Based on the scaling idea of local slopes by Lopez et al. [Phys. Rev. Lett. 94 （2005） 166103], we investigate anomalous dynamic scaling of （d ＋ 1）-dimensional surface growth equations with spatially and temporall...Based on the scaling idea of local slopes by Lopez et al. [Phys. Rev. Lett. 94 （2005） 166103], we investigate anomalous dynamic scaling of （d ＋ 1）-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang （KPZ）, Sun-Guo-Grant （SGG）, and Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.展开更多
We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformat...We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.展开更多
This review article commences with a comprehensive historical review of the evolution and application of various density surfaces in atmospheric and oceanic studies. The background provides a basis for the birth of th...This review article commences with a comprehensive historical review of the evolution and application of various density surfaces in atmospheric and oceanic studies. The background provides a basis for the birth of the neutral density idea. Attention is paid to the development of the neutral density surface concept from the nonlinearity of the equation of state of seawater. The definition and properties of neutral density surface are described in detail as developed from the equations of state of seawater and the buoyancy frequency when the squared buoyancy frequency N2 is zero, a neutral state of stability. In order to apply the neutral density surface to intermediate water-mass analysis, this review also describes in detail its practical oceanographic application. The mapping technique is focused for the first time on applying regularly gridded data in this review. It is reviewed how a backbone and ribs framework was designed to flesh out from a reference cast and first mapped the global neutral surfaces in the world’s oceans. Several mapped neutral density surfaces are presented as examples for each world ocean. The water-mass property is analyzed in each ocean at mid-depth. The characteristics of neutral density surfaces are compared with those of potential density surfaces.展开更多
The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux prof...The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.展开更多
The Chinese Academy of Sciences Flexible Global Ocean-Atmosphere-Land System atmospheric component model(FGOALS-f3-L)participated in Phase 6 of the Coupled Model Intercomparison Project,but its reproducibility of surf...The Chinese Academy of Sciences Flexible Global Ocean-Atmosphere-Land System atmospheric component model(FGOALS-f3-L)participated in Phase 6 of the Coupled Model Intercomparison Project,but its reproducibility of surface temperature(T_(s))over the Tibetan Plateau(TP)as a key climatically sensitive region remains unclear.This study evaluates the capability of FGOALS-f3-L in reproducing the climatological T_(s)over the TP relative to the Climate Forecast System Reanalysis.The results show that FGOALS-f3-L can reasonably capture the spatial pattern of T_(s)but underestimates the annual mean T_(s)for the whole TP.The simulated T_(s)for the whole TP shows a cold bias in winter and spring and a warm bias in summer and autumn.Further quantitative analysis based on the surface energy budget equation shows that the surface albedo feedback(SAF)term strongly contributes to the annual,winter,and spring mean cold bias in the western TP and to the warm bias in the eastern TP.Compared with the SAF term,the surface sensible and latent heat flux terms make nearly opposite contributions to the T_(s)bias and considerably offset the bias due to the SAF term.The cloud radiative forcing term strongly contributes to the annual and seasonal mean weak cold bias in the eastern TP.The longwave radiation term associated with the overestimated water vapor content accounts for a large portion of the warm bias over the whole TP in summer and autumn.Improving land surface and cloud processes in FGOALS-f3-L is critical to reduce the T_(s)bias over the TP.展开更多
According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of （1＋ 1）-dimensional growth equation for molecular-beam epitaxy. The growth model inclu...According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of （1＋ 1）-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy （LMBE） and the nonlinear Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.展开更多
Current surface integral equations used for computing scattering from targets with negative impedance boundary condition（IBC）are not efficient.A modified surface dual integral equation（M-SDIE）for targets with nega...Current surface integral equations used for computing scattering from targets with negative impedance boundary condition（IBC）are not efficient.A modified surface dual integral equation（M-SDIE）for targets with negative IBC is presented.A pure imaginary number is used to balance the formulations.It is proved that the M-SDIE is accurate and efficient with three numerical examples.The first numerical example shows that the M-SDIE is accurate compared with Mie.The second example shows that the presented SIE is efficient.In the third example,a missile head is selected to present the computing power of the M-SDIE.All the examples show that the M-SDIE is an efficient algorithm for negative IBC.展开更多
