Defect engineering is a commonly methodology used to enhance the thermoelectric performance of thermoelectric PbTe by improving its electronic transport properties.At the nanoscale,defects can induce quantum tunneling...Defect engineering is a commonly methodology used to enhance the thermoelectric performance of thermoelectric PbTe by improving its electronic transport properties.At the nanoscale,defects can induce quantum tunneling effects that significantly impact the electrical properties of materials.To understand the specific mechanisms underlying the quantum transport properties of PbTe,we employ the non-equilibrium Green's function(NEGF)method to investigate the effects of intrinsic defects(point defects and grain boundaries)on the electronic transport properties of PbTe-based nanodevices from a quantum mechanical perspective.Our results show that the Pb vacancy(VPb)has the highest conduction.The conduction depends on the defect type,chemical potential and bias voltage.The presence of intrinsic point defects introduces impurity levels,facilitating the electron tunneling and leading to an increase in the transmission coefficient,thereby enhancing the electronic transport properties.For PbTe containing grain boundaries,these boundaries suppress the electronic transport properties.The Te occupied twin boundary(Te-TB)exerts a stronger inhibitory effect than the Pb occupied twin boundary(Pb-TB).Nevertheless,the combined effect between twin boundaries and point defects can enhance the electrical properties.Therefore,in order to obtain highly conductive of PbTe materials,a Te-rich synthesis environment should be used to promote the effective formation of Pb vacancy.Our work offers a comprehensive understanding of the impact of defects on electron scattering in thermoelectric materials.展开更多
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil...In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.展开更多
Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential...Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.展开更多
This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function ...This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].展开更多
The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, ...The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.展开更多
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
We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is intro...We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.展开更多
The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the co...The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency.展开更多
Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including at...Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.展开更多
Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system a...Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system.Based on a delicate analysis of the corresponding Green function,L^(2) decay estimate of the solution is obtained.展开更多
In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style...In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where <span style="white-space:nowrap;">f <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈ C([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;">α <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈ [0,6) and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . 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.展开更多
A three-dimensional panel method is developed to investigate the seakeeping performance of two parallel ships advancing in head and oblique waves. In this method, the fluid domain is partitioned into two regions by in...A three-dimensional panel method is developed to investigate the seakeeping performance of two parallel ships advancing in head and oblique waves. In this method, the fluid domain is partitioned into two regions by introducing a virtual control surface. In the inner part, the Taylor expansion boundary element method is used, whose kernel function is the Rankine source;in the outer part, the free surface Green function with the forward speed effect considered is adopted. The velocity potentials and normal velocities on the virtual control surface are equal for the inner and outer domains. Moreover, the numerical estimation method for viscous roll damping recommended by the ITTC is included in the present method. This hybrid method is validated through the previously measured motions of two ship models, and the present numerical results are in good agreement with those of the experiments. Furthermore, the influences of longitudinal distances and wave heading angles on six-degree-of-freedom motions and the hydrodynamic interaction between the present two ship models are discussed in detail.展开更多
A finite equilibrium current density arises in the anomalous Hall effect(AHE)as a result of time-reversal symmetry breaking,affecting both the differential current density and total current.In this paper,we illustrate...A finite equilibrium current density arises in the anomalous Hall effect(AHE)as a result of time-reversal symmetry breaking,affecting both the differential current density and total current.In this paper,we illustrate the equilibrium current density in a ribbon-shaped system within the AHE regime,consisting of two sets of counterpropagating channels arranged in a zebra stripes pattern.While the middle channels are susceptible to scattering,the edge channels remain relatively robust.Despite this difference,all channels exhibit the same differential current density when subjected to a differential voltage across the two ends of the ribbon.When a differential voltage is applied to both sides of the ribbon,it results in a snaking pattern of differential current density forming across it.Furthermore,in a four-terminal device comprising the ribbon and two normal leads,it is found that Hall conductance is independent of ribbon width within certain scattering strengths due to the differences in robustness between middle and edge channels.These findings disclose the details of the AHE transport in a finite-sized system under weak scattering.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
How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was der...How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.展开更多
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 unitformly distributed loads acting on an inclined line...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 unitformly distributed loads acting on an inclined line in a poroelastie 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.展开更多
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This fu...The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.展开更多
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 equatio...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.展开更多
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 signific...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.展开更多
In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we i...In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.展开更多
基金financial support from the National Natural Science Foundation of China(No.12474016)the program of“Distinguished Expert of Taishan Scholar”(No.tstp20221124)+4 种基金the National Natural Science Foundation of China(Nos.52172212,12474017)the Shandong Provincial Science Foundation(ZR2021YQ03)the program for“Young Scientists of Taishan Scholars”(No.tsqn202306184)financial support from the National Natural Science Foundation of China(No.12464034)the Natural Science Foundation of Ningxia,China(No.2024AAC05070)。
文摘Defect engineering is a commonly methodology used to enhance the thermoelectric performance of thermoelectric PbTe by improving its electronic transport properties.At the nanoscale,defects can induce quantum tunneling effects that significantly impact the electrical properties of materials.To understand the specific mechanisms underlying the quantum transport properties of PbTe,we employ the non-equilibrium Green's function(NEGF)method to investigate the effects of intrinsic defects(point defects and grain boundaries)on the electronic transport properties of PbTe-based nanodevices from a quantum mechanical perspective.Our results show that the Pb vacancy(VPb)has the highest conduction.The conduction depends on the defect type,chemical potential and bias voltage.The presence of intrinsic point defects introduces impurity levels,facilitating the electron tunneling and leading to an increase in the transmission coefficient,thereby enhancing the electronic transport properties.For PbTe containing grain boundaries,these boundaries suppress the electronic transport properties.The Te occupied twin boundary(Te-TB)exerts a stronger inhibitory effect than the Pb occupied twin boundary(Pb-TB).Nevertheless,the combined effect between twin boundaries and point defects can enhance the electrical properties.Therefore,in order to obtain highly conductive of PbTe materials,a Te-rich synthesis environment should be used to promote the effective formation of Pb vacancy.Our work offers a comprehensive understanding of the impact of defects on electron scattering in thermoelectric materials.
