simplicity of the analysis and calculations.

Axial heat conduction effects in natural convection along a vertical cylinder

MANY TRANSPORprTo cesses occur in nature and in industrial applications in which the transfer of heat is governed by the process of natural convection. Natural convection arises in fluids when the temperature changes cause density variations leading to buoyancy forces. An excellent review of natural convection flows has been given by Ede [I]. Recently, Minkowycz and Sparrow [2, 31, Cebeci [4], and Aziz and Na [S] have studied the steady, laminar, incompressible, natural convection flow over a vertical cylinder using a local nonsimilarity method, a finite-difference scheme, and an improved perturbation method, respectively. However, they did not take into account the effect ofaxial heat conduction for small Prandtl number. It is known that the axial heat conductioneffect becomesimportant for low-Prandtl-number fluids such as a liquid metal.

Complex modal properties of coupled moderately light equipment-structure systems

A new improved perturbation method for evaluating complex modal properties of coupled equipment-structure systems is presented. The method is applicable even when the equipment is not very light, and when the secondary system (equipment) introduces static constraint on the primary system (structure). The new method is applied to nine 8DOF coupled multiply connected equipment-structure systems. It is shown that the new method yields results which are in excellent agreement with the corresponding exact results.

Analysis of Periodic Ferrite Slab Waveguides by Means of Improved Perturbation Method

Periodic ferrite slab waveguides are analyzed by means of an improved perturbation method, and nonreciprocal leakage phenomena are shown theoretically. As an application of these phenomena, new planar isolators and circulators are proposed. Numerical examples are also provided.