Body surface area（BSA）was regarded as a more readily quantifiable parameter relative to body mass in the normalization of comparative biochemistry and physiology.The BSA prediction has attracted unceasing research b...Body surface area（BSA）was regarded as a more readily quantifiable parameter relative to body mass in the normalization of comparative biochemistry and physiology.The BSA prediction has attracted unceasing research back more than a century on animals,especially on humans and rats.Few studies in this area for anurans were reported,and the equation for body surface area（S）and body mass（W）：S=9.9 W 0.56,which was concluded from toads of four species in 1969,was generally adopted to estimate the body surface areas for anurans until recent years.However,this equation was not applicable to Odorrana grahami.The relationship between body surface area and body mass for this species was established as：S=15.4 W 0.579.Our current results suggest estimation equations should be used cautiously across different species and body surface area predictions on more species need to be conducted.展开更多
To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE met...To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.展开更多
A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The disconti...A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.展开更多
Aiming at improving the mechanical vibrating equipment,the axial thrust roller-exciting vibrating tables and its motor-control system based on co-simulation were put forward. First, the structures of vibrating table a...Aiming at improving the mechanical vibrating equipment,the axial thrust roller-exciting vibrating tables and its motor-control system based on co-simulation were put forward. First, the structures of vibrating table and its surface equations and boundary conditions were established through reversal process. Second,waveform distortion influenced by random and harmonic waves was analyzed by equivalent parametric transition. These two steps were both technological challenge and contribution for the vibrating table.Finally, based on research above, a proportion integration differentiation( PID) motor-control system was built to show its rapid operation and convenient control. All the results show that not only does vibrating table have lower waveform distortion than traditional ones,but its control system narrows down the fluctuation and improves anti-interference performance. Hence,it provides a more extensive selection for efficient and practical mechanical vibrating table.展开更多
The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analy...The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute展开更多
This paper introduces the research work on the extension of multilevel fast multipole algorithm （MLFMA） to 3D complex structures including coating object, thin dielectric sheet, composite dielectric and conductor, c...This paper introduces the research work on the extension of multilevel fast multipole algorithm （MLFMA） to 3D complex structures including coating object, thin dielectric sheet, composite dielectric and conductor, cavity. The impedance boundary condition is used for scattering from the object coated by thin lossy material. Instead of volume integral equation, surface integral equation is applied in case of thin dielectric sheet through resistive sheet boundary condition. To realize the fast computation of scattering from composite homogeneous dielectric and conductor, the surface integral equation based on equivalence principle is used. Compared with the traditional volume integral equation, the surface integral equation reduces greatly the number of unknowns. To computc conducting cavity with electrically large aperture, an electric field integral equation is applied. Some numerical results are given to demonstrate the validity and accuracy of the present methods.展开更多
In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F b...In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.展开更多
Based on the combined tangential formulation of surface integral equation, a fast algo- rithm is presented for calculating electromagnetic scattering from electrically large 3D homogeneous objects. In the algorithm, t...Based on the combined tangential formulation of surface integral equation, a fast algo- rithm is presented for calculating electromagnetic scattering from electrically large 3D homogeneous objects. In the algorithm, the lower triangular approximate Schur preconditioner is combined with the multilevel fast multipole algorithm （MLFMA）. The coefficient matrix of the near-field coupling element is selected to set up the approximate matrix. For large problems, the incomplete LU factori- zation with dual threshold （ILUT） has better performance than sparse approximate inverse （SAI） of accelerating the convergence of the generalized minimal residual method （ GMRES ） iteration. Nu- merical experiments validate the efficiency and robustness of the presented fast algorithm for homo- geneous dielectric objects.展开更多