基金supported by the National Natural Science Foundation of China(No.12461086)the Natural Science Foundation of Hubei Province(No.2022CFC016)。
文摘In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12272269, 11972257,11832014 and 11472193)the Shanghai Pilot Program for Basic Researchthe Shanghai Gaofeng Project for University Academic Program Development。
文摘Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.
基金Project supported by the National Natural Science Foundation of China(Grant No.11934020)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302402).
文摘This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].
文摘The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.
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 CNSF(Granted No.40874050)Chinese High Technology Project(Granted No.2011YQ05006010)
文摘We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.
基金Supported by the National Natural Science Foundation of China under Grant No.50779007the National Science Foundation for Young Scientists of China under Grant No.50809018+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070217074the Defence Advance Research Program of Science and Technology of Ship Industry under Grant No.07J1.1.6Harbin Engineering University Foundation under Grant No.HEUFT07069
文摘The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency.
基金supported by the Basic Science Center Project of the National Natural Science Foundation of China(42388102)the National Natural Science Foundation of China(42174030)+2 种基金the Special Fund of Hubei Luojia Laboratory(220100020)the Major Science and Technology Program for Hubei Province(2022AAA002)the Fundamental Research Funds for the Central Universities of China(2042022dx0001 and 2042023kfyq01)。
文摘Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.
基金Supported by the National Natural Science Foundation of China (12271141)。
文摘Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in R^(2) is studied.Through the reformulation of unknown functions,we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system.Based on a delicate analysis of the corresponding Green function,L^(2) decay estimate of the solution is obtained.
文摘In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where <span style="white-space:nowrap;">f <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈ C([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;">α <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈ [0,6) and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . 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.
基金financially supported by the National Natural Science Foundation of China (Grant Nos. 52071148 and 51509256)the Aeronautical Science Foundation of China (Grant No. 202000023079001)the Fundamental Research Funds for the Central Universities (Grant No.YCJJ20242103)。
文摘A three-dimensional panel method is developed to investigate the seakeeping performance of two parallel ships advancing in head and oblique waves. In this method, the fluid domain is partitioned into two regions by introducing a virtual control surface. In the inner part, the Taylor expansion boundary element method is used, whose kernel function is the Rankine source;in the outer part, the free surface Green function with the forward speed effect considered is adopted. The velocity potentials and normal velocities on the virtual control surface are equal for the inner and outer domains. Moreover, the numerical estimation method for viscous roll damping recommended by the ITTC is included in the present method. This hybrid method is validated through the previously measured motions of two ship models, and the present numerical results are in good agreement with those of the experiments. Furthermore, the influences of longitudinal distances and wave heading angles on six-degree-of-freedom motions and the hydrodynamic interaction between the present two ship models are discussed in detail.
基金supported by the National Natural Science Foundation of China(Grant No.12304062)supported by the National Natural Science Foundation of China(Grant No.12074107)+1 种基金the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Teams of Colleges and Universities in Hubei Province(Grant No.T2020001)the Innovation Group Project of the Natural Science Foundation of Hubei Province of China(Grant No.2022CFA012)。
文摘A finite equilibrium current density arises in the anomalous Hall effect(AHE)as a result of time-reversal symmetry breaking,affecting both the differential current density and total current.In this paper,we illustrate the equilibrium current density in a ribbon-shaped system within the AHE regime,consisting of two sets of counterpropagating channels arranged in a zebra stripes pattern.While the middle channels are susceptible to scattering,the edge channels remain relatively robust.Despite this difference,all channels exhibit the same differential current density when subjected to a differential voltage across the two ends of the ribbon.When a differential voltage is applied to both sides of the ribbon,it results in a snaking pattern of differential current density forming across it.Furthermore,in a four-terminal device comprising the ribbon and two normal leads,it is found that Hall conductance is independent of ribbon width within certain scattering strengths due to the differences in robustness between middle and edge channels.These findings disclose the details of the AHE transport in a finite-sized system under weak scattering.
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.
基金This work was financially supported by Key Program of the National Natural Science Foundation of China(No.50639020)the National High Technology Research and Development Program of China(863Program)(No.2006AA09Z332)
文摘How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.
基金National Natural Science Foundation of China Under Grant No.50378063
文摘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 unitformly distributed loads acting on an inclined line in a poroelastie 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.
文摘The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.
基金National Natural Science Foundation of China Key Project,under Grant No.50538030Postdoctoral Science Foundation of China under Grant No.2013M531084Natural Science Foundation of Heilongjiang Province of China under Grant No.E201221
文摘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.
文摘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.
基金supported by National Science Foundation of China(11071162)Shanghai Municipal Natural Science Foundation (09ZR1413500)
文摘In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.
