New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions

Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.

Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Kernel polynomial representation for imaginary-time Green's functions in continuous-time quantum Monte Carlo impurity solver

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green s functions G(τ),we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver.This representation is based on the kernel polynomial method,which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly.As an illustration of the new representation,we re-examine the imaginary-time Green's functions of the single-band Hubbard model in the framework of dynamical mean-field theory.The calculated results suggest that with carefully chosen integral kernel functions,whether the system is metallic or insulating,the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green's functions have been obtained.

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

预测规则波浪中船舶运动和载荷的频域三维计算机程序

The development of an in-house computer program for determining the motions and loads of advancing ships through sea waves in the frequency domain,is described in this paper.The code is based on the potential flow formulation and originates from a double-body code enhanced with the regular part of the velocity potential computed using the pulsing source Green function.The code is fully developed in C++language with extensive use of the object-oriented paradigm.The code is capable of estimating the excitation and inertial radiation loads or arbitrary incoming wave frequencies and incidence angles.The hydrodynamic responses such as hydrodynamic coefficients,ship motions,the vertical shear force and the vertical bending moment are estimated.A benchmark container ship and an LNG carrier are selected for testing and validating the computer code.The obtained results are compared with the available experimental data which demonstrate the acceptable compliance for the zero speed whereas there are some discrepancies over the range of frequencies for the advancing ship in different heading angles.

Green's function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green’s function,an essential representation of water-saturated ground under moving excitation,to simulate ground borne vibration from trains.First,general solutions to the governing equations of poroelastic medium are derived by means of integral transform.Secondly,the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground,which results in the matrix of the Green’s function.Then the Green’s function is combined into a train-track-ground model,and is verified by typical examples and a field test.Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area.The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure.The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil.When the train speed is equal to the velocity of the Rayleigh wave,the Mach cone appears in the simulated wave field.The proposed Green’s function is an appropriate representation for a layered ground with shallow ground water table,and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.

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.

Estimated Green's function extracted from superconducting gravimeters and seismometers

Estimated Green's function (EGF) between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical derivations assuming diffusive wave field, equi-partition of modes or random sources on an enclosed surface. This method provides a new approach to study the crust and mantle structure at regional scale, continental scale and global scale. Following the achievements with seismometer records, the records of infrasonic station, hydrophone and microphone were also used to obtain the EGFs of different wave fields. Since superconducting gravimeter is a better long period instrument than regular seismometer, EGF at longer period is expected to be obtained with the cross correlation of gravity data. In this paper, we will show the EGFs extracted by cross-correlations between the superconducting gravimeters and the seismometers. Both the travel times and dispersion curves obtained from different data types are consistent. The result shows that it is possible to retrieve the deep structure by the cross correlation of gravity data.

Green's function solution for transient heat conduction in annular fin during solidification of phase change material

The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.

From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials

In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green’s function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.

Practical Green’s function for the thermal stress field induced by a heat source in plane thermoelasticity

The classical Green’s functions used in the literature for a heat source in a homogeneous elastic medium cannot lead to ?nite remote thermal stresses in the medium,so that they may not work well in practical thermal stress analyses. In this paper, we develop a practical Green’s function for a heat source disposed eccentrically into an elastic disk/cylinder subject to plane deformation. The edge of the disk/cylinder is assumed to be thermally permeable and traction-free. The full thermal stress ?eld induced by the heat source in the disk/cylinder is determined exactly and explicitly via the Cauchy integral techniques. In particular, a very simple formula is obtained to describe the hoop thermal stress on the edge of the disk/cylinder, which may be conveniently useful for analyzing the thermal stresses in microelectronic components.

Equipartitioning is not sufficient for Green's function extraction

The extraction of the Earth's Green's function from field fluctuations is a rapidly growing area of research.The principle of Green's function extraction is often related to the requirement of equipartitioning,which stipulates that the energy of field fluctuations is distributed evenly in some sense.We show the meaning of equipartitioning for a variety of different formulations for Green's function retrieval.We show that equipartitioning is not a sufficient condition,and provide several examples that illustrate this point.We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green's function in seismology.The theory for Green's function extraction is usually based on a statistical theory that relies on ensemble averages.Since there is only one Earth,one usually replaces the ensemble average with a time average.We show that such a replacement only makes sense when attenuation is taken into account,and show how the theory for Green's function extraction for oscillating systems can be extended to incorporate attenuation.

Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

In this article, by using a fixed point theorem, we study following fourth-order three-point BVP: where f ∈ C([0,1]×[0,+∞),[0,+∞)) α ∈ [0,6) and . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions.

Numerical Green’s function method:Application to quantifying ground motion variations of M7 earthquakes

The concept of "numerical Green’s functions" (NGF or Green’s function database) is developed. The basic idea is: a large seismic fault is divided into subfaults of appropriate size, for which synthetic Green’s functions at the surface (NGF) are calculated and stored. Consequently, ground motions from arbitrary kinematic sources can be simulated, rapidly, for the whole fault or parts of it by superposition. The target fault is a simplified, vertical model of the Newport-Inglewood fault in the Los Angeles basin. This approach and its functionality are illustrated by investigating the variations of ground motions (e.g. peak ground velocity and synthetic seismograms) due to the source complexity. The source complexities are considered with two respects: hypocenter location and slip history. The results show a complex behavior, with dependence of absolute peak ground velocity and their variation on source process directionality, hypocenter location, local structure, and static slip asperity location. We concluded that combining effect due to 3-D structure and finite-source is necessary to quan- tify ground motion characteristics and their variations. Our results will facilitate the earthquake hazard assessment projects.

Searching for single-particle resonances with the Green’s function method

Single-particle resonances in the continuum are crucial for studies of exotic nuclei.In this study,the Green’s function approach is employed to search for single-particle resonances based on the relativistic-mean-field model.Taking^(120)Sn as an example,we identify singleparticle resonances and determine the energies and widths directly by probing the extrema of the Green’s functions.In contrast to the results found by exploring for the extremum of the density of states proposed in our recent study[Chin.Phys.C,44:084105(2020)],which has proven to be very successful,the same resonances as well as very close energies and widths are obtained.By comparing the Green’s functions plotted in different coordinate space sizes,we also found that the results very slightly depend on the space size.These findings demonstrate that the approach by exploring for the extremum of the Green’s function is also very reliable and effective for identifying resonant states,regardless of whether they are wide or narrow.

Green Function of Generalized Time Fractional Diffusion Equation Using Addition Formula of Mittag-Leffler Function

In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.

Ambient Noise Tomography, Green’s Function and Earthquakes

Green’s function is well-known, among others, in the application of ambient noise tomography methodologies that may demonstrate the potential of hydrocarbon entrapment in the study area. Here it is also shown to be of key importance in identifying the fractal dimension in the unified scaling law for earthquakes as well as in studying an explicit relationship of a future strong earthquake epicenter to the average earthquake potential score. Such studies are now in progress.

Three-dimensional acoustic propagation model for shallow waters based on an indirect boundary element method

This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.