With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for c...In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.展开更多
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where ...In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.展开更多
We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schr¨odinger equation,the Feinberg–Horodecki equation,with a combined Kratzer p...We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schr¨odinger equation,the Feinberg–Horodecki equation,with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials.The present work is illustrated with two special cases of the general form:the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.展开更多
We develop a numerical scheme for solving the one-dimensional(1D)time-dependent Schrödinger equation(TDSE),and use it to study the strong-field photoionization of the atomic hydrogen.The photoelectron energy spec...We develop a numerical scheme for solving the one-dimensional(1D)time-dependent Schrödinger equation(TDSE),and use it to study the strong-field photoionization of the atomic hydrogen.The photoelectron energy spectra obtained for pulses ranging from XUV to near infrared are compared in detail to the spectra calculated with our well-developed code for accurately solving the three-dimensional(3D)TDSE.For XUV pulses,our discussions cover intensities at which the ionization is in the perturbative and nonperturbative regimes.For pulses of 400 nm or longer wavelengths,we distinguish the multiphoton and tunneling regimes.Similarities and discrepancies between the 1D and 3D calculations in each regime are discussed.The observed discrepancies mainly originate from the differences in the transition matrix elements and the energy level structures created in the 1D and 3D calculations.展开更多
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdin...In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.展开更多
A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Enler predietor-corrector method and the three-point finite-di...A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Enler predietor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones, respectively, thus leading both the time and spatial derivatives to the second-order accuracy. The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift. Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach, respectively, and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor. From comparison of numerical results with theoretical or experimental ones, it is found that they are in reasonable agreement.展开更多
In engineering practice, tubular X-joints have been widely used in offshore structures. The fatigue failure of tubular X-joints in offshore engineering is mainly caused by axial tensile stress. In this study, the stre...In engineering practice, tubular X-joints have been widely used in offshore structures. The fatigue failure of tubular X-joints in offshore engineering is mainly caused by axial tensile stress. In this study, the stress concentration factor distribution along the weld toe in the hot spot stress region for tubular X-joints subject to axial loads have been analyzed by use of finite element method. Through numerical analysis, it has been found that the peak stress concentration factor is located at the saddle position. Thereafter, 80 models have been analyzed, and the effect of the geometric parameters of a tubular X-joint on the stress concentration factor has been investigated. Based on the experimental values of the numerical stress concentration factor, a parametric equation to calculate the stress concentration factor of tubular X-joints has been proposed. The accuracy of this equation has been verified against the requirement of the Fatigue Guidance Review Panel, and the proposed equation is found capable of producing reasonably accurate stress concentration factor values for tubular X-joints subject to axial loads.展开更多
Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm eff...Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect （AB） and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ（r - R）. Consequently, the problem becomes more complicated. In order to avoid this dimculty, we replace the radius R by ρ（t）R, where ρ（t） is a positive time-dependent function. Then at the end of calculations we take the limit R →0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by p（t）, i.e., C 〉 0, C = 0, and C 〈0. Following the C＇s values the spectrum of quantum states is discrete （C 〉 0） or continuous （C ≤ 0）.展开更多
In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,...In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.展开更多
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretizatio...A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.展开更多
We obtain an approximate value of the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, together with the space-like coherent eigenvectors for the space-like counterpart of the Schr<sp...We obtain an approximate value of the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, together with the space-like coherent eigenvectors for the space-like counterpart of the Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.展开更多
Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth ...Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.展开更多
The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation ot concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentrati...The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation ot concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.展开更多
For two common types of liquid-solid heterogeneous reactions,the kinetic equations have been established which involved both the variation of liquid reactant concentration and the va- riation of solid reactant geornet...For two common types of liquid-solid heterogeneous reactions,the kinetic equations have been established which involved both the variation of liquid reactant concentration and the va- riation of solid reactant geornetry with the reaction time.The experimental results show that the kinetic equations are more accurate and reasonable than those appeared in previous litera- tures.Moreover,they are also suitable for gas-solid heterogeneous reactions in principle.展开更多
On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion tha...On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.展开更多
We study space-time transformations of the time-dependent Schrodingerequation (TDSE) with time- and position-dependent (effective) mass. We obtain the most generalspace-time transformation that maps such a TDSE onto a...We study space-time transformations of the time-dependent Schrodingerequation (TDSE) with time- and position-dependent (effective) mass. We obtain the most generalspace-time transformation that maps such a TDSE onto another one of its kind. The transformedpotential is given in explicit form.展开更多
In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle(GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potenti...In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle(GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In(1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials.展开更多
We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schr?dinger equation(TDSE) in spherical coordinates. This method is realized by com...We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schr?dinger equation(TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula(RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos(SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation(HHG) in these interaction systems.展开更多
A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-n...A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.展开更多
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金Project supported by National Natural Science Foundation of China and China State Key project for Basic Researchcs.
文摘In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.
基金supported by Natural Science Foundation of China(11371159 and 11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT_17R46
文摘In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
文摘We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schr¨odinger equation,the Feinberg–Horodecki equation,with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials.The present work is illustrated with two special cases of the general form:the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
基金Project supported by the National Natural Science Foundation of China(Gant Nos.12074265,11804233,and 11575118)the National Key Research and Development Project of China(Grant No.2017YFF0106500)+1 种基金the Natural Science Foundation of Guangdong,China(Grant Nos.2018A0303130311 and 2021A1515010082)the Shenzhen Fundamental Research Program(Grant Nos.KQJSCX20180328093801773,JCYJ20180305124540632,and JCYJ20190808121405740).
