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.

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.

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.

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

ＳｏｕｒｃｅｔｉｍｅｆｕｎｃｔｉｏｎｓｏｆｔｈｅＧｏｎｇｈｅ，Ｃｈｉｎａｅａｒｔｈｑｕａｋｅｒｅｔｒｉｅｖｅｄｆｒｏｍｌｏｎｇ－ｐｅｒｉｏｄｄｉｇｉｔａｌｗａｖｅｆｏｒｍｄａｔａｕｓｉｎｇｅｍｐｉｒｉｃａｌＧｒｅｅｎ＇ｓｆｕｎｃｔｉｏｎｔｅｃｈｎｉｑ...

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Green's functions for Biot's dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering,rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green's functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term "decoupling coefficient" for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green's functions. The correctness of the solution is demonstrated by numerically comparing the current solution with Cheng's previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green's functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method(BEM) and other applications.

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.

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.

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 Biot's equation,was deduced by introducing wave potentials. Then exact dynamic-stiffness matrices for a poroelastic soil layer and halfspace 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.

Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions

Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied.

GREEN FUNCTIONS FOR A DECAGONAL QUASICRYSTALLINE MATERIAL WITH A PARABOLIC BOUNDARY

This investigation presents the Green functions for a decagonal quasicrystalline ma- terial with a parabolic boundary subject to a line force and a line dislocation by means of the complex variable method. The surface Green functions are treated as a special case, and the explicit expressions of displacements and hoop stress at the parabolic boundary are also given. Finally, the stresses and displacements induced by a phonon line force acting at the origin of the lower half-space are presented.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot's equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green's functions were derived for uniformly distributed loads acting on an inclined line in a poroelastic layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green's functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

TIME-HARMONIC DYNAMIC GREEN'S FUNCTIONS FOR ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS

Quasicrystals have additional phason degrees of freedom not found in conventional crystals. In this paper, we present an exact solution for time-harmonic dynamic Green's function of one-dimensional hexagonal quasicrystals with the Laue classes 6/mh and 6/mhmm. Through the introduction of two new functions ψ and ψ, the original problem is reduced to the determination of Green's functions for two independent Helmholtz equations. The explicit expressions of displacement and stress fields are presented and their asymptotic behaviors are discussed. The static Green's function can be obtained by letting the circular frequency approach zero.

Green Functions with Pulsating Sources in A Two-Layer Fluid of Finite Depth

The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.

An integrated approach to evaluation on ecological service functions for urban green space and its application

ＡｎｉｎｔｅｇｒａｔｅｄａｐｐｒｏａｃｈｔｏｅｖａｌｕａｔｉｏｎｏｎｅｃｏｌｏｇｉｃａｌｓｅｒｖｉｃｅｆｕｎｃｔｉｏｎｓｆｏｒｕｒｂａｎｇｒｅｎｓｐａｃｅａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎＨｕＤａｎ，ＷａｎｇＲｕｓｏｎｇＲｅｓｅａｒｃｈＣｅｎｔｅ...

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

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎａｎａｌｙｚｉｎｇｔｈｅｄｙｎａｍｉｃｉｎｔｅｒａｃｔｉｏｎｏｆａｓｏｉｌ＿ｓｔｒｕｃｔｕｒｅｓｙｓｔｅｍ，ｔｈｅｋｅｙｓｔｅｐｉｓｔｏｃａｌｃｕｌａｔｅｔｈｅｄｙｎａｍｉｃｓｔｉｆｆｎｅｓｓｍａｔｒｉｘｏｆｔｈｅｓｏ...

Controllable precision of the projective truncation approximation for Green's functions

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.

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.

Comprehensive form of solution for Lamb's dynamic problem expressed by Green's functions

By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld's identity as well as Green's functions of Stokes' solution pertaining the conventional elastic dynamic equation,the results of Green's function in an infinite space of an axisymmetric coordinate are shown in this paper.After employing a supplementary influence field and the boundary conditions in the free surface of a semi-space,the authors obtain the solutions of Green's function for Lamb's dynamic problem.Besides,the vertical displacement u_(zz) and the radial displacement u_(rz) can match Lamb's previous results,and the solutions of the linear expansion source u_(rr) and the linear torsional source u_(θθ) are also given in the paper.The authors reveal that Green's function of Stokes' solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb's problem for various situations.It may benefit the investigation of deepening and development of Lamb's problems and solution for pertinent dynamic problems conveniently.

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 simpleexphcit Green’s functions of a piezoelectric anisotropic body with a free or fixed hyperbolic boundary.Thecorresponding 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 thefracture mechanics parameters are found.The solutions obtained are valid not only for plane and antiplaneproblems but also for the coupled ones between inplane and outplane deformations.