Surface deformation calculations due to environmental loading typically rely on the Preliminary Reference Earth Model(PREM),which assumes a homogeneous and isotropic Earth structure,leading to noticeable errors.To enh...Surface deformation calculations due to environmental loading typically rely on the Preliminary Reference Earth Model(PREM),which assumes a homogeneous and isotropic Earth structure,leading to noticeable errors.To enhance accuracy,the high-precision crustal model CRUST 1.0 is used to refine calculations of regional surface deformation caused by hydrological and non-tidal atmospheric loading.The improved model is applied to 27 Global Navigation Satellite System(GNSS)reference stations in the first phase of the Crustal Movement Observation Network of China(CMONOC),considering their geographical locations.Green's functions are employed to compute surface deformation at each site.Results indicate relative discrepancies of 11.78%and 14.14%for non-tidal atmospheric and hydrological loading compared to PREM,with vertical deformation differences reaching an average of 18.95%.Additionally,the distinct spatial distribution characteristics of the relative differences in each direction indicate that the improved RPREM model is more responsive to the mass variations derived from Gravity Recovery and Climate Experiment(GRACE).The results suggest that the improved PRREM model demonstrates higher sensitivity to loading variations than the PREM model.Utilizing the enhanced method of calculating surface deformation through the utilization of Green's function at the site could effectively reduce the calculation error caused by regional structure,leading to enhanced uniformity and isotropy of PREM.展开更多
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 distributio...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.展开更多
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...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.展开更多
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 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.展开更多
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...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.展开更多
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 pro...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.展开更多
Using the entangled state representation we present a formulation of Green'sfunction in solving Schrodinger equation for bipartite system with kinetic coupling.
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 th...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.展开更多
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...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.展开更多
In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expre...In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.展开更多
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...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.展开更多
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 app...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.展开更多
New general expressions of spectral Green's functions for scalar and vector potentialsof vertical and horizontal electric as well as magnetic dipoles in a multi-layered medium are pre-sented and verified theoretic...New general expressions of spectral Green's functions for scalar and vector potentialsof vertical and horizontal electric as well as magnetic dipoles in a multi-layered medium are pre-sented and verified theoretically.In addition to their amplicity,the quasi-static images of theseexpressions can be extracted without any difficulty.It is the most important that the spatialGreen's functions in representation of Sommerfeld integrals can be easily obtained by using dis-crete complex image theory.Some numerical results for different kinds of multi-layered mediumpresented in the end are used to verify the correctness of the general expressions.展开更多
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...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.展开更多
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 ...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.展开更多
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...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.展开更多
The Schrödinger equation with Woods-Saxon type potentials is solved using the Green's function(GF)method.Taking nucleus^(40)Ca as an example,we show that the GF results for both bound and resonant single-neut...The Schrödinger equation with Woods-Saxon type potentials is solved using the Green's function(GF)method.Taking nucleus^(40)Ca as an example,we show that the GF results for both bound and resonant single-neutron states are consistent with those obtained using the shooting and scattering matrix methods,respectively.Explicitly,three different recipes(GFⅠ,GFⅡ,and GFⅢ)are used to determine the energies and widths of resonant states.The GFⅠ method directly extracts the resonant energy and width from the calculated density of states after removing the contributions of free particles.The GFⅡ method identifies the resonant states by examining the flip of the density of states,whereas the GFⅢ method searches for the resonant states as poles of the modulus of GF on the complex energy plane.We find that the GFⅠ method is effective for resonant states with narrow widths.For resonant states with broad widths,the GFⅡ and GFⅢ methods are more accurate and effective.We also verify that the energies,widths,and density distributions of resonant states obtained using the GF method exhibit a rather weak dependence on the box size.展开更多
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...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant 42204006)the Education Commission of Hubei Province of China(Grant D20232802)+1 种基金the Open Fund of Wuhan,Gravitationand Solid EarthTides,National Observationand Research Station(Grant WHYWZ202407)the Open Fund of Hubei Luojia Laboratory(Grant 230100020,230100019).
