We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The p...A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10^(-5),spectral efficiency can be raised by roughly 12.4%.展开更多
Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau...Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma （Langmuir） waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized （r, q） distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.展开更多
New renewable energy exploitation technologies in offshore structures are vital for future energy production systems.Offshore hybrid wind-wave power generation(HWWPG)systems face increased component failure rates beca...New renewable energy exploitation technologies in offshore structures are vital for future energy production systems.Offshore hybrid wind-wave power generation(HWWPG)systems face increased component failure rates because of harsh weather,significantly affecting the maintenance procedures and reliability.Different types of failure rates of the wind turbine(WT)and wave energy converter(WEC),e.g.,the degradation and failure rates during regular wind speed fluctuation,the degradation and failure rates during intense wind speed fluctuation are considered.By incorporating both WT and WEC,the HWWPG system is designed to enhance the overall amount of electrical energy produced by the system over a given period under varying weather conditions.The universal generating function technique is used to calculate the HWWPG system dependability measures in a structured and efficient manner.This research highlights that intense weather conditions increase the failure rates of both WT and WEC,resulting in higher maintenance costs and more frequent downtimes,thus impacting the HWWPG system’s reliability.Although the HWWPG system can meet the energy demands in the presence of high failure rates,the reliance of the hybrid system on both WT and WEC helps maintain a relatively stable demand satisfaction during periods of high energy demand despite adverse weather conditions.To confirm the added value and applicability of the developed model,a case study of an offshore hybrid platform is conducted.The findings underscore the system’s robustness in maintaining energy production under varied weather conditions,though higher failure rates and maintenance costs arise in intense scenarios.展开更多
In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized...In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.展开更多
The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained...The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.展开更多
The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperaturedependen...The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperaturedependent functionally graded anisotropic(FGA)structures.The system of governing equations of the considered problem is extremely very difficult or impossible to solve analytically due to nonlinearity,fractional order diffusion and strongly anisotropic mechanical and physical properties of considered porous structures.Therefore,an efficient boundary element method(BEM)has been proposed to overcome this difficulty,where,the nonlinear terms were treated using the Kirchhoff transformation and the domain integrals were treated using the Cartesian transformation method(CTM).The generalized modified shift-splitting(GMSS)iteration method was used to solve the linear systems resulting from BEM,also,GMSS reduces the iterations number and CPU execution time of computations.The numerical findings show the effects of fractional order parameter,anisotropy and functionally graded material on the nonlinear porothermoelastic stress waves.The numerical outcomes are in very good agreement with those from existing literature and demonstrate the validity and reliability of the proposed methodology.展开更多
The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-g...The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.展开更多
The normal and abnormal cylindrical vector wave functions are constructed. Some impor-tant conversion relations in circular, elliptic and parabolic cylindrical coordinate systems are discussedin detail, where the resu...The normal and abnormal cylindrical vector wave functions are constructed. Some impor-tant conversion relations in circular, elliptic and parabolic cylindrical coordinate systems are discussedin detail, where the result in circular cylindrical coordinate system is the same as the one given bythe author (1984).展开更多
In this paper. a new kind of generalized BBM equation is introduced and discussed Some existence theorems of periodic traveling wave solutions for this kind generalized BBM equation are given.