We propose a method that combines isogeometric analysis(IGA)with the discontinuous Galerkin(DG)method for solving elliptic equations on 3-dimensional(3D)surfaces consisting of multiple patches.DG ideology is adopted a...We propose a method that combines isogeometric analysis(IGA)with the discontinuous Galerkin(DG)method for solving elliptic equations on 3-dimensional(3D)surfaces consisting of multiple patches.DG ideology is adopted across the patch interfaces to glue the multiple patches,while the traditional IGA,which is very suitable for solving partial differential equations(PDEs)on(3D)surfaces,is employed within each patch.Our method takes advantage of both IGA and the DG method.Firstly,the time-consuming steps in mesh generation process in traditional finite element analysis(FEA)are no longer necessary and refinements,including h-refinement and p-refinement which both maintain the original geometry,can be easily performed by knot insertion and order-elevation(Farin,in Curves and surfaces for CAGD,2002).Secondly,our method can easily handle the cases with non-conforming patches and different degrees across the patches.Moreover,due to the geometric flexibility of IGA basis functions,especially the use of multiple patches,we can get more accurate modeling of more complex surfaces.Thus,the geometrical error is significantly reduced and it is,in particular,eliminated for all conic sections.Finally,this method can be easily formulated and implemented.We generally describe the problem and then present our primal formulation.A new ideology,which directly makes use of the approximation property of the NURBS basis functions on the parametric domain rather than that of the IGA functions on the physical domain(the former is easier to get),is adopted when we perform the theoretical analysis including the boundedness and stability of the primal form,and the error analysis under both the DG norm and the L2 norm.The result of the error analysis shows that our scheme achieves the optimal convergence rate with respect to both the DG norm and the L2 norm.Numerical examples are presented to verify the theoretical result and gauge the good performance of our method.展开更多
Exact doubly periodic standing wave patterns of the Davey-Stewartson （DS） equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly n...Exact doubly periodic standing wave patterns of the Davey-Stewartson （DS） equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli （periods） are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered.展开更多
In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obt...In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.展开更多
We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We s...We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse.展开更多
基金National Natural Science Foundation of China under Grant No.10674177
文摘Based on the scaling idea of local slopes by Lopez et al. [Phys. Rev. Lett. 94 （2005） 166103], we investigate anomalous dynamic scaling of （d ＋ 1）-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang （KPZ）, Sun-Guo-Grant （SGG）, and Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.
基金Supported by the Natural Science Foundation of the Inner Mongolia Autonomous Region
文摘Some exact travelling wave solutions and rational travelling wave solutions of a surface wave equation in a convecting fluid are given in this paper.
基金Supported by the National Natural Science Foundation of China under Grants Nos 11047020,11404157,11274166,11275097,11475085 and 11535005the Natural Science Foundation of Shangdong Province under Grants Nos ZR2012AM022 and ZR2011AM019
文摘We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.
文摘This review article commences with a comprehensive historical review of the evolution and application of various density surfaces in atmospheric and oceanic studies. The background provides a basis for the birth of the neutral density idea. Attention is paid to the development of the neutral density surface concept from the nonlinearity of the equation of state of seawater. The definition and properties of neutral density surface are described in detail as developed from the equations of state of seawater and the buoyancy frequency when the squared buoyancy frequency N2 is zero, a neutral state of stability. In order to apply the neutral density surface to intermediate water-mass analysis, this review also describes in detail its practical oceanographic application. The mapping technique is focused for the first time on applying regularly gridded data in this review. It is reviewed how a backbone and ribs framework was designed to flesh out from a reference cast and first mapped the global neutral surfaces in the world’s oceans. Several mapped neutral density surfaces are presented as examples for each world ocean. The water-mass property is analyzed in each ocean at mid-depth. The characteristics of neutral density surfaces are compared with those of potential density surfaces.
基金supported partially by the US NSF CAREER award program (ECCS-0645086)National Natural Science Foundation of China (No.F030119)+2 种基金Zhejiang Provincial Natural Science Foundation of China (Nos.Y1110354, Y6110751)the Fundamental Research Funds for the Central Universities of China (No.1A5000-172210101)the Natural Science Foundation of Ningbo (No.2010A610096)
文摘The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.