文摘Surface deformation calculations due to environmental loading typically rely on the Preliminary Reference Earth Model(PREM),which assumes a homogeneous and isotropic Earth structure,leading to noticeable errors.To enhance accuracy,the high-precision crustal model CRUST 1.0 is used to refine calculations of regional surface deformation caused by hydrological and non-tidal atmospheric loading.The improved model is applied to 27 Global Navigation Satellite System(GNSS)reference stations in the first phase of the Crustal Movement Observation Network of China(CMONOC),considering their geographical locations.Green's functions are employed to compute surface deformation at each site.Results indicate relative discrepancies of 11.78%and 14.14%for non-tidal atmospheric and hydrological loading compared to PREM,with vertical deformation differences reaching an average of 18.95%.Additionally,the distinct spatial distribution characteristics of the relative differences in each direction indicate that the improved RPREM model is more responsive to the mass variations derived from Gravity Recovery and Climate Experiment(GRACE).The results suggest that the improved PRREM model demonstrates higher sensitivity to loading variations than the PREM model.Utilizing the enhanced method of calculating surface deformation through the utilization of Green's function at the site could effectively reduce the calculation error caused by regional structure,leading to enhanced uniformity and isotropy of PREM.
文摘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.
基金National Natural Science Foundation of China Under Grant No.50378063
文摘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.
基金supported by the National Natural Science Foundation of China(10572129)
文摘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.
文摘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.
基金the Aeronautical Science Foundation of China (No.99C53026).
文摘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.
文摘Using the entangled state representation we present a formulation of Green'sfunction in solving Schrodinger equation for bipartite system with kinetic coupling.
基金Project supported by the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. ZDBS-LY-7023)。
文摘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.
文摘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.
基金The first author,Mrs.Yan Hong,was partially supported by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007)by the Science Research Fund of Inner Mongolia University for Nationalities(Grant No.NMDBY15019)by the Foun-dation of the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZY19157 and NJZY20119)in China。
文摘In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.
文摘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.
基金This project was supported by the Key Project of National Nature Science Foundation of China(69931020).
文摘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.
文摘New general expressions of spectral Green's functions for scalar and vector potentialsof vertical and horizontal electric as well as magnetic dipoles in a multi-layered medium are pre-sented and verified theoretically.In addition to their amplicity,the quasi-static images of theseexpressions can be extracted without any difficulty.It is the most important that the spatialGreen's functions in representation of Sommerfeld integrals can be easily obtained by using dis-crete complex image theory.Some numerical results for different kinds of multi-layered mediumpresented in the end are used to verify the correctness of the general expressions.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11934020 and 11874421)the Natural Science Foundation of Beijing(Grant No.Z180013)。
文摘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.
文摘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.
基金supported by the National Key R&D Program of China 2024YFE0109803the National Natural Science Foundation of China(12435006,12475149)+2 种基金the Natural Science Foundation of Guangdong Province(2024A1515010911)the National Key Laboratory of Neutron Science and Technology(NST202401016)the High-performance Computing Platform of Peking University。
文摘The Schrödinger equation with Woods-Saxon type potentials is solved using the Green's function(GF)method.Taking nucleus^(40)Ca as an example,we show that the GF results for both bound and resonant single-neutron states are consistent with those obtained using the shooting and scattering matrix methods,respectively.Explicitly,three different recipes(GFⅠ,GFⅡ,and GFⅢ)are used to determine the energies and widths of resonant states.The GFⅠ method directly extracts the resonant energy and width from the calculated density of states after removing the contributions of free particles.The GFⅡ method identifies the resonant states by examining the flip of the density of states,whereas the GFⅢ method searches for the resonant states as poles of the modulus of GF on the complex energy plane.We find that the GFⅠ method is effective for resonant states with narrow widths.For resonant states with broad widths,the GFⅡ and GFⅢ methods are more accurate and effective.We also verify that the energies,widths,and density distributions of resonant states obtained using the GF method exhibit a rather weak dependence on the box size.
文摘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.