The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the ...The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described.展开更多
A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. T...A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation （nonlinear convection- diffusion problem） and KdV equation（single solitary and 2-solitary wave problems）, where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.展开更多
The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensio...The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.展开更多
In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tio...In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.展开更多
This paper presents a closed-loop vector control structure based on adaptive Fuzzy Logic Sliding Mode Controller (FL-SMC) for a grid-connected Wave Energy Conversion System (WECS) driven Self-Excited Induction Generat...This paper presents a closed-loop vector control structure based on adaptive Fuzzy Logic Sliding Mode Controller (FL-SMC) for a grid-connected Wave Energy Conversion System (WECS) driven Self-Excited Induction Generator (SEIG). The aim of the developed control method is to automatically tune and optimize the scaling factors and the membership functions of the Fuzzy Logic Controllers (FLC) using Multi-Objective Genetic Algorithms (MOGA) and Multi-Objective Particle Swarm Optimization (MOPSO). Two Pulse Width Modulated voltage source PWM converters with a carrier-based Sinusoidal PWM modulation for both Generator- and Grid-side converters have been connected back to back between the generator terminals and utility grid via common DC link. The indirect vector control scheme is implemented to maintain balance between generated power and power supplied to the grid and maintain the terminal voltage of the generator and the DC bus voltage constant for variable rotor speed and load. Simulation study has been carried out using the MATLAB/Simulink environment to verify the robustness of the power electronics converters and the effectiveness of proposed control method under steady state and transient conditions and also machine parameters mismatches. The proposed control scheme has improved the voltage regulation and the transient performance of the wave energy scheme over a wide range of operating conditions.展开更多
Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigen...Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.展开更多
An inversion method was applied to crustal earthquakes dataset to find S-wave attenuation characteristics beneath the Eastern Tohoku region of Japan. Accelerograms from 85 shallow crustal earthquakes up to 25 km depth...An inversion method was applied to crustal earthquakes dataset to find S-wave attenuation characteristics beneath the Eastern Tohoku region of Japan. Accelerograms from 85 shallow crustal earthquakes up to 25 km depth and magnitude range between 3.5 and 5.5 were analyzed to estimate the seismic quality factor Qs. A homogeneous attenuation model Qs for the wave propagation path was evaluated from spectral amplitudes, at 24 different frequencies between 0.5 and 20 Hz by using generalized inversion technique. To do this, non-parametric attenuation functions were calculated to observe spectral amplitude decay with hypocentral distance. Then, these functions were parameterized to estimate Qs. It was found that in Eastern Tohoku region, the Qs frequency dependence can be approximated with the function 33 f 1.22 within a frequency range between 0.5 and 20 Hz. However, the frequency dependence of Qs in the frequency range between 0.5 and 6 Hz is best approximated by Qs （f） = 36 f 0.94 showing relatively weaker frequency dependence as compared to the relation Qs （f） = 6 f^ 2.09 for the frequency range between 6 and 15 Hz. These results could be used to estimate source and site parameters for seismic hazard assessment in the region.展开更多
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurati...Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.展开更多
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
基金supported by the China National Postdoctoral Program for Innovative Talents(BX20200039)the Special Fund Project of“Mount Taishan Scholars”Construction Project in Shandong Province(ts20081130).
文摘A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10^(-5),spectral efficiency can be raised by roughly 12.4%.
基金The project supported by National Natural Science Foundation of China under Grant No. 40390150 and the International Collaboration Research Team Program of the Chinese Academy of Sciences
文摘Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma （Langmuir） waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized （r, q） distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.
文摘New renewable energy exploitation technologies in offshore structures are vital for future energy production systems.Offshore hybrid wind-wave power generation(HWWPG)systems face increased component failure rates because of harsh weather,significantly affecting the maintenance procedures and reliability.Different types of failure rates of the wind turbine(WT)and wave energy converter(WEC),e.g.,the degradation and failure rates during regular wind speed fluctuation,the degradation and failure rates during intense wind speed fluctuation are considered.By incorporating both WT and WEC,the HWWPG system is designed to enhance the overall amount of electrical energy produced by the system over a given period under varying weather conditions.The universal generating function technique is used to calculate the HWWPG system dependability measures in a structured and efficient manner.This research highlights that intense weather conditions increase the failure rates of both WT and WEC,resulting in higher maintenance costs and more frequent downtimes,thus impacting the HWWPG system’s reliability.Although the HWWPG system can meet the energy demands in the presence of high failure rates,the reliance of the hybrid system on both WT and WEC helps maintain a relatively stable demand satisfaction during periods of high energy demand despite adverse weather conditions.To confirm the added value and applicability of the developed model,a case study of an offshore hybrid platform is conducted.The findings underscore the system’s robustness in maintaining energy production under varied weather conditions,though higher failure rates and maintenance costs arise in intense scenarios.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013QNA41Natural Sciences Foundation of China under Grant Nos.11301527 and 11371361the Construction Project of the Key Discipline in Universities for 12th Five-year Plans by Jiangsu Province
文摘In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.
文摘The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.
文摘The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperaturedependent functionally graded anisotropic(FGA)structures.The system of governing equations of the considered problem is extremely very difficult or impossible to solve analytically due to nonlinearity,fractional order diffusion and strongly anisotropic mechanical and physical properties of considered porous structures.Therefore,an efficient boundary element method(BEM)has been proposed to overcome this difficulty,where,the nonlinear terms were treated using the Kirchhoff transformation and the domain integrals were treated using the Cartesian transformation method(CTM).The generalized modified shift-splitting(GMSS)iteration method was used to solve the linear systems resulting from BEM,also,GMSS reduces the iterations number and CPU execution time of computations.The numerical findings show the effects of fractional order parameter,anisotropy and functionally graded material on the nonlinear porothermoelastic stress waves.The numerical outcomes are in very good agreement with those from existing literature and demonstrate the validity and reliability of the proposed methodology.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61302007 and 60977065)the Fundamental Research Funds for the Central Universities of China(Grant No.FRF-SD-12-016A)the Engineering Research Center of Industrial Spectrum Imaging of Beijing,China
文摘The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.
