Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results ...Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.展开更多
In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. W...In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain the bifurcations of phase portraits of the system under different parameters conditions. Through phase portraits, we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compactons, kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions are given. Additionally, we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation, which are summarized as follows: i) We confirm that two types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system. ii) We confirm that two types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center,and the homoclinic orbit of associated system, which is tangent to the singular line at the singular point of associated system.展开更多
This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of pla...This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.展开更多
This paper presents examples of field data of extreme seiche waves measured at Coffs Harbour by MHL and describes the generation and measuring methodology to detect and reduce seiche agitation in the Coifs Harbour boa...This paper presents examples of field data of extreme seiche waves measured at Coffs Harbour by MHL and describes the generation and measuring methodology to detect and reduce seiche agitation in the Coifs Harbour boat ramp using a 3D physical model. The paper also discusses the techniques in investigating a short wave problem of stability in the same model where a long wave is simulated. Waves offshore of Coffs Harbour at 80 m depth have been recorded by MHL for a period of over 30 years. Long waves have been simultaneously measured in the harbour over a period of a decade. These data enabled the model to be verified on two dates （4/6/12, 5/9/14） when high long waves were recorded at the boat ramp harbour under storm and non-storm conditions. Long waves are generated in harbours due to group bounded long wave and surf beat or edge waves. The paper presents methodologies of generating long waves both numerically and by using physical models, and discusses the advantages and disadvantages of these generation techniques. Numerical modelling carried out using long period regular waves in a previous investigation predicted reductions up to 50% due to change of planform of the boat ramp harbour where an area next to the boat ramp was excavated and roughness elements introduced to dampen long periods. The 3D physical model simulated a 25% decrease in the long wave energy in the boat ramp when a suitable change in the planform was made. A 3D undistorted model of scale 1：58 was used in the investigation.展开更多
On the basis of the new type Boussinesq equations （Madsen et al., 2002）, a set of equations explicitly including the effects of currents on waves are derived. A numerical implementation of the present equations in o...On the basis of the new type Boussinesq equations （Madsen et al., 2002）, a set of equations explicitly including the effects of currents on waves are derived. A numerical implementation of the present equations in one dimension is described. The numerical model is tested for wave propagation in a wave flume of uniform depth with current present. The present numerical results are compared with those of other researchers. It is validated that the present numerical model can reasonably reflect the nonlinear influences of currents on waves. Moreover, the effects of inputting different incident boundary conditions on the calculated results are studied.展开更多
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation t...We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number <em>l</em> and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.展开更多
We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the c...We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the constrained optimization together which can inverse the slowness effectively. One advantage of slowness inversion is that there is no further approximation in the gradient derivation. Moreover, a new algorithm named the skip method for solving the constrained optimization problem is proposed. The TV regularization has good ability to inverse slowness at its discontinuities while the constrained optimization can keep the inversion converging in the right direction. Numerical computations both for noise free data and noisy data show the robustness and effectiveness of our method and good inversion results are yielded.展开更多
An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has bee...An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schrödinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.展开更多
随着柔性直流电网的发展,其边界结构将发生改变,从“有边界电网”转变为“无边界电网”。如果在配置保护时,能够在原理上尽量适用于两种边界结构,则可以大大降低电网结构变化时保护验证的繁复性、提升保护应用的经济性。为提升线路行波...随着柔性直流电网的发展,其边界结构将发生改变,从“有边界电网”转变为“无边界电网”。如果在配置保护时,能够在原理上尽量适用于两种边界结构,则可以大大降低电网结构变化时保护验证的繁复性、提升保护应用的经济性。为提升线路行波保护对不同边界结构的适用性,该文提出一种新型的行波保护方案。该保护方案主要通过非故障极电流首行波积分(first current integration of non-fault pole,FCINP)实现。基于FCINP在不同边界结构电网下的距离特性和边界特性,可有效地提升保护在有边界电网和无边界电网下的故障识别性能,从而提升保护适用性。所提保护在基于PSCAD/EMTDC直流电网仿真模型中进行了性能验证。展开更多
The capacity to predict X-ray transition and K-edge energies in dense finite-temperatur plasmas with high precision is of primary importance for atomic physics of matter under extreme conditions.The dual characteristi...The capacity to predict X-ray transition and K-edge energies in dense finite-temperatur plasmas with high precision is of primary importance for atomic physics of matter under extreme conditions.The dual characteristics of bound and continuum states in dense matter are modeled by a valence-band-like structure in a generalized ion-sphere approach with states that are either bound,free,or mixed.The self-consistent combination of this model with the Dirac wave equations of multielectron bound states allows one to fully respect the Pauli principle and to take into account the exact nonlocal exchange terms.The generalized method allows very high precision without implication of calibration shifts and scaling parameters and therefore has predictive power.This leads to new insights in the analysis of various data.The simple ionization model representing the K-edge is generalized to excitation–ionization phenomena resulting in an advanced interpretation of ionization depression data in near-solid-density plasmas.The model predicts scaling relations along the isoelectronic sequences and the existence of bound M-states that are in excellent agreement with experimental data,whereas other methods have failed.The application to unexplained data from compound materials also gives good agreement without the need to invoke any additional assumptions in the generalized model,whereas other methods have lacked consistency.展开更多
基金The National Major Research High Performance Computing Program of China under contract 2016YFB0200800the Strategic Priority Research Program of Chinese Academy of Sciences under contract No.XDA20060501
文摘Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.
