The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wav...The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.展开更多
A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations...A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.展开更多
This study proposes an elastic finite difference(FD)time domain method with variable grids in three-dimensional cylindrical coordinates.The calculations will diverge and become less accurate by conventional cylindrica...This study proposes an elastic finite difference(FD)time domain method with variable grids in three-dimensional cylindrical coordinates.The calculations will diverge and become less accurate by conventional cylindrical FD as the grid size gradually becomes more extensive with the increasing radius.To prevent grids from being too coarse in far fields,we compensate for the grid cell infl ation by refi ning the grid step in the azimuthal direction.The variable grid FD in the cylindrical coordinate systems has a higher effi ciency in solving acoustic logging while drilling(LWD)problems because the grid boundaries are consistent with those of the drill collar and the borehole.The proposed algorithm saves approximately 94%of the FD grids,80%of the computation time,and memory with a higher calculation accuracy than the FD on rectangular grids for the same models.We also calculate the acoustic LWD responses of the fl uid-fi lled borehole intersecting with fractures.Refl ections are generated at the fractures,which can be equivalent to an additional scattering source.The mode conversions between the collar and the Stoneley waves are revealed.The Stoneley spectra are more sensitive to the fracture.Finally,the logs in a heterogeneous formation with two refl ectors far from the borehole are modeled,and a means of estimating the azimuth of geological interfaces from refl ections is proposed.展开更多
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations....In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.展开更多
A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD (magnetohydrodynamic) for steady state three-dimensional laminar flow in horizontal and vertical cylindr...A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD (magnetohydrodynamic) for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media (sand silica) with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum (using Darcy's law) and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within (102 ~ Ra* 〈 104), and MHD (Mn) (0 〈_ Mn 〈_ 100) and radius ratio Rr (0.225, 0.338 and 0.435). The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra* and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra* and Mn, has been developed for the inner cylinder.展开更多
A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady s...A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq's approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within (10≤ Ra ≤ 103), aspect ratio (1 ≤ As 〈 5) and the volume fraction (0 ≤0 〈 0.2). The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.展开更多
This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corr...This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.展开更多
In this paper,a system of elliptic equations is investigated,which involves multiple critical Sobolev exponents and symmetric multi-polar potentials.By variational methods and analytic techniques,the relevant best con...In this paper,a system of elliptic equations is investigated,which involves multiple critical Sobolev exponents and symmetric multi-polar potentials.By variational methods and analytic techniques,the relevant best constants are studied and the existence of(Zk×SO(N.2))2-invariant solutions to the system is established.展开更多
In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Pal...In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.展开更多
A new approach is proposed to solve the elastic-plastic fields near the major-axis line of an elliptical hole. The complex variable method is used to determine the elastic fields near the major-axis line of the ellipt...A new approach is proposed to solve the elastic-plastic fields near the major-axis line of an elliptical hole. The complex variable method is used to determine the elastic fields near the major-axis line of the elliptical hole. Then, by using the line field analysis method, the exact and new solutions of the stresses, strains in the plastic zone, the size of the plastic region and the unit normal vector of the elastic-plastic boundary near the major-axis line of the elliptical hole are obtained for an anti-plane elliptical hole in a perfectly elastic-plastic solid. The usual small scale yielding assumptions are not adopted in the analysis. The present method is simple, easy and efficient. The influences of applied mechanical loading on the size of plastic zone are discussed.展开更多
Target dimension is important information in underwater target classification. An intrinsic mode characteristic extraction method in underwater cylindrical shell acoustic radiation was studied in this paper based on t...Target dimension is important information in underwater target classification. An intrinsic mode characteristic extraction method in underwater cylindrical shell acoustic radiation was studied in this paper based on the mechanism of shell vibration to gain the information about its dimension instead of accurate inversion processing. The underwater cylindrical shell vibration and acoustic radiation were first analyzed using mode decomposition to solve the wave equation. The characteristic of acoustic radiation was studied with different cylindrical shell lengths, radii, thickness, excitation points and fine structures. Simulation results show that the intrinsic mode in acoustic radiation spectrum correlates closely with the geometry dimensions of cylindrical shells. Through multifaceted analysis, the strongest intrinsic mode characteristic extracted from underwater shell acoustic radiated signal was most likely relevant to the radiated source radius. Then, partial information about unknown source dimension could be gained from intrinsic mode characteristic in passive sonar applications for underwater target classification. Experimental data processing results verified the effectiveness of the method in this paper.展开更多