文摘The normal and abnormal cylindrical vector wave functions are constructed. Some impor-tant conversion relations in circular, elliptic and parabolic cylindrical coordinate systems are discussedin detail, where the result in circular cylindrical coordinate system is the same as the one given bythe author (1984).
文摘In this paper. a new kind of generalized BBM equation is introduced and discussed Some existence theorems of periodic traveling wave solutions for this kind generalized BBM equation are given.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975143)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2018MA017)+1 种基金the Taishan Scholars Program of Shandong Province,China(Grant No.ts20190936)the Shandong University of Science and Technology Research Fund(Grant No.2015TDJH102).
文摘The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described.
基金Project supported by the National Natural Science Foundation of China (No.10272118) the Hong Kong Polytechnic University Research Grant (No.A-PE28) the Research Fund for the Doctoral Program of Ministry of Education of China (No.20020558013)
文摘A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation （nonlinear convection- diffusion problem） and KdV equation（single solitary and 2-solitary wave problems）, where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.
文摘The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.
基金supported by the National Natural Science Foundation of China (11002115,10972182,11172239)the Science Foundation of Aviation of China (2010ZB53021)+5 种基金the China Postdoctoral Science Special Foundation (201003682)111 project(B07050) to the Northwestern Polytechnical Universitythe NPU Foundation for Fundamental Research (JC200938,JC20110259)the Doctoral Program Foundation of Education Ministry of China(20106102110019)the Open Foundation of State Key Laboratory of Mechanical System & Vibration (MSV-2011-21)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (GZ0802)
文摘In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.
文摘This paper presents a closed-loop vector control structure based on adaptive Fuzzy Logic Sliding Mode Controller (FL-SMC) for a grid-connected Wave Energy Conversion System (WECS) driven Self-Excited Induction Generator (SEIG). The aim of the developed control method is to automatically tune and optimize the scaling factors and the membership functions of the Fuzzy Logic Controllers (FLC) using Multi-Objective Genetic Algorithms (MOGA) and Multi-Objective Particle Swarm Optimization (MOPSO). Two Pulse Width Modulated voltage source PWM converters with a carrier-based Sinusoidal PWM modulation for both Generator- and Grid-side converters have been connected back to back between the generator terminals and utility grid via common DC link. The indirect vector control scheme is implemented to maintain balance between generated power and power supplied to the grid and maintain the terminal voltage of the generator and the DC bus voltage constant for variable rotor speed and load. Simulation study has been carried out using the MATLAB/Simulink environment to verify the robustness of the power electronics converters and the effectiveness of proposed control method under steady state and transient conditions and also machine parameters mismatches. The proposed control scheme has improved the voltage regulation and the transient performance of the wave energy scheme over a wide range of operating conditions.
文摘Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.
基金a part of author’s M.Sc Research under the project:‘‘Strengthening of Earthquake Engineering Center’’,funded by Higher Education Commission,Government of Pakistan
文摘An inversion method was applied to crustal earthquakes dataset to find S-wave attenuation characteristics beneath the Eastern Tohoku region of Japan. Accelerograms from 85 shallow crustal earthquakes up to 25 km depth and magnitude range between 3.5 and 5.5 were analyzed to estimate the seismic quality factor Qs. A homogeneous attenuation model Qs for the wave propagation path was evaluated from spectral amplitudes, at 24 different frequencies between 0.5 and 20 Hz by using generalized inversion technique. To do this, non-parametric attenuation functions were calculated to observe spectral amplitude decay with hypocentral distance. Then, these functions were parameterized to estimate Qs. It was found that in Eastern Tohoku region, the Qs frequency dependence can be approximated with the function 33 f 1.22 within a frequency range between 0.5 and 20 Hz. However, the frequency dependence of Qs in the frequency range between 0.5 and 6 Hz is best approximated by Qs （f） = 36 f 0.94 showing relatively weaker frequency dependence as compared to the relation Qs （f） = 6 f^ 2.09 for the frequency range between 6 and 15 Hz. These results could be used to estimate source and site parameters for seismic hazard assessment in the region.
文摘Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.
