Generation of new solutions of the stationary axisymmetric Einstein equations by a double complex function method

1985 ◽  
Vol 26 (10) ◽  
pp. 2589-2595 ◽  
Author(s):  
Zai‐Zhe Zhong
Keyword(s):  
Function Method ◽  
Complex Function ◽  
Einstein Equations ◽  
Double Complex ◽  
Complex Function Method

Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Chun-Yan Wang ◽  
Yuan-Xing Gui ◽  
Ya-Jun Gao
Keyword(s):  
Inverse Scattering ◽  
Function Method ◽  
Complex Function ◽  
Soliton Solutions ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Field Equations ◽  
Double Complex ◽  
Gravitation Field ◽  
Symmetric Vacuum

AbstractWe present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.

Scattering of SH waves around circular canyon in inhomogeneous wedge space

2020 ◽  
Vol 223 (1) ◽  
pp. 45-56
Author(s):  
Zailin Yang ◽  
Xinzhu Li ◽  
Yunqiu Song ◽  
Guanxixi Jiang ◽  
Menghan Sun ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Helmholtz Equation ◽  
Ground Motion ◽  
Governing Equation ◽  
Function Method ◽  
Complex Function ◽  
Variable Coefficients ◽  
Sh Waves ◽  
Free Condition ◽  
Complex Function Method

SUMMARY Scattering of SH waves around a circular canyon in radial inhomogeneous wedge space is investigated in this paper. Based on the complex function method, the governing equation with variable coefficients is transformed into a standard Helmholtz equation and the corresponding analytical solution to this problem is derived. The unknown coefficients in the wavefield is obtained by enforcing the stress-free condition in the circular canyon, then the incident, reflected and scattering waves in the total wavefield are all acquired. Through the calculation and analysis of the parameters that affect the ground motion, the influence of the circular canyon on the ground motion in the radial inhomogeneous wedge space is obtained. Moreover, combined with graphical results, the effects by inhomogeneous parameter on ground motion with circular canyon in wedge space are conspicuous.

A Method for Stress Intensity Factor Calculation of Typical MSD Configurations

2013 ◽  
Vol 700 ◽  
pp. 149-152 ◽  
Author(s):  
Jin Fang Zhao ◽  
Qun Zhao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Function Method ◽  
Complex Function ◽  
Calculation Process ◽  
Complex Function Method

This paper introduced compounding method to calculate the SIF of typical MSD configurations. Complex function method was proposed to calculate the modification coefficient of the adjacent holes. Combining the method with compounding method, the SIF calculation of typical MSD configurations was achieved. The calculation process is easy to operate and the results are reliable which can be verified by FEM calculation. By studying the SIF results of typical MSD configurations, a series of conclusions with practical value in engineering can be obtained.

DOUBLE STRUCTURES AND DOUBLE SYMMETRIES FOR THE EINSTEIN–KALB–RAMOND THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 361-372 ◽  
Author(s):  
YA-JUN GAO
Keyword(s):  
Function Method ◽  
Equations Of Motion ◽  
Complex Function ◽  
Complex Method ◽  
Complex Matrix ◽  
Fractional Linear Transformation ◽  
Double Complex ◽  
Ernst Potential ◽  
Double Symmetry ◽  
Double Symmetries

We further study the two-dimensional reduced Einstein–Kalb–Ramond (EKR) theory in the axisymmetric case by using the so-called double-complex function method. We find a doubleness symmetry of this theory and exploit it so that some double-complex d×d matrix Ernst-like potential can be constructed, and the associated equations of motion can be extended into a double-complex matrix Ernst-like form. Then we give a double symmetry group [Formula: see text] for the EKR theory and verify that its action can be realized concisely by a double-complex matrix, form generalization of the fractional linear transformation on the Ernst potential. These results demonstrate that the theory under consideration possesses more and richer symmetry structures. Moreover, as an application, we obtain an infinite chain of double-solutions of the EKR theory showing that the double-complex method is more effective. Some of the results in this paper cannot be obtained by the usual (nondouble) scheme.

A complex function method of SH wave scattering in inhomogeneous medium

2017 ◽  
Vol 228 (10) ◽  
pp. 3469-3481 ◽  
Author(s):  
Zai-lin Yang ◽  
Chong-qun Zhang ◽  
Guan-xi-xi Jiang ◽  
Pei-lei Yan ◽  
Yong Yang
Keyword(s):  
Inhomogeneous Medium ◽  
Wave Scattering ◽  
Function Method ◽  
Complex Function ◽  
Sh Wave ◽  
Complex Function Method

scholarly journals The Complex Function Method Roadway Section Design of the Soft Coal Seam

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Shihao Tu ◽  
Zhaoxin Li ◽  
Zhiwei Ye ◽  
Cun Zhang ◽  
Lei Zhang
Keyword(s):  
Coal Seam ◽  
Function Method ◽  
Vertical Wall ◽  
Complex Function ◽  
Surrounding Rock ◽  
Type Steel ◽  
Soft Coal ◽  
Distribution Laws ◽  
Soft Coal Seam ◽  
Complex Function Method

As for the sophisticated advanced support technique of vertical wall semicircle arch roadway in the three-soft coal seam, a design of flat top U-shape roadway section was put forward. Based on the complex function method, the surrounding rock displacement and stress distribution laws both of vertical wall semicircle arch roadway and of flat top U-shape roadway were obtained. The results showed that the displacement distribution laws in the edge of roadway surrounding rock were similar between the two different roadways and the area of plasticity proportion of flat top U-shape roadway approximately equals that of vertical wall semicircle arch roadway. Based on finite element method, the bearing behaviors of the U-type steel support under the interaction of surrounding rock in vertical wall semicircle arch roadway and flat top U-shape roadway were analyzed. The results showed that, from a mechanics perspective, U-type steel support can fulfill the requirement of surrounding rock supporting in flat top U-shape roadway and vertical wall semicircle arch roadway. The field measurement of mining roadway surrounding rock displacement in Zouzhuang coal mine working face 3204 verified the accuracy of theoretical analysis and numerical simulation.

An analysis of highly viscous flow using Imai's complex function method with application to screen printing

1992 ◽  
Vol 10 (1) ◽  
pp. 11-23
Author(s):  
Jun-ichi Kawabata ◽  
Hiroyoshi Shi-igai ◽  
Kohei Yabuno ◽  
Tadayuki Saito
Keyword(s):  
Viscous Flow ◽  
Function Method ◽  
Screen Printing ◽  
Complex Function ◽  
Complex Function Method

scholarly journals Exact solutions of interfacial cracking problem of elliptic inclusion in thermoelectric material

2021 ◽  
Vol 261 ◽  
pp. 02089
Author(s):  
Xin-Kun Du ◽  
Ya-Li Zhang ◽  
Sheng-Hu Ding
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Thermoelectric Material ◽  
Function Method ◽  
Complex Function ◽  
Interfacial Crack ◽  
Uniform Heat Flux ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elliptical Inclusion

In the present work, the problem for elliptical inclusion with interfacial crack in thermoelectric material is studied. The inclusion and matrix are assumed to be imperfect bonding, which is subjected to uniform heat flux and energy flux at infinity. The interfacial cracking problem of elliptic inclusion in thermoelectric material is investigated by using conformal mapping and complex function method. The complex expressions of temperature field and electric field in inclusion and matrix are obtained. The energy release rate of thermoelectric material under the influence of inclusion is given. The effects of elliptic inclusion with interfacial crack on temperature field and electric potential also are compared by numerical examples. The results show that inclusion reduces the conversion efficiency of thermoelectric material.

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