There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle th...There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.展开更多
The interaction between a solute atom and an extended dislocation was investigated using a continuum approximation method with force multipoles.The dislocation core structure of extended dislocation was modeled with t...The interaction between a solute atom and an extended dislocation was investigated using a continuum approximation method with force multipoles.The dislocation core structure of extended dislocation was modeled with the Peierls-Nabarro model discretized with a number of infinitesimal Volterra dislocations.The interaction energy and force between a nickel solute atom and perfect and extended dislocation in copper were successfully calculated using the force multipoles.The results clearly show that the core structure of extended dislocation weakens the interaction with solute atoms.The interaction energy and force for extended dislocations are almost the half of those for perfect dislocations.展开更多
The Buckingham expansion is important for understanding molecular multipoles and(hyper)polarizabilities.In this study,we give a complete derivation of the Buckingham expansion in the traced form using successive Taylo...The Buckingham expansion is important for understanding molecular multipoles and(hyper)polarizabilities.In this study,we give a complete derivation of the Buckingham expansion in the traced form using successive Taylor series.Based on the derivation results,a general Buckingham expansion in the traced form is proposed,from which highly accurate numerical calculations using the finite field method can be achieved.The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient.The applications of thefinite field method in this study show good agreements with previous theoretical calculations and experimental measurements.展开更多
In order to calculate the multipoles in real materials with considerable intersite Coulomb interaction V,we develop a self-consistent program which starts from the frst-principles calculations to solve the tight-bindi...In order to calculate the multipoles in real materials with considerable intersite Coulomb interaction V,we develop a self-consistent program which starts from the frst-principles calculations to solve the tight-binding Hamiltonian including onsite Coulomb repulsion U,V,and spin-orbital couplingλ.The program is applied to Ba_(2)MgReO_(6)to fgure out the mechanism of structural instability and magnetic ordering.A comprehensive quadrupole phase diagram versus U and V withλ=0.28 eV is calculated.Our results demonstrate that the easy-plane anisotropy and the intersite Coulomb repulsion V must be considered to remove the orbital frustration.The increase of V to>20 meV would arrange quadrupole Q_(x^(2)-y^(2))antiparallelly,accompanied by small parallel Q_(3z)^(2)-r^(2),and stabilize Ba_(2)MgReO_(6)into the body-centered tetragonal structure.Such antiparallel Q_(x^(2)-y^(2))provides a new mechanism for the Dzyaloshinskii-Moriya interaction and gives rise to the canted antiferromagnetic(CAF)state along the[110]axis.Moreover,sizable octupoles such as O_(21)^(31),O_(21)^(33),O_(21)^(34)and O_(21)^(36)are discovered for the frst time in the CAF state.Our study not only provides a comprehensive understanding of the experimental results in Ba_(2)MgReO_(6),but also serves as a general and useful tool for the study of multipole physics in 5d compounds.展开更多
At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise con...At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.展开更多
A method to derive the atomic multipole moments cumulatively up to quadrupole mo- ments was developed.The multipole moments are obtained by least-square simulating the molecular electrostatic potentials.Only the compo...A method to derive the atomic multipole moments cumulatively up to quadrupole mo- ments was developed.The multipole moments are obtained by least-square simulating the molecular electrostatic potentials.Only the components of the term of highest order in the atomic multipole expansion are optimized while the lower terms remain fixed.The calculations on HF,H_2O and NH_2 show that the cumulative method can give reasonable qualitative and fairly good quantitative results.展开更多
In this paper,we develop an efcient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration.Firstly,we briefy review ...In this paper,we develop an efcient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration.Firstly,we briefy review the principles of multipole decomposition,highlighting two numerical projection methods including surface and volume integration.Secondly,we discuss the Lebedev and Gaussian quadrature methods,provide a detailed recipe to select the quadrature points and the corresponding weighting factor,and illustrate the integration accuracy and numerical efciency(that is,with very few sampling points)using a unit sphere surface and regular tetrahedron.In the demonstrations of an isotropic dielectric nanosphere,a symmetric scatterer,and an anisotropic nanosphere,we perform multipole decomposition and validate our numerical projection procedure.The obtained results from our procedure are all consistent with those from Mie theory,symmetry constraints,and fnite element simulations.展开更多
It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth ...It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.展开更多
Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufact...Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.展开更多
In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated por...In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.展开更多
