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.

Parabose Coherent States Based on Green's Ansatz

The coherent states of parabose oscillator of order p based on the well-known Green's ansatz have been constructed. Furthermore, it is shown that the completeness relation for these coherent states may be expressed in the form of 2×2 matrix.

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.

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 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 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.

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.

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.

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 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.

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).

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.

Thermal bridging of graphene nanosheets via covalent molecular junctions: A non-equilibrium Green's functions-density functional tightbinding study

Despite the uniquely high thermal conductivity of graphene is well known,the exploitation of graphene into thermally conductive nanomaterials and devices is limited by the inefficiency of thermal contacts between the individual nanosheets.A fascinating yet experimentally challenging route to enhance thermal conductance at contacts between graphene nanosheets is through molecular junctions,allowing covalently connecting nanosheets,otherwise interacting only via weak Van der Waals forces.Beside the bare existence of covalent connections,the choice of molecular structures to be used as thermal junctions should be guided by their vibrational properties,in terms of phonon transfer through the molecular junction.In this paper,density functional tight-binding combined with Green's functions formalism was applied for the calculation of thermal conductance and phonon spectra of several different aliphatic and aromatic molecular junctions between graphene nanosheets.Effects of molecular junction length,conformation,and aromaticity were studied in detail and correlated with phonon tunnelling spectra.The theoretical insight provided by this work can guide future experimental studies to select suitable molecular junctions,in order to enhance the thermal transport by suppressing the interfacial thermal resistances.This is attractive for various systems,including graphene nanopapers and graphene polymer nanocomposites,as well as related devices.In a broader view,the possibility to design molecular junctions to control phonon transport currently appears as an efficient way to produce phononic devices and controlling heat management in nanostructures.

A new algorithm for the extraction of the surface waves for the Green's function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green's function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green's function. The numerical results demonstrated the accuracy and efficiency of the proposed method.

Source time-function as discriminant using empirical Green's function

The source mechanism of underground nuclear explosions is remarkably different from that of earthquakes in both spatial radiation pattern and source time-function (STF). Small underground nuclear explosions can be used as empirical Green’s functions (EGF) to isolate the source-time spectrum of a large suspected earthquake occurred in a Nuclear Test Site (target area) by the spectral division method. As this study shows, with high-quality data, the quotient spectrum can be transformed to the time domain, yielding the apparent far-field source-time function of the large suspected event. The relative source time-function (RSTF) of a nuclear ex-plosion is usually a simple pulse with a duration of about 1 s., while an earthquake’s is more complicated with a series of pulses and a longer duration. The RSTF can be used as a nice dis-criminant to distinguish the nature earthquakes from underground nuclear explosions in target areas.