Characteristic analysis of scattering field in two-layer media by Green's function

The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.

Analysis of a Cavity Used for Medical Purposes with the Dyadic Green's Functions and the Moment method

The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions

Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

Solutions of Green's function for Lamb's problem of a two-phase saturated medium

The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space.

Lattice Green's Function for Infinite Square Lattice in the Second Nearest-Neighbour Interaction Approximation

In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green's function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green's function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.

NEW TYPE OF DUAL BEM AND GREEN'S-FUNCTION-LIBRARY STRATEGY FOR FRACTURE ANALYSIS IN COMPLEX STRUCTURES

A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional problems is proposed.The exact formula for the hypersingular integral over the non-con- forming crack tip element is given next.By virtue of Green's-function-library strategy,a series of stress in- tensity factors(SIF)of different crack orientations,locations and/or sizes in a complicated structure can be obtained easily and efficiently.Finally,several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Formulation of Green's Function in Solving Schroedinger Equation forBipartite System with Kinetic Coupling Gained by Virtue of Entangled States

Using the entangled state representation we present a formulation of Green'sfunction in solving Schrodinger equation for bipartite system with kinetic coupling.

GREEN'S FUNCTIONS OF INTERNAL ELECTRODES BETWEEN TWO DISSIMILAR PIEZOELECTRIC MEDIA

The generalized 2-D problem of a half-infinite interfacial electrode layer between two arbitrary piezoelectric half-spaces is studied. Based on the Stroh formalism, exact expressions for the (Green's) functions of a line force, a line charge and a line electric dipole applied at an arbitrary point near the electrode edge,were presented, respectively. The corresponding solutions for the intensity factors of fields were also obtained in an explicit form. These results can be used as the foundational solutions in boundary element method (BEM) to solve more complicated fracture problems of piezoelectric composites.

THE NUMERICAL SOLUTIONS OF GREEN'S FUNCTIONS FOR TRANSVERSELY ISOTROPIC ELASTIC STRATA

In this paper, a model of transversely isotropic elastic strata is used to simulate the soil layers situated on a half space. Instead of the half space, an artificial transmitting boundary is used to absorb the vibration energy. The displacement formulas at any soil layer interface under vertical or horizontal harmonic ring loads are obtained by using the thin layer element method. From these formulas, the explicit solutions of Green's functions_the displacement responses at any interface of these strata under vertical and horizon harmonic point loads_are derived. The examples show that the method presented in this paper is close to the theoretical method and the transversely isotropic property has evident influence on the Green's functions.

GREEN'S FUNCTIONS FOR A 2D ANISOTROPIC MEDIUM WITH A HYPERBOLIC BOUNDARY

By using Stroh's formalism and the conformal mapping technique,this paper derives simple exphcit Green's functions of a piezoelectric anisotropic body with a free or fixed hyperbolic boundary.The corresponding elastic fields in the medium are obtained,too.In particular,degenerated solutions of an ex- ternal crack from those of a hyperbolic problem are analysed in detail.Then the singular stress fields and the fracture mechanics parameters are found.The solutions obtained are valid not only for plane and antiplane problems but also for the coupled ones between inplane and outplane deformations.

Complex fitting 3D closed-form Green's function and its application for silicon RF IC's

An approximate three-dimensional closed-form Green's function with the type of exponential function is derived over a lossy multilayered substrate by means of the Fourier transforms and a novel complex fitting approach. This Green's function is used to extract the capacitance matrix for an arbitrary three-dimensional arrangement of conductors located anywhere in the silicon IC substrate. Using this technique, the substrate loss in silicon integrated circuits can be analyzed. An example of inductor modeling is presented to show that the technique is quite effective.

GREEN'S FUNCTIONS FOR 2D PROBLEMS OF ANISOTROPIC PIEZOELECTRIC MATERIAL WITH A STRIP REGION

By using Stroh's formalism and the conformal mapping technique,we derive the simple ex- plicit elastic fields of a generalized line dislocation and a generalized line force in a general anisotropic piezo- electric strip with fixed surfaces,which are two fixed conductor electrodes.The solutions obtained are usually considered as Green's functions which play important roles in the boundary element methods.The Coulomb forces of the distributed charges along the region boundaries on the line charge q at z^0 are analysed in detail. The results are valid not only for plane and antiplane problems but also for the coupled problems between in- plane and outplane deformations.

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J_(1)–J_(2)Heisenberg model

Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.

ELECTRO-ELASTIC GREEN'S FUNCTIONS FOR APIEZOELECTRIC HALF-SPACE ANDTHEIR APPLICATION

In this paper, as is studied are the electro-elastic solutions for a piezoelectric halfspace subjected Io a line force, a line charge and a line dislocation, i. e.. Green sfunclions on the basis of Stroh formalism and the concept of analytical continuation,explicit expressions for Green's functions are derived. As a direct application of theresults obtained, an infinite piezoelectric solid containing a semi-infinite crack isexammed. Attention iffocused on the stress and electric displacement fields of a cracktip. The stress and electric displacement intensity .factors are given explicitly.