In this work,trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densi...In this work,trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities.The impermeable cylinder is fully immersed in either the bottom layer or the upper layer.The effect of surface tension at the surface of separation is neglected.In this set-up,there exist three wave numbers:the lowest one on the free surface and the other two on the internal interfaces.For each wave number,there exist two modes for which trapped waves exist.The existence of these trapped modes is shown by numerical evidence.We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth.We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity.The existence of trapped modes shows that in general,a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.展开更多
It is well-known that if p is a homogeneous polynomial of degree k in n variables, p ∈ P;, then the ordinary derivative p（）(r;) has the form A;Y（x）r;where A;is a constant and where Y is a harmonic homogeneous pol...It is well-known that if p is a homogeneous polynomial of degree k in n variables, p ∈ P;, then the ordinary derivative p（）(r;) has the form A;Y（x）r;where A;is a constant and where Y is a harmonic homogeneous polynomial of degree k, Y ∈ H;, actually the projection of p onto H;. Here we study the distributional derivative p（）(r;) and show that the ordinary part is still a multiple of Y, but that the delta part is independent of Y, that is, it depends only on p-Y. We also show that the exponent 2-n is special in the sense that the corresponding results for p（）(r;)do not hold if α≠2-n. Furthermore, we establish that harmonic polynomials appear as multiples of r;when p（） is applied to harmonic multipoles of the form Y’（x）r;for some Y ∈H;.展开更多
A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is pr...A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.展开更多
The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（M...The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（MLFMA） memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.展开更多
An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is pos...An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is possible in the anomalous dispersion regime between the two zero-dispersion wavelengths. Using 200 fs Ti： sapphire laser of 820, 830 and 840nm, the anti-Stokes line around 530nm can be generated efficiently. The maximum ratio of the anti-Stokes signal energy to the pump component in the output spectrum is estimated to be 1.03 and the conversion efficiency is above 50%.展开更多
In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on ...In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.展开更多
文摘There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.
文摘The interaction between a solute atom and an extended dislocation was investigated using a continuum approximation method with force multipoles.The dislocation core structure of extended dislocation was modeled with the Peierls-Nabarro model discretized with a number of infinitesimal Volterra dislocations.The interaction energy and force between a nickel solute atom and perfect and extended dislocation in copper were successfully calculated using the force multipoles.The results clearly show that the core structure of extended dislocation weakens the interaction with solute atoms.The interaction energy and force for extended dislocations are almost the half of those for perfect dislocations.
基金the National Natural Science Foundation of China(Grant Nos.21573112 and 21421001)。
文摘The Buckingham expansion is important for understanding molecular multipoles and(hyper)polarizabilities.In this study,we give a complete derivation of the Buckingham expansion in the traced form using successive Taylor series.Based on the derivation results,a general Buckingham expansion in the traced form is proposed,from which highly accurate numerical calculations using the finite field method can be achieved.The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient.The applications of thefinite field method in this study show good agreements with previous theoretical calculations and experimental measurements.
基金was supported by the National Key Research and Development Program of China(Grant Nos.2024YFA1611200 and 2018YFA0307000)the National Natural Science Foundation of China(Grant Nos.12274154 and 12404182)。
文摘In order to calculate the multipoles in real materials with considerable intersite Coulomb interaction V,we develop a self-consistent program which starts from the frst-principles calculations to solve the tight-binding Hamiltonian including onsite Coulomb repulsion U,V,and spin-orbital couplingλ.The program is applied to Ba_(2)MgReO_(6)to fgure out the mechanism of structural instability and magnetic ordering.A comprehensive quadrupole phase diagram versus U and V withλ=0.28 eV is calculated.Our results demonstrate that the easy-plane anisotropy and the intersite Coulomb repulsion V must be considered to remove the orbital frustration.The increase of V to>20 meV would arrange quadrupole Q_(x^(2)-y^(2))antiparallelly,accompanied by small parallel Q_(3z)^(2)-r^(2),and stabilize Ba_(2)MgReO_(6)into the body-centered tetragonal structure.Such antiparallel Q_(x^(2)-y^(2))provides a new mechanism for the Dzyaloshinskii-Moriya interaction and gives rise to the canted antiferromagnetic(CAF)state along the[110]axis.Moreover,sizable octupoles such as O_(21)^(31),O_(21)^(33),O_(21)^(34)and O_(21)^(36)are discovered for the frst time in the CAF state.Our study not only provides a comprehensive understanding of the experimental results in Ba_(2)MgReO_(6),but also serves as a general and useful tool for the study of multipole physics in 5d compounds.
