By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at t...By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.展开更多
Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be ...Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.展开更多
Based on the analogy to gas dynamics, the kinetic flux vector splitting (KFVS) method is used to stimulate the shallow water wave equations. The flux vectors of the equations are split on the basis of the local equili...Based on the analogy to gas dynamics, the kinetic flux vector splitting (KFVS) method is used to stimulate the shallow water wave equations. The flux vectors of the equations are split on the basis of the local equilibrium Maxwell-Boltzmann distribution. One dimensional examples including a dam breaking wave and flows over a ridge are calculated. The solutions exhibit second-order accuracy with no spurious oscillation.展开更多
Rogue waves are a class of nonlinear waves with extreme amplitudes,which usually appear suddenly and disappear without any trace.Recently,the parity-time(PT)-symmetric vector rogue waves(RWs)of multi-component nonline...Rogue waves are a class of nonlinear waves with extreme amplitudes,which usually appear suddenly and disappear without any trace.Recently,the parity-time(PT)-symmetric vector rogue waves(RWs)of multi-component nonlinear Schrödinger equation(n-NLSE)are usually derived by the methods of integrable systems.In this paper,we utilize the multi-stage physics-informed neural networks(MS-PINNs)algorithm to derive the data-driven symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition.The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.展开更多
The normal and abnormal cylindrical vector wave functions are constructed. Some impor-tant conversion relations in circular, elliptic and parabolic cylindrical coordinate systems are discussedin detail, where the resu...The normal and abnormal cylindrical vector wave functions are constructed. Some impor-tant conversion relations in circular, elliptic and parabolic cylindrical coordinate systems are discussedin detail, where the result in circular cylindrical coordinate system is the same as the one given bythe author (1984).展开更多
Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-...Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.展开更多
An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical...An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.展开更多
The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is m...The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is motivated by solving an EM problem on the Fourier side in order to relate the resolvent and the Green’s function. Methods used include Matrix Theory, Fourier Transforms, and Green’s function. A closed form of the resolvent is derived for the electromagnetic Helmholtz reduced vector wave equation, with Dirichlet boundary conditions. The resolvent is then used to derive expressions for the solution of the EM wave equation and provide Sobolev estimates for the solution.展开更多
A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behave...A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.展开更多
The conversion theory of vector wave function is one of important problems in electromagnetic. This paper presents a systematic treatment of the conversion technique and some applications. In this paper, the conversio...The conversion theory of vector wave function is one of important problems in electromagnetic. This paper presents a systematic treatment of the conversion technique and some applications. In this paper, the conversion relations of standard and non-standard spherical vector wave functions, standard and non-standard cylindrical vector wave functions, and spherical and cylindrical vector wave functions are developed. As an example of application of vector wave function expansion, the expansion of plane wave and dipole field in two-medium half-spaces are given. As an example of application of vector wave function conversion, the scattering patterns of buried conducting and dielectric spheres are presented. Inspection on the numerical results shows that the technique and associated programs presented in this paper are efficient.展开更多
In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the sa...In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.展开更多
Originally, the kinetic flux vector splitting (KFVS) scheme was developed as a numerical method to solve gas dynamic problems. The main idea in the approach is to construct the flux based on the microscopical descript...Originally, the kinetic flux vector splitting (KFVS) scheme was developed as a numerical method to solve gas dynamic problems. The main idea in the approach is to construct the flux based on the microscopical description of the gas. In this paper, based on the analogy between the shallow water wave equations and the gas dynamic equations, we develop an explicit KFVS method for simulating the shallow water wave equations. A 1D steady flow and a 2D unsteady flow are presented to show the robust and accuracy of the KFVS scheme.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10172038).
文摘By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.
基金financially supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51321065)the Research Fund of State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University(Grant No.1104)
文摘Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.
基金Subsidized by the Special Funds for Major State Basic Research Early Stage Project(2002CCA 01200)the Project-sponsored by SRF for ROCS,SME.
文摘Based on the analogy to gas dynamics, the kinetic flux vector splitting (KFVS) method is used to stimulate the shallow water wave equations. The flux vectors of the equations are split on the basis of the local equilibrium Maxwell-Boltzmann distribution. One dimensional examples including a dam breaking wave and flows over a ridge are calculated. The solutions exhibit second-order accuracy with no spurious oscillation.
基金supported by National Natural Science Foundation of China(Grant Nos.11771151,61571005,and 61901160)the Science and Technology Program of Guangzhou(Grant No.201904010362)the Fundamental Research Program of Guangdong Province,China(Grant No.2020B1515310023)。
文摘Rogue waves are a class of nonlinear waves with extreme amplitudes,which usually appear suddenly and disappear without any trace.Recently,the parity-time(PT)-symmetric vector rogue waves(RWs)of multi-component nonlinear Schrödinger equation(n-NLSE)are usually derived by the methods of integrable systems.In this paper,we utilize the multi-stage physics-informed neural networks(MS-PINNs)algorithm to derive the data-driven symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition.The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.
文摘The normal and abnormal cylindrical vector wave functions are constructed. Some impor-tant conversion relations in circular, elliptic and parabolic cylindrical coordinate systems are discussedin detail, where the result in circular cylindrical coordinate system is the same as the one given bythe author (1984).
基金Project supported by the BUPT Excellent Ph.D.Students Foundation(Grant No.CX2019201)the National Natural Science Foundation of China(Grant Nos.11772017 and 11805020)+1 种基金the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(Grant No.IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China(Grant No.2011BUPTYB02)。
文摘Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.
基金This work is supported by the National Natural Science Foundation of China
文摘An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.
文摘The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is motivated by solving an EM problem on the Fourier side in order to relate the resolvent and the Green’s function. Methods used include Matrix Theory, Fourier Transforms, and Green’s function. A closed form of the resolvent is derived for the electromagnetic Helmholtz reduced vector wave equation, with Dirichlet boundary conditions. The resolvent is then used to derive expressions for the solution of the EM wave equation and provide Sobolev estimates for the solution.
文摘A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.
文摘The conversion theory of vector wave function is one of important problems in electromagnetic. This paper presents a systematic treatment of the conversion technique and some applications. In this paper, the conversion relations of standard and non-standard spherical vector wave functions, standard and non-standard cylindrical vector wave functions, and spherical and cylindrical vector wave functions are developed. As an example of application of vector wave function expansion, the expansion of plane wave and dipole field in two-medium half-spaces are given. As an example of application of vector wave function conversion, the scattering patterns of buried conducting and dielectric spheres are presented. Inspection on the numerical results shows that the technique and associated programs presented in this paper are efficient.
文摘In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.
基金Foundation item:Supported by the National Key Grant Program of Basic(2002CCA01200)original funding of Jilin Universitythe Project-sponsord by SRF for ROCS,SME
文摘Originally, the kinetic flux vector splitting (KFVS) scheme was developed as a numerical method to solve gas dynamic problems. The main idea in the approach is to construct the flux based on the microscopical description of the gas. In this paper, based on the analogy between the shallow water wave equations and the gas dynamic equations, we develop an explicit KFVS method for simulating the shallow water wave equations. A 1D steady flow and a 2D unsteady flow are presented to show the robust and accuracy of the KFVS scheme.