基金Supported by the National Natural Science Foundation of China under Grant No.11701191Program for Innovative Research Team in Science and Technology in Fujian Province UniversityQuanzhou High-Level Talents Support Plan under Grant No.2017ZT012
文摘In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain the bifurcations of phase portraits of the system under different parameters conditions. Through phase portraits, we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compactons, kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions are given. Additionally, we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation, which are summarized as follows: i) We confirm that two types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system. ii) We confirm that two types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center,and the homoclinic orbit of associated system, which is tangent to the singular line at the singular point of associated system.
基金Project supported by the National Natural Science Foundation of China(No.11071164)the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ118)+1 种基金the Shanghai Leading Academic Discipline Project(No.XTKX2012)the Innovation Fund Project for Graduate Stu-dent of Shanghai(No.JWCXSL1201)
文摘This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
文摘This paper presents examples of field data of extreme seiche waves measured at Coffs Harbour by MHL and describes the generation and measuring methodology to detect and reduce seiche agitation in the Coifs Harbour boat ramp using a 3D physical model. The paper also discusses the techniques in investigating a short wave problem of stability in the same model where a long wave is simulated. Waves offshore of Coffs Harbour at 80 m depth have been recorded by MHL for a period of over 30 years. Long waves have been simultaneously measured in the harbour over a period of a decade. These data enabled the model to be verified on two dates （4/6/12, 5/9/14） when high long waves were recorded at the boat ramp harbour under storm and non-storm conditions. Long waves are generated in harbours due to group bounded long wave and surf beat or edge waves. The paper presents methodologies of generating long waves both numerically and by using physical models, and discusses the advantages and disadvantages of these generation techniques. Numerical modelling carried out using long period regular waves in a previous investigation predicted reductions up to 50% due to change of planform of the boat ramp harbour where an area next to the boat ramp was excavated and roughness elements introduced to dampen long periods. The 3D physical model simulated a 25% decrease in the long wave energy in the boat ramp when a suitable change in the planform was made. A 3D undistorted model of scale 1：58 was used in the investigation.
基金supported by the National Natural Science Foundation of China (Grant No.40676053)theNational High Technology Research and Development Program of China (863 Program,Grant No.2006AA09A107)the Science and Technology Committee of Shanghai (Grant Nos.08DZ1203005 and 07DZ22027)
文摘On the basis of the new type Boussinesq equations （Madsen et al., 2002）, a set of equations explicitly including the effects of currents on waves are derived. A numerical implementation of the present equations in one dimension is described. The numerical model is tested for wave propagation in a wave flume of uniform depth with current present. The present numerical results are compared with those of other researchers. It is validated that the present numerical model can reasonably reflect the nonlinear influences of currents on waves. Moreover, the effects of inputting different incident boundary conditions on the calculated results are studied.
文摘We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number <em>l</em> and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.
文摘We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the constrained optimization together which can inverse the slowness effectively. One advantage of slowness inversion is that there is no further approximation in the gradient derivation. Moreover, a new algorithm named the skip method for solving the constrained optimization problem is proposed. The TV regularization has good ability to inverse slowness at its discontinuities while the constrained optimization can keep the inversion converging in the right direction. Numerical computations both for noise free data and noisy data show the robustness and effectiveness of our method and good inversion results are yielded.
文摘An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schrödinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.
文摘随着柔性直流电网的发展,其边界结构将发生改变,从“有边界电网”转变为“无边界电网”。如果在配置保护时,能够在原理上尽量适用于两种边界结构,则可以大大降低电网结构变化时保护验证的繁复性、提升保护应用的经济性。为提升线路行波保护对不同边界结构的适用性,该文提出一种新型的行波保护方案。该保护方案主要通过非故障极电流首行波积分(first current integration of non-fault pole,FCINP)实现。基于FCINP在不同边界结构电网下的距离特性和边界特性,可有效地提升保护在有边界电网和无边界电网下的故障识别性能,从而提升保护适用性。所提保护在基于PSCAD/EMTDC直流电网仿真模型中进行了性能验证。
基金supported by the NSFC under Grant Nos.11374315 and 12074395the Invited Scientist Program of CNRS at Ecole Polytechnique,Palaiseau,France。
文摘The capacity to predict X-ray transition and K-edge energies in dense finite-temperatur plasmas with high precision is of primary importance for atomic physics of matter under extreme conditions.The dual characteristics of bound and continuum states in dense matter are modeled by a valence-band-like structure in a generalized ion-sphere approach with states that are either bound,free,or mixed.The self-consistent combination of this model with the Dirac wave equations of multielectron bound states allows one to fully respect the Pauli principle and to take into account the exact nonlocal exchange terms.The generalized method allows very high precision without implication of calibration shifts and scaling parameters and therefore has predictive power.This leads to new insights in the analysis of various data.The simple ionization model representing the K-edge is generalized to excitation–ionization phenomena resulting in an advanced interpretation of ionization depression data in near-solid-density plasmas.The model predicts scaling relations along the isoelectronic sequences and the existence of bound M-states that are in excellent agreement with experimental data,whereas other methods have failed.The application to unexplained data from compound materials also gives good agreement without the need to invoke any additional assumptions in the generalized model,whereas other methods have lacked consistency.