基金the support from the 2025 Henan Provincial Science and Technology Research Project,the Zhumadian 2023 Major Science and Technology Special Projectthe Postgraduate Education Reform and Quality Improvement Project of Henan Province.
文摘At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.
基金This work was supported by the National Natural Science Foundation of China.
文摘A method to derive the atomic multipole moments cumulatively up to quadrupole mo- ments was developed.The multipole moments are obtained by least-square simulating the molecular electrostatic potentials.Only the components of the term of highest order in the atomic multipole expansion are optimized while the lower terms remain fixed.The calculations on HF,H_2O and NH_2 show that the cumulative method can give reasonable qualitative and fairly good quantitative results.
基金funded by the National Key Research and Development Program of China(No.2021YFB2800303)Innovation Project of Optics Valley Laboratory,and the National Natural Science Foundation of China(Grant No.61405067).
文摘In this paper,we develop an efcient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration.Firstly,we briefy review the principles of multipole decomposition,highlighting two numerical projection methods including surface and volume integration.Secondly,we discuss the Lebedev and Gaussian quadrature methods,provide a detailed recipe to select the quadrature points and the corresponding weighting factor,and illustrate the integration accuracy and numerical efciency(that is,with very few sampling points)using a unit sphere surface and regular tetrahedron.In the demonstrations of an isotropic dielectric nanosphere,a symmetric scatterer,and an anisotropic nanosphere,we perform multipole decomposition and validate our numerical projection procedure.The obtained results from our procedure are all consistent with those from Mie theory,symmetry constraints,and fnite element simulations.
文摘It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.
基金supported in part by the National Key Research and Development Program of China(No.2022YFA1603402)in part by the National Natural Science Foundation of China(No.11875272)。
文摘Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.
基金Project supported by the National Natural Science Foundation of China (Grant No.42074139)the Natural Science Foundation of Jilin Province,China (Grant No.20210101140JC)。
文摘In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.
文摘In this work,trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities.The impermeable cylinder is fully immersed in either the bottom layer or the upper layer.The effect of surface tension at the surface of separation is neglected.In this set-up,there exist three wave numbers:the lowest one on the free surface and the other two on the internal interfaces.For each wave number,there exist two modes for which trapped waves exist.The existence of these trapped modes is shown by numerical evidence.We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth.We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity.The existence of trapped modes shows that in general,a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.
文摘It is well-known that if p is a homogeneous polynomial of degree k in n variables, p ∈ P;, then the ordinary derivative p（）(r;) has the form A;Y（x）r;where A;is a constant and where Y is a harmonic homogeneous polynomial of degree k, Y ∈ H;, actually the projection of p onto H;. Here we study the distributional derivative p（）(r;) and show that the ordinary part is still a multiple of Y, but that the delta part is independent of Y, that is, it depends only on p-Y. We also show that the exponent 2-n is special in the sense that the corresponding results for p（）(r;)do not hold if α≠2-n. Furthermore, we establish that harmonic polynomials appear as multiples of r;when p（） is applied to harmonic multipoles of the form Y’（x）r;for some Y ∈H;.
基金The project supported by the National Nature Science Foundation of China(10172053)the Ministry of Education
文摘A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.
基金supported by the National Basic Research Program of China (973 Program) (61320)
文摘The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（MLFMA） memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.
基金Supported by the National Key Basic Research Programme of China under Grant No 2003CB314905, and the National Natural Science Foundation of China under Grant No 60637010.
文摘An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is possible in the anomalous dispersion regime between the two zero-dispersion wavelengths. Using 200 fs Ti： sapphire laser of 820, 830 and 840nm, the anti-Stokes line around 530nm can be generated efficiently. The maximum ratio of the anti-Stokes signal energy to the pump component in the output spectrum is estimated to be 1.03 and the conversion efficiency is above 50%.
基金The project supported by the National Natural Science Foundation of China (10472051)
文摘In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.