In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will...In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.展开更多
A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomt...A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev–Petviashvili equation, some B¨acklund transformations(BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further,by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev–Petviashvili equation is proved consistent Riccati expansion(CRE)solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.展开更多
In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu-...In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.展开更多
In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by ...In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by the integral equation approach. The numerical results show that the increase of the electrical conductivity or magnetic permeability of the walls of the cylindrical vessel can reduce the critical magnetic Reynolds number. Furthermore, the critical magnetic Reynolds number is more sensi- tive to the varying electrical conductivity of the end wall or magnetic permeability of the side wall. For the anisotropic dynamo which is the mean field model of the Karlsruhe experiment, when the relative electrical conductivity of the side wall or the rel- ative magnetic permeability of the end wall is less than some critical value, the m=l (m is the azimuthal wave number) mag- netic mode is the dominant mode, otherwise the m=0 mode predominates the excited magnetic field. Therefore, by changing the material of the walls of the cylindrical vessel, one can select the magnetic mode excited by the anisotropic dynamo.展开更多
A novel equal diameter circular-hole photonic crystal fiber(PCF) with high birefringence is proposed and numerically analyzed by employing the finite-element method. The proposed PCF's birefringence is 10^(-3), wh...A novel equal diameter circular-hole photonic crystal fiber(PCF) with high birefringence is proposed and numerically analyzed by employing the finite-element method. The proposed PCF's birefringence is 10^(-3), which can reach 2 orders higher than that of traditional high birefringence fiber, and this equal diameter circular-hole structure reduces the difficulty of the actual drawing process. The effect of different parameters on the birefringence of this PCF is investigated, and the application of the Sagnac interferometer based on fiber filling technology in temperature sensing is studied. The result shows that the high birefringence PCF can be used in both optical communication and optical sensing fields.展开更多
文摘The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
基金supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province
文摘A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.
基金supported by the National Natural Science Foundation of China(Grant Nos.12174421,11774373,11734017,and 42074215).
文摘This study proposes an elastic finite difference(FD)time domain method with variable grids in three-dimensional cylindrical coordinates.The calculations will diverge and become less accurate by conventional cylindrical FD as the grid size gradually becomes more extensive with the increasing radius.To prevent grids from being too coarse in far fields,we compensate for the grid cell infl ation by refi ning the grid step in the azimuthal direction.The variable grid FD in the cylindrical coordinate systems has a higher effi ciency in solving acoustic logging while drilling(LWD)problems because the grid boundaries are consistent with those of the drill collar and the borehole.The proposed algorithm saves approximately 94%of the FD grids,80%of the computation time,and memory with a higher calculation accuracy than the FD on rectangular grids for the same models.We also calculate the acoustic LWD responses of the fl uid-fi lled borehole intersecting with fractures.Refl ections are generated at the fractures,which can be equivalent to an additional scattering source.The mode conversions between the collar and the Stoneley waves are revealed.The Stoneley spectra are more sensitive to the fracture.Finally,the logs in a heterogeneous formation with two refl ectors far from the borehole are modeled,and a means of estimating the azimuth of geological interfaces from refl ections is proposed.
文摘In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
文摘A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD (magnetohydrodynamic) for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media (sand silica) with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum (using Darcy's law) and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within (102 ~ Ra* 〈 104), and MHD (Mn) (0 〈_ Mn 〈_ 100) and radius ratio Rr (0.225, 0.338 and 0.435). The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra* and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra* and Mn, has been developed for the inner cylinder.
文摘A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq's approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within (10≤ Ra ≤ 103), aspect ratio (1 ≤ As 〈 5) and the volume fraction (0 ≤0 〈 0.2). The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.
基金supported by National Natural Science Foundation of China (Grant No. 10771219, 11071092)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20100144110001)
文摘This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.
基金supported by the Science Foundation of State Ethnic Affairs Commission of the People’s Republic of China(Grant No.12ZNZ004)
文摘In this paper,a system of elliptic equations is investigated,which involves multiple critical Sobolev exponents and symmetric multi-polar potentials.By variational methods and analytic techniques,the relevant best constants are studied and the existence of(Zk×SO(N.2))2-invariant solutions to the system is established.