基金supported by the National Key Research and Development Program of China[grant number 2018YFC1505706]the National Natural Science Foundation of China[grant numbers 91937302,91737306,41975109]the Strategic Priority Research Program of the Chinese Academy of Sciences[grant number XDA17010105]。
文摘The Chinese Academy of Sciences Flexible Global Ocean-Atmosphere-Land System atmospheric component model(FGOALS-f3-L)participated in Phase 6 of the Coupled Model Intercomparison Project,but its reproducibility of surface temperature(T_(s))over the Tibetan Plateau(TP)as a key climatically sensitive region remains unclear.This study evaluates the capability of FGOALS-f3-L in reproducing the climatological T_(s)over the TP relative to the Climate Forecast System Reanalysis.The results show that FGOALS-f3-L can reasonably capture the spatial pattern of T_(s)but underestimates the annual mean T_(s)for the whole TP.The simulated T_(s)for the whole TP shows a cold bias in winter and spring and a warm bias in summer and autumn.Further quantitative analysis based on the surface energy budget equation shows that the surface albedo feedback(SAF)term strongly contributes to the annual,winter,and spring mean cold bias in the western TP and to the warm bias in the eastern TP.Compared with the SAF term,the surface sensible and latent heat flux terms make nearly opposite contributions to the T_(s)bias and considerably offset the bias due to the SAF term.The cloud radiative forcing term strongly contributes to the annual and seasonal mean weak cold bias in the eastern TP.The longwave radiation term associated with the overestimated water vapor content accounts for a large portion of the warm bias over the whole TP in summer and autumn.Improving land surface and cloud processes in FGOALS-f3-L is critical to reduce the T_(s)bias over the TP.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010LKWL04)the Youth Foundation of China University of Mining & Technology,China (Grant No. 2008A035)
文摘According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of （1＋ 1）-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy （LMBE） and the nonlinear Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.
基金Supported by the National Key Basic Research Program of China(973 Program)(2012CB720702)(61320601-1)the 111 Project of China(B14010)the National Natural Science Foundation of China(61421001,61371002)
文摘Current surface integral equations used for computing scattering from targets with negative impedance boundary condition（IBC）are not efficient.A modified surface dual integral equation（M-SDIE）for targets with negative IBC is presented.A pure imaginary number is used to balance the formulations.It is proved that the M-SDIE is accurate and efficient with three numerical examples.The first numerical example shows that the M-SDIE is accurate compared with Mie.The second example shows that the presented SIE is efficient.In the third example,a missile head is selected to present the computing power of the M-SDIE.All the examples show that the M-SDIE is an efficient algorithm for negative IBC.
基金supported by National Natural Science Foundation of China (30800100)Science and Technology Offi ce of Guiyang, China (2012204-28)
文摘Body surface area（BSA）was regarded as a more readily quantifiable parameter relative to body mass in the normalization of comparative biochemistry and physiology.The BSA prediction has attracted unceasing research back more than a century on animals,especially on humans and rats.Few studies in this area for anurans were reported,and the equation for body surface area（S）and body mass（W）：S=9.9 W 0.56,which was concluded from toads of four species in 1969,was generally adopted to estimate the body surface areas for anurans until recent years.However,this equation was not applicable to Odorrana grahami.The relationship between body surface area and body mass for this species was established as：S=15.4 W 0.579.Our current results suggest estimation equations should be used cautiously across different species and body surface area predictions on more species need to be conducted.
基金Project supported by the National Natural Science Foundation of China(Grant No.51025622)
文摘To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.
基金Partially Supported by a DST Research Project to RG(No.SR/FTP/MS-020/2010)
文摘A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.
基金Technological Innovation of Science-Technology Oriented Small to Medium Enterprises,China(No.12C2621440522)Guangdong Province's Transportation Ministry Planning Program of Science and Technology,China(No.201202088)
文摘Aiming at improving the mechanical vibrating equipment,the axial thrust roller-exciting vibrating tables and its motor-control system based on co-simulation were put forward. First, the structures of vibrating table and its surface equations and boundary conditions were established through reversal process. Second,waveform distortion influenced by random and harmonic waves was analyzed by equivalent parametric transition. These two steps were both technological challenge and contribution for the vibrating table.Finally, based on research above, a proportion integration differentiation( PID) motor-control system was built to show its rapid operation and convenient control. All the results show that not only does vibrating table have lower waveform distortion than traditional ones,but its control system narrows down the fluctuation and improves anti-interference performance. Hence,it provides a more extensive selection for efficient and practical mechanical vibrating table.
