scholarly journals Matrix Generation by First-Order Taylor Expansion in a Localized Manner

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Jun Hu ◽  
Wen Zhang ◽  
Tong-Tong Qiu ◽  
Xue Lan
Keyword(s):  
Method Of Moments ◽  
Taylor Expansion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Common Factors ◽  
Numerical Examples ◽  
First Order ◽  
Filling Method ◽  
The Common ◽  
Double Surface

The method of moments is widely used, but its matrix generation is time-consuming. In the present paper, a localized multifrequency matrix-filling method is proposed. The method is based on the retarded first-order Taylor expansion of Green’s functions on each field point, which can reduce the number of callback Green’s functions and hence can solve double-surface integrals quickly. It is also based on the extraction of the common factors of different frequencies, and hence can sweep the frequency points quickly. Numerical examples are provided to validate the efficiencies of the proposed method.

scholarly journals Steady-Periodic Green’s Functions and Thermal-Measurement Applications in Rectangular Coordinates

2005 ◽  
Author(s):  
Kevin D. Cole
Keyword(s):  
Heat Transfer ◽  
Green's Functions ◽  
Green’S Functions ◽  
Two Dimensional ◽  
Thermal Measurement ◽  
Numerical Examples ◽  
Independent Verification ◽  
Rectangular Coordinates ◽  
Alternate Forms ◽  
Periodic Heat

Two-dimensional steady-periodic heat transfer in rectangles, slabs, and semi-infinite bodies is treated with the method of Green’s functions. The application is the measurement of thermal properties. Several types of boundary conditions are treated systematically, including convection conditions and boundaries containing a thin, high-conductivity film. Alternate forms of the Green’s function are given for several geometries, which allow for independent verification of numerical values. The method may be extended to multilayer bodies. Numerical examples are given for the steady-periodic response to a strip heater.

scholarly journals An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 140
Author(s):  
Nobuoki Eshima ◽  
Claudio Giovanni Borroni ◽  
Minoru Tabata ◽  
Takeshi Kurosawa
Keyword(s):  
Factor Analysis ◽  
Correlation Analysis ◽  
Canonical Correlation ◽  
Common Factor ◽  
Common Factors ◽  
Correlation Coefficients ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Numerical Examples ◽  
The Common

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.

scholarly journals Repositioning Error Compensation in Discontinuous Ground-Based SAR Monitoring

2021 ◽  
Vol 13 (13) ◽  
pp. 2461
Author(s):  
Cheng Hu ◽  
Jiaxin Zhu ◽  
Yunkai Deng ◽  
Weiming Tian ◽  
Peng Yin
Keyword(s):  
Error Compensation ◽  
Taylor Expansion ◽  
Deformation Monitoring ◽  
The Other ◽  
Synthetic Aperture ◽  
Model Simulations ◽  
First Order ◽  
The Common ◽  
Discontinuous Mode ◽  
Deformation Measurements

The discontinuous mode of ground-based synthetic aperture radar (GB-SAR) is suitable for monitoring creep landslides. However, the instrument needs to be installed and disassembled repeatedly, which could inevitably cause repositioning error, and severely affect the accuracy of deformation measurements. This paper performs a detailed theoretical analysis of the repositioning error based on the Taylor expansion of a ternary function, and it can be built as a linear multi-parameter model. Simulations are made to validate the effectiveness of this model compared with two common first-order and second-order models. Then a compensation method based on the permanent scatterer (PS) technique is proposed. Two experiments of discontinuous monitoring are discussed. The first one is an equivalent discontinuous experiment, which utilizes two corner reflectors to evaluate the compensation accuracy. The other one is a discontinuous experiment taken on a steep mountain. Compared with the common methods, the proposed method can better compensate for the error phase and benefit high-precision deformation monitoring.

Green’s functions for an anisotropic half-space and bimaterial incorporating anisotropic surface elasticity and surface van der Waals forces

2016 ◽  
Vol 22 (3) ◽  
pp. 557-572 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Differential Equations ◽  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Van Der Waals ◽  
Surface Elasticity ◽  
Positive Real ◽  
First Order ◽  
Anisotropic Surface ◽  
First Order Differential Equations

In this paper we derive explicit expressions for the Green’s functions in the case of an anisotropic elastic half-space and bimaterial subjected to a line force and a line dislocation. In contrast to previous studies in this area, our analysis includes the contributions of both anisotropic surface elasticity and surface van der Waals interaction forces. By means of the Stroh sextic formalism, analytical continuation and the state-space approach, the corresponding boundary value problem is reduced to a system of six (for a half-space) or 12 (for a bimaterial) coupled first-order differential equations. By employing the orthogonality relations among the corresponding eigenvectors, the coupled system of differential equations is further decoupled to six (for a half-space) or 12 (for a bimaterial) independent first-order differential equations. The latter is solved analytically using exponential integrals. In addition, we identify four and seven non-zero intrinsic material lengths for a half-space and a bimaterial, respectively, due entirely to the incorporation of the surface elasticity and surface van der Waal forces. We prove that these material lengths can be only either real and positive or complex conjugates with positive real parts.

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