基金supported by National Natural Science Foundation of China(Grant Nos.10771219 and 11071092)the PhD Specialized Grant of the Ministry of Education of China(Grant No.20110144110001)
文摘In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10932001 and 11072015)the Scientific Research Key Program of Beijing Municipal Commission of Education (Grant No. KZ201010005003)the PhD Innovative Foundation of Beihang University (Grant No. 300351)
文摘A new approach is proposed to solve the elastic-plastic fields near the major-axis line of an elliptical hole. The complex variable method is used to determine the elastic fields near the major-axis line of the elliptical hole. Then, by using the line field analysis method, the exact and new solutions of the stresses, strains in the plastic zone, the size of the plastic region and the unit normal vector of the elastic-plastic boundary near the major-axis line of the elliptical hole are obtained for an anti-plane elliptical hole in a perfectly elastic-plastic solid. The usual small scale yielding assumptions are not adopted in the analysis. The present method is simple, easy and efficient. The influences of applied mechanical loading on the size of plastic zone are discussed.
基金supported by the Project of the Key Laboratory of Science and Technology on Underwater Test and Control(Grant No.9140C260505120C26104)the National Natural Science Foundation of China(Grant No. 11104029)
文摘Target dimension is important information in underwater target classification. An intrinsic mode characteristic extraction method in underwater cylindrical shell acoustic radiation was studied in this paper based on the mechanism of shell vibration to gain the information about its dimension instead of accurate inversion processing. The underwater cylindrical shell vibration and acoustic radiation were first analyzed using mode decomposition to solve the wave equation. The characteristic of acoustic radiation was studied with different cylindrical shell lengths, radii, thickness, excitation points and fine structures. Simulation results show that the intrinsic mode in acoustic radiation spectrum correlates closely with the geometry dimensions of cylindrical shells. Through multifaceted analysis, the strongest intrinsic mode characteristic extracted from underwater shell acoustic radiated signal was most likely relevant to the radiated source radius. Then, partial information about unknown source dimension could be gained from intrinsic mode characteristic in passive sonar applications for underwater target classification. Experimental data processing results verified the effectiveness of the method in this paper.
基金This research is supported by the Special Funds for Major State Research Projects of China(G 1999032804)
文摘In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of under Grant Nos.11275072 and 11435005+3 种基金Doctoral Program of Higher Education of China under Grant No.20120076110024the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213Zhejiang Provincial Natural Science Foundation of China under Grant No.LY14A010005
文摘A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev–Petviashvili equation, some B¨acklund transformations(BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further,by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev–Petviashvili equation is proved consistent Riccati expansion(CRE)solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.
文摘In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.
基金supported by the National Natural Science Foundation of China(Grant No.11272187)
文摘In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by the integral equation approach. The numerical results show that the increase of the electrical conductivity or magnetic permeability of the walls of the cylindrical vessel can reduce the critical magnetic Reynolds number. Furthermore, the critical magnetic Reynolds number is more sensi- tive to the varying electrical conductivity of the end wall or magnetic permeability of the side wall. For the anisotropic dynamo which is the mean field model of the Karlsruhe experiment, when the relative electrical conductivity of the side wall or the rel- ative magnetic permeability of the end wall is less than some critical value, the m=l (m is the azimuthal wave number) mag- netic mode is the dominant mode, otherwise the m=0 mode predominates the excited magnetic field. Therefore, by changing the material of the walls of the cylindrical vessel, one can select the magnetic mode excited by the anisotropic dynamo.
基金supported by the National Natural Science Foundation of China(Nos.61301124,61471075 and 61671091)the Basic Research Project of Chongqing Science and Technology Commission(Nos.cstc2014gjhz40001,cstc2015jcyj BX0068,cstc2014jcyj A1350,cstc2015jcyj B0360 and KJZH17115)+3 种基金the University Innovation Team Construction Plan of Smart Medical System and Core Technologythe Enhancement Plan of Chongqing Key Laboratory of Photoelectronic Information Sensing and Transmitting Technologythe Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJ1704091)the Funds of Chongqing University of Posts and Telecommunications(No.A2016-72)
文摘A novel equal diameter circular-hole photonic crystal fiber(PCF) with high birefringence is proposed and numerically analyzed by employing the finite-element method. The proposed PCF's birefringence is 10^(-3), which can reach 2 orders higher than that of traditional high birefringence fiber, and this equal diameter circular-hole structure reduces the difficulty of the actual drawing process. The effect of different parameters on the birefringence of this PCF is investigated, and the application of the Sagnac interferometer based on fiber filling technology in temperature sensing is studied. The result shows that the high birefringence PCF can be used in both optical communication and optical sensing fields.