The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow fo...The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.展开更多
Because most piezoelectric devices have interfaces with fluid in engineering,it is valuable to study the coupled field between fluid and piezoelectric media.As the fundamental problem,the 3 D Green's functions for...Because most piezoelectric devices have interfaces with fluid in engineering,it is valuable to study the coupled field between fluid and piezoelectric media.As the fundamental problem,the 3 D Green's functions for point forces and point charge loaded in the fluid and piezoelectric bimaterials are studied in this paper.Based on the 3 D general solutions expressed by harmonic functions,we constructed the suitable harmonic functions with undetermined constants at first.Then,the couple field in the fluid and piezoelectric bimaterials can be derived by substitution of harmonic functions into general solutions.These constants can be obtained by virtue of the compatibility,boundary,and equilibrium conditions.At last,the characteristics of the electromechanical coupled fields are shown by numerical results.展开更多
The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is a...The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter δ(<<1), which measures the smallness of the deformation, the governing Boundary Value Problem(BVP) is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green's integral theorem with the introduction of suitable Green's function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.展开更多
We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The rel...We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relationobtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] andgeneralizes former work of Dodonov et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992)359.]展开更多
Using the entangled state representation we present a formulation of Green's function in solving Schrǒdinger equation for bipartite system with kinetic coupling.
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 a...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.展开更多
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 fu...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.展开更多
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 co...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.展开更多
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 soluti...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.展开更多
For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-al...For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.展开更多
By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equ...By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.展开更多
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 G...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.展开更多
Indocyanine green(ICG) kinetics(PDR/R15) used to quantitatively assess hepatic function in the perioperative period of major resective surgery and liver transplantation have been the object of an extensive, updated an...Indocyanine green(ICG) kinetics(PDR/R15) used to quantitatively assess hepatic function in the perioperative period of major resective surgery and liver transplantation have been the object of an extensive, updated and critical review. New, non invasive bedside monitors(pulse dye densitometry technology) make this opportunity widely available in clinical practice. After having reviewed basic concepts of hepatic clearance, we analysed the most common indications ICG kinetic parameters have nowadays in clinical practice, focusing in particular on the diagnostic and prognostic role of PDR and R15 in the perioperative period of major liver surgery and liver transplantation. As recently pointed out, even if of extreme interest, ICG clearance parameters have still some limitations, to be considered when using these tests.展开更多
Transarterial chemoembolization(TACE)may ravage normal liver tissues apart from the neoplastic nodules which offset the anti-tumor effect.This study aimed to evaluate the recovery of liver reserve function(LRF)after T...Transarterial chemoembolization(TACE)may ravage normal liver tissues apart from the neoplastic nodules which offset the anti-tumor effect.This study aimed to evaluate the recovery of liver reserve function(LRF)after TACE by indocyanine green(ICG)clearance test and other routine liver function tests.Forty-six newly diagnosed HCC patients who had undergone TACE as the initial treatment from January 2011 to January 2012 were enrolled in this study.The effects of age,basic ICG clearance rate and interval time between two assessments on the recovery of LRF were analyzed.We found that ICG retention rate at the 15 minutes(ICGR15)was significantly increased after TACE(12.3±8.1%vs 16.8±12.1%,P<0.01)in all the 46 patients.In particular,the ICGR15 value was increased in older patients(age>55 years,20.3±12.5%vs 13.7±7.2%,P<0.01).The interval of ICG test also affected the ICGR15 value(≤47days,17.8±11.4%after vs 12.1±7.1%before TACE,P<0.01).Our data suggested that TACE decreased LRF,especially in older patients.ICG test was more sensitive to evaluate the recovery of LRF after TACE than the Child-Pugh grade and routine liver function tests.展开更多
In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem u′′+ (1/2+ ε)~2*u = λg(t)f(u), t∈[0, 2π], u(0) = u(2π), u′(0) = u′(2π),where 0 <ε <12, g ...In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem u′′+ (1/2+ ε)~2*u = λg(t)f(u), t∈[0, 2π], u(0) = u(2π), u′(0) = u′(2π),where 0 <ε <12, g : [0, 2π]→ R is continuous, f : [0, ∞)→R is continuous and λ > 0 is a parameter.展开更多
基金Project(51304220) supported by the National Natural Science Foundation of ChinaProject(3144033) supported by the Beijing Natural Science Foundation,ChinaProject(20130007120014) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.