文摘The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute
基金the National Natural Science Foundation of China (60431010, 60601008)New Century 0Excellent Talent Support Plan of China (NCET-05-0805)+3 种基金the International Joint Research Project(607048)in part by the "973" Programs(61360, 2008CB317110)Research Founding (9110A03010708DZ0235)Young Doctor Discipline Platform of UESTC
文摘This paper introduces the research work on the extension of multilevel fast multipole algorithm （MLFMA） to 3D complex structures including coating object, thin dielectric sheet, composite dielectric and conductor, cavity. The impedance boundary condition is used for scattering from the object coated by thin lossy material. Instead of volume integral equation, surface integral equation is applied in case of thin dielectric sheet through resistive sheet boundary condition. To realize the fast computation of scattering from composite homogeneous dielectric and conductor, the surface integral equation based on equivalence principle is used. Compared with the traditional volume integral equation, the surface integral equation reduces greatly the number of unknowns. To computc conducting cavity with electrically large aperture, an electric field integral equation is applied. Some numerical results are given to demonstrate the validity and accuracy of the present methods.
文摘In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
基金Supported by the National Natural Science Foundation of China(60901005)
文摘Based on the combined tangential formulation of surface integral equation, a fast algo- rithm is presented for calculating electromagnetic scattering from electrically large 3D homogeneous objects. In the algorithm, the lower triangular approximate Schur preconditioner is combined with the multilevel fast multipole algorithm （MLFMA）. The coefficient matrix of the near-field coupling element is selected to set up the approximate matrix. For large problems, the incomplete LU factori- zation with dual threshold （ILUT） has better performance than sparse approximate inverse （SAI） of accelerating the convergence of the generalized minimal residual method （ GMRES ） iteration. Nu- merical experiments validate the efficiency and robustness of the presented fast algorithm for homo- geneous dielectric objects.
基金Yan Xu:Research supported by NSFC grant No.11371342,No.11031007Fok Ying Tung Education Foundation No.131003+1 种基金Falai Chen:Research supported by NSFC grant No.11031007the National Basic Research Program of China(2011CB302400).
文摘We propose a method that combines isogeometric analysis(IGA)with the discontinuous Galerkin(DG)method for solving elliptic equations on 3-dimensional(3D)surfaces consisting of multiple patches.DG ideology is adopted across the patch interfaces to glue the multiple patches,while the traditional IGA,which is very suitable for solving partial differential equations(PDEs)on(3D)surfaces,is employed within each patch.Our method takes advantage of both IGA and the DG method.Firstly,the time-consuming steps in mesh generation process in traditional finite element analysis(FEA)are no longer necessary and refinements,including h-refinement and p-refinement which both maintain the original geometry,can be easily performed by knot insertion and order-elevation(Farin,in Curves and surfaces for CAGD,2002).Secondly,our method can easily handle the cases with non-conforming patches and different degrees across the patches.Moreover,due to the geometric flexibility of IGA basis functions,especially the use of multiple patches,we can get more accurate modeling of more complex surfaces.Thus,the geometrical error is significantly reduced and it is,in particular,eliminated for all conic sections.Finally,this method can be easily formulated and implemented.We generally describe the problem and then present our primal formulation.A new ideology,which directly makes use of the approximation property of the NURBS basis functions on the parametric domain rather than that of the IGA functions on the physical domain(the former is easier to get),is adopted when we perform the theoretical analysis including the boundedness and stability of the primal form,and the error analysis under both the DG norm and the L2 norm.The result of the error analysis shows that our scheme achieves the optimal convergence rate with respect to both the DG norm and the L2 norm.Numerical examples are presented to verify the theoretical result and gauge the good performance of our method.
基金support of the Hong Kong Research Grants Council through contracts 711807E and 712008E
文摘Exact doubly periodic standing wave patterns of the Davey-Stewartson （DS） equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli （periods） are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered.
基金jointly supported by the National Nature Science Foundation of China(Grants No.11774157,No.11934008,No.12075117,No.51721001,No.11890702,No.11625418,No.11535005,No.11690030)funded by the Natural Science Foundation of Shandong Province of China(Grant No.ZR2020MA091)。
文摘In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.
基金The first author is supported by the National Natural Science Foundation of China(Grant Nos.11571347,11688101)the Youth Innovation Promotion Association,CAS(Grant No.2017003)。
文摘We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse.