A simple and fast method to calculate the coil currents and the external poloidal flux and magnetic field for fixed boundary equilibria

A simple and fast method to calculate the coil currents and the external poloidal flux and magnetic field consistent with a given internal magnetohydrodynamic(MHD) equilibrium and coil geometry is presented. The constrained optimization technique employed allows to fix the exact position of the X-points. The external poloidal flux and field are calculated using Green's functions expressed in terms of elliptic integrals that are calculated using a fast and accurate routine.The calculation can be limited to the region between the plasma and the device wall. An example for a double null configuration is presented.

Quantitative Green's function estimates for lattice quasi-periodic Schrodinger operators

In this paper,we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrodinger operators.The resonances in the estimates can be described via a pair of symmetric zeros of certain functions,and the estimates apply to the sub-exponential-type non-resonance conditions.As the application of quantitative Green’s function estimates,we prove both the arithmetic version of Anderson localization and the finite volume version of(1/2-)-Holder continuity of the integrated density of states(IDS)for such QP Schrodinger operators.This gives an affirmative answer to Bourgain’s problem in Bourgain(2000).

Source time functions of the Gonghe，China earthquake retrieved from long－period digital waveform data using empirical Green＇s function technique

An earthquake of Ms= 6, 9 occurred at the Gonghe, Qinghai Province, China on April 26, 1990. Three larger aftershocks took place at the same region, Ms= 5. 0 on May 7, 1990, Ms= 6. 0 on Jan. 3, 1994 and Ms= 5. 7on Feb. 16, 1994. The long-period recordings of the main shock from China Digital Seismograph Network (CDSN) are deconvolved for the source time functions by the correspondent0 recordings of the three aftershocks asempirical Green's functions (EGFs). No matter which aftershock is taken as EGF, the relative source time functions (RSTFs) Obtained are nearly identical. The RSTFs suggest the Ms= 6. 9 event consists of at least two subevents with approximately equal size whose occurrence times are about 30 s apart, the first one has a duration of 12 s and a rise time of about 5 s, and the second one has a duration of 17 s and a rise time of about & s. COmParing the RSTFs obtained from P- and SH-phases respectively, we notice that those from SH-phases are a slightly more complex than those from p-phases, implying other finer subevents exist during the process of the main shock. It is interesting that the results from the EGF deconvolution of long-Period way form data are in good agreement with the results from the moment tensor inversion and from the EGF deconvolution of broadband waveform data. Additionally, the two larger aftershocks are deconvolved for their RSTFs. The deconvolution results show that the processes of the Ms= 6. 0 event on Jan. 3, 1994 and the Ms= 5. 7 event on Feb. 16,1994 are quite simple, both RSTFs are single impulses.The RSTFs of the Ms= 6. 9 main shock obtained from different stations are noticed to be azimuthally dependent, whose shapes are a slightly different with different stations. However, the RSTFs of the two smaller aftershocks are not azimuthally dependent. The integrations of RSTFs over the processes are quite close to each other, i. e., the scalar seismic moments estimated from different stations are in good agreement. Finally the scalar seismic moments of the three aftershocks are compared. The relative scalar seismic moment Of the three aftershocks deduced from the relative scalar seismic moments of the Ms=6. 9 main shock are very close to those inverted directly from the EGF deconvolution. The relative scalar seismic moment of the Ms =6. 9 main shock calculated using the three aftershocks as EGF are 22 (the Ms= 6. 0 aftershock being EGF), 26 (the Ms= 5. 7 aftershock being EGF) and 66 (the Ms= 5. 5 aftershock being EGF), respectively. Deducingfrom those results, the relative scalar sesimic moments of the Ms= 6. 0 to the Ms= 5. 7 events, the Ms= 6. 0 tothe Ms= 5. 5 events and the Ms= 5. 7 to the Ms= 5. 5 events are 1. 18, 3. 00 and 2. 54, respectively. The correspondent relative scalar seismic moments calculated directly from the waveform recordings are 1. 15, 3. 43, and 3. 05.

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

Finite Volume Time Domain with the Green Function Method for Electromagnetic Scattering in Schwarzschild Spacetime

The finite volume time domain(FVTD) algorithm and Green function algorithm are extended to Schwarzschild spacetime for numerical simulation of electromagnetic scattering. The FVTD method in Schwarzschild spacetime is developed by filling the flat spacetime with an equivalent medium. The Green function in Schwarzschild spacetime is acquired by solving initial value problems. Both the FVTD code and the Green function code are validated by numerical results. Scattering in Schwarzschild spacetime is simulated with these methods.