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
Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study a...Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.展开更多
Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple ...Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and functional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern region but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant positive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that preserving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.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 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
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
Amino acids have emerged as promising green alternatives to replace toxic inhibitors in corrosion protection applications.In this study,we present a one-step synthetic approach to get 4-(tert-butyl)benzoyl)methionine(...Amino acids have emerged as promising green alternatives to replace toxic inhibitors in corrosion protection applications.In this study,we present a one-step synthetic approach to get 4-(tert-butyl)benzoyl)methionine(P-Meth)and 4-(tert-butyl)benzoyl)cysteine(P-Cys)through the acylation reactions between methionine or cysteine and p-tert-butylbenzoic acid,respectively,which exhibit a super protective performance toward metals against corrosion.The corrosion rates of Q235 steel in 1 M HCl were reduced from 4.542 to 0.202and 0.312 mg·h^(-1)·cm^(-2)in the presence of 100 mg·L^(-1)P-Meth and P-Cys,respectively.The surface structures of Q235 steel remained unbroken after 12 h in 1 M HCl medium.The charge transfer resistances of corrosion reactions were enhanced by 12 and 9 times in the presence of P-Meth and P-Cys,respectively.P-Meth and P-Cys were adsorbed onto the Q235 steel via chemical actions,which were accompanied by minimal physical action.Molecular dynamic simulations demonstrate the higher binding energy of P-Meth onto Q235 steel than P-Cys.The study contributes to the corrosion protection of metals with green and environmentally friendly methods.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
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
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
The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field ...The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.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funded by the National Non Profit Research Institutions of the Chinese Academy of Forestry(CAFYBB2020ZB008)National Natural Science Foundation of China(32371936)the Research Projects in Anhui Universities in 2022(natural sciences)(2022AH051874).
文摘Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.
基金Under the auspices of the Innovation Program of Chinese Academy of Agricultural Sciences(No.CAAS-STNY-2024)。
文摘Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and functional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern region but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant positive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that preserving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.
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.
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 the Shenzhen Science and Technology Research Fund(Nos.JSGG20201103153807021,GXWD20220811173736002,and KCXFZ20230731094904009)We are also grateful to the Natural Science Foundation of Guangdong Province,China(No.2021 A1515110366)+1 种基金the National Natural Science Foundation of China(Nos.22302048,82204231,and 22004024)the Shenzhen High Tech Zone Development Special Plan Innovation Platform Construction Project,China(No.29853MKCJ-2023-002-11)。
文摘Amino acids have emerged as promising green alternatives to replace toxic inhibitors in corrosion protection applications.In this study,we present a one-step synthetic approach to get 4-(tert-butyl)benzoyl)methionine(P-Meth)and 4-(tert-butyl)benzoyl)cysteine(P-Cys)through the acylation reactions between methionine or cysteine and p-tert-butylbenzoic acid,respectively,which exhibit a super protective performance toward metals against corrosion.The corrosion rates of Q235 steel in 1 M HCl were reduced from 4.542 to 0.202and 0.312 mg·h^(-1)·cm^(-2)in the presence of 100 mg·L^(-1)P-Meth and P-Cys,respectively.The surface structures of Q235 steel remained unbroken after 12 h in 1 M HCl medium.The charge transfer resistances of corrosion reactions were enhanced by 12 and 9 times in the presence of P-Meth and P-Cys,respectively.P-Meth and P-Cys were adsorbed onto the Q235 steel via chemical actions,which were accompanied by minimal physical action.Molecular dynamic simulations demonstrate the higher binding energy of P-Meth onto Q235 steel than P-Cys.The study contributes to the corrosion protection of metals with green and environmentally friendly methods.
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 National Natural Science Foundation of China (Grant No. 50879090)
文摘The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.