文摘We develop a numerical scheme for solving the one-dimensional(1D)time-dependent Schrödinger equation(TDSE),and use it to study the strong-field photoionization of the atomic hydrogen.The photoelectron energy spectra obtained for pulses ranging from XUV to near infrared are compared in detail to the spectra calculated with our well-developed code for accurately solving the three-dimensional(3D)TDSE.For XUV pulses,our discussions cover intensities at which the ionization is in the perturbative and nonperturbative regimes.For pulses of 400 nm or longer wavelengths,we distinguish the multiphoton and tunneling regimes.Similarities and discrepancies between the 1D and 3D calculations in each regime are discussed.The observed discrepancies mainly originate from the differences in the transition matrix elements and the energy level structures created in the 1D and 3D calculations.
基金supported by National Science Foundation of China (11071177)
文摘In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.
基金This work wasjointlysupported by the National Natural Science Foundation of China(Grant No.40106008) the National Natural Science Fundfor Distinguished Young Scholars(Grant No.40225014)
文摘A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Enler predietor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones, respectively, thus leading both the time and spatial derivatives to the second-order accuracy. The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift. Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach, respectively, and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor. From comparison of numerical results with theoretical or experimental ones, it is found that they are in reasonable agreement.
基金The research work was financially supported by the National Natural Scientice Foundation of China(Grant No.10142001)by the Shandong Provincial Natural Scientice Foundation(Grant No.Y2006F46)
文摘In engineering practice, tubular X-joints have been widely used in offshore structures. The fatigue failure of tubular X-joints in offshore engineering is mainly caused by axial tensile stress. In this study, the stress concentration factor distribution along the weld toe in the hot spot stress region for tubular X-joints subject to axial loads have been analyzed by use of finite element method. Through numerical analysis, it has been found that the peak stress concentration factor is located at the saddle position. Thereafter, 80 models have been analyzed, and the effect of the geometric parameters of a tubular X-joint on the stress concentration factor has been investigated. Based on the experimental values of the numerical stress concentration factor, a parametric equation to calculate the stress concentration factor of tubular X-joints has been proposed. The accuracy of this equation has been verified against the requirement of the Fatigue Guidance Review Panel, and the proposed equation is found capable of producing reasonably accurate stress concentration factor values for tubular X-joints subject to axial loads.
文摘Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect （AB） and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ（r - R）. Consequently, the problem becomes more complicated. In order to avoid this dimculty, we replace the radius R by ρ（t）R, where ρ（t） is a positive time-dependent function. Then at the end of calculations we take the limit R →0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by p（t）, i.e., C 〉 0, C = 0, and C 〈0. Following the C＇s values the spectrum of quantum states is discrete （C 〉 0） or continuous （C ≤ 0）.
基金The NSF(11001103)the SRFDP(200801831002) of China
文摘In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.
基金supported by the National Natural Science Foundation of China(No.10771150)the National Basic Research Program of China(No.2005CB321701)+1 种基金the Program for New Century Excellent Talents in University(No.NCET-07-0584)the Natural Science Foundation of Sichuan Province(No.07ZB087)
文摘A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.
文摘We obtain an approximate value of the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, together with the space-like coherent eigenvectors for the space-like counterpart of the Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.
基金the National Natural Science Foundation of China(Grant Nos.12074265 and 11804233).
文摘Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055)
文摘The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation ot concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.
文摘For two common types of liquid-solid heterogeneous reactions,the kinetic equations have been established which involved both the variation of liquid reactant concentration and the va- riation of solid reactant geornetry with the reaction time.The experimental results show that the kinetic equations are more accurate and reasonable than those appeared in previous litera- tures.Moreover,they are also suitable for gas-solid heterogeneous reactions in principle.
基金supported by the Meteorological Special Project of China(GYHY200806005)the National Natural Sciences Foundation of China(40805028,40675039,40575036)the Key Technologies R&D Program of China(2009BAC51B04)
文摘On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.
文摘We study space-time transformations of the time-dependent Schrodingerequation (TDSE) with time- and position-dependent (effective) mass. We obtain the most generalspace-time transformation that maps such a TDSE onto another one of its kind. The transformedpotential is given in explicit form.
基金Supported by the National Natural Science Foundation of China under Grant No.11565009
文摘In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle(GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In(1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11534004,11627807,11774131,and 11774130)the Scientific and Technological Project of Jilin Provincial Education Department in the Thirteenth Five-Year Plan,China(Grant No.JJKH20170538KJ)
文摘We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schr?dinger equation(TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula(RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos(SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation(HHG) in these interaction systems.
基金the National Natural Science Foundation of China(Grant Nos.11072117 and 61074142)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6110007)+3 种基金the Scientific Research Fund of Zhejiang Provincial Education Department,China(Grant No.Z201119278)the Natural Science Foundation of Ningbo,China(Grant Nos.2012A610152 and 2012A610038)the K.C.Wong Magna Fund in Ningbo University,Chinathe Research Grant Council,Government of the Hong Kong Administrative Region,China(Grant Nos.CityU9041370 and CityU9041499)
文摘A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.
