scholarly journals Vacuum polarization for strong external fields and the self-consistent method in quantum electrodynamics

1971 ◽  
Vol 2 (6) ◽  
pp. 279-284 ◽  
Author(s):  
L. P. Fulcher ◽  
W. Greiner
Keyword(s):  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
The Self ◽  
External Fields ◽  
Self Consistent ◽  
Consistent Method

Self-consistent estimates for the viscoelastic creep compliances of composite materials

1978 ◽  
Vol 359 (1697) ◽  
pp. 251-273 ◽  
Keyword(s):  
Composite Materials ◽  
Numerical Solutions ◽  
The Self ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Viscoelastic Creep ◽  
Self Consistent ◽  
Title Problem ◽  
Consistent Method ◽  
Selection Of

In this paper the viscoelastic creep compliances of various composites are estimated by the self-consistent method. The phases may be arbitrarily anisotropic and in any concentrations but we demand that one of the phases be a matrix and the remaining phases consist of ellipsoidal inclusions. The theory is succinctly formulated with the help of Stieltjes convolutions. In order to solve the title problem, we first solve the misfitting viscoelastic inclusion problem. Numerical solutions are given for a selection of inclusion problems and for two common composite materials, namely an isotropic dispersion of spheres, and a uni-directional fibre reinforced material.

scholarly journals Sinc-Self-consistent method to solve a class of nonlinear eigenvalue differential equation

2021 ◽  
Author(s):  
Seyed Mohammad Ali Aleomraninejad ◽  
Mehdi Solaimani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Subsequent Development ◽  
The Self ◽  
Infinite Domain ◽  
Numerical Examples ◽  
Smallest Eigenvalue ◽  
Sinc Methods ◽  
Self Consistent ◽  
Consistent Method

In this paper, we combine the sinc and self-consistent methods to solve a class of non-linear eigenvalue differential equations. Some properties of the self-consistent and sinc methods required for our subsequent development are given and employed. Numerical examples are included to demonstrate the validity and applicability of the introduced technique and a comparison is made with the existing results. The method is easy to implement and yields accurate results. We show that the sinc-self-consistent method can solve the equations on an infinite domain and produces the smallest eigenvalue with the most accuracy

Analysis of Mixed Mode Cracks in Two-Dimensional Magnetoelectroelastic Media

2006 ◽  
Vol 324-325 ◽  
pp. 403-406 ◽  
Author(s):  
Han Wang ◽  
Xian Hui Ke ◽  
Ming Hao Zhao
Keyword(s):  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
The Self ◽  
Two Dimensional ◽  
Elliptical Cavity ◽  
Self Consistent ◽  
The Matrix ◽  
Consistent Method ◽  
Magnetoelectroelastic Medium

Based on the analytical solution for an elliptical cavity and the self-consistent method, the exact solutions for a crack in a two-dimensional magnetoelectroelastic medium is derived. The strain energy density factors are calculated for mixed mode cracks in a composite made of BaTiO3 as the inclusion and CoFe2O4 as the matrix.

scholarly journals Correction of Radar Reflectivity and Differential Reflectivity for Rain Attenuation at X Band. Part I: Theoretical and Empirical Basis

2005 ◽  
Vol 22 (11) ◽  
pp. 1621-1632 ◽  
Author(s):  
S-G. Park ◽  
V. N. Bringi ◽  
V. Chandrasekar ◽  
M. Maki ◽  
K. Iwanami
Keyword(s):  
Rain Attenuation ◽  
Mean Value ◽  
Radar Reflectivity ◽  
The Self ◽  
Band Frequency ◽  
X Band ◽  
Wide Range ◽  
Self Consistent ◽  
Consistent Method ◽  
Differential Reflectivity

Abstract In this two-part paper, a correction for rain attenuation of radar reflectivity (ZH) and differential reflectivity (ZDR) at the X-band wavelength is presented. The correction algorithm that is used is based on the self-consistent method with constraints proposed by Bringi et al., which was originally developed and evaluated for C-band polarimetric radar data. The self-consistent method is modified for the X-band frequency and is applied to radar measurements made with the multiparameter radar at the X-band wavelength (MP-X) operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) in Japan. In this paper, characteristic properties of relations among polarimetric variables, such as AH–KDP, ADP–AH, AH–ZH, and ZDR–ZH, that are required in the correction methodology are presented for the frequency of the MP-X radar (9.375 GHz), based on scattering simulations using drop spectra measured by disdrometers at the surface. The scattering simulations were performed under conditions of three different temperatures and three different relations for drop shapes, in order to consider variability of polarimetric variables for these conditions. For the X-band wavelength, the AH–KDP and ADP–AH relations can be assumed to be nearly linear. The coefficient α of the AH–KDP relation varies over a wide range from 0.139 to 0.335 dB (°)−1 with a mean value of 0.254 dB (°)−1. The coefficient γ of the ADP–AH relation varies from 0.114 to 0.174, with a mean value of 0.139. The exponent b of the AH–ZH relation does not depend on drop shapes and is almost constant for a given temperature (about 0.78 at the temperature of 15°C). The ZDR–ZH relation depends primarily on drop shape, and does not vary with temperature.

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