基金financial support from the National Natural Science Foundation of China(11572119)
文摘Because most piezoelectric devices have interfaces with fluid in engineering,it is valuable to study the coupled field between fluid and piezoelectric media.As the fundamental problem,the 3 D Green's functions for point forces and point charge loaded in the fluid and piezoelectric bimaterials are studied in this paper.Based on the 3 D general solutions expressed by harmonic functions,we constructed the suitable harmonic functions with undetermined constants at first.Then,the couple field in the fluid and piezoelectric bimaterials can be derived by substitution of harmonic functions into general solutions.These constants can be obtained by virtue of the compatibility,boundary,and equilibrium conditions.At last,the characteristics of the electromechanical coupled fields are shown by numerical results.
基金Partially Supported by a Research from Department of Science and Technology(DST),India under Grant No.SB/FTP/MS-003/2013
文摘The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter δ(<<1), which measures the smallness of the deformation, the governing Boundary Value Problem(BVP) is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green's integral theorem with the introduction of suitable Green's function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.
文摘We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relationobtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] andgeneralizes former work of Dodonov et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992)359.]
文摘Using the entangled state representation we present a formulation of Green's function in solving Schrǒdinger equation for bipartite system with kinetic coupling.
文摘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.
基金supported by National Natural Science Foundation of China(11671100 and 12171104)the National Science Fund for Excellent Young Scholars(11922107)Guangxi Natural Science Foundation(2018GXNSFAA138210 and 2019JJG110010)。
文摘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.
基金the National Natural Science Foundation of China(No.U2032141)the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology(No.NLK2022-02)+4 种基金the Central Government Guidance Funds for Local Scientific and Technological Development,China(Guike ZY22096024)the Natural Science Foundation of Henan Province(No.202300410479)the Guizhou Provincial Science and Technology Projects(No.ZK[2022]203)the Foundation of Fundamental Research for Young Teachers of Zhengzhou University(No.JC202041041)the Physics Research and Development Program of Zhengzhou University(No.32410217).
文摘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.
基金the National Natural Science Foundation of China(Nos.11972365 and 12102458)。
文摘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.
文摘For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.
基金State Natural Science Foundation (59879012) and Doctoral Foundation from State Education Commission (98024832).
文摘By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.
基金The paper was financially supported by the National Natural Science Foundation of China (No. 19802008)Excellent Doctoral Dissertation Grant of the Ministry of Education of China (No. 199927)
文摘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.
文摘Indocyanine green(ICG) kinetics(PDR/R15) used to quantitatively assess hepatic function in the perioperative period of major resective surgery and liver transplantation have been the object of an extensive, updated and critical review. New, non invasive bedside monitors(pulse dye densitometry technology) make this opportunity widely available in clinical practice. After having reviewed basic concepts of hepatic clearance, we analysed the most common indications ICG kinetic parameters have nowadays in clinical practice, focusing in particular on the diagnostic and prognostic role of PDR and R15 in the perioperative period of major liver surgery and liver transplantation. As recently pointed out, even if of extreme interest, ICG clearance parameters have still some limitations, to be considered when using these tests.
文摘Transarterial chemoembolization(TACE)may ravage normal liver tissues apart from the neoplastic nodules which offset the anti-tumor effect.This study aimed to evaluate the recovery of liver reserve function(LRF)after TACE by indocyanine green(ICG)clearance test and other routine liver function tests.Forty-six newly diagnosed HCC patients who had undergone TACE as the initial treatment from January 2011 to January 2012 were enrolled in this study.The effects of age,basic ICG clearance rate and interval time between two assessments on the recovery of LRF were analyzed.We found that ICG retention rate at the 15 minutes(ICGR15)was significantly increased after TACE(12.3±8.1%vs 16.8±12.1%,P<0.01)in all the 46 patients.In particular,the ICGR15 value was increased in older patients(age>55 years,20.3±12.5%vs 13.7±7.2%,P<0.01).The interval of ICG test also affected the ICGR15 value(≤47days,17.8±11.4%after vs 12.1±7.1%before TACE,P<0.01).Our data suggested that TACE decreased LRF,especially in older patients.ICG test was more sensitive to evaluate the recovery of LRF after TACE than the Child-Pugh grade and routine liver function tests.
基金Supported by the National Natural Science Foundation of China(No.11321627,11401479,71561024,11561063)China Postdoctoral Science Foundation(2014M562472)+1 种基金Postdoctoral Science Foundation of Gansu Provincethe Science Research Project for Colleges and Universities of Gansu Province(2016A-003)
文摘In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem u′′+ (1/2+ ε)~2*u = λg(t)f(u), t∈[0, 2π], u(0) = u(2π), u′(0) = u′(2π),where 0 <ε <12, g : [0, 2π]→ R is continuous, f : [0, ∞)→R is continuous and λ > 0 is a parameter.