To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy u...To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy under different conditions are obtained and the flow stress increases with ascending strain rate and descending temperature.For Arrhenius constitutive equation,each material parameter is set as a constant,which will bring forth large error for predicting flow behavior.In this work,material parameters are fitted as a function of temperature or strain rate based on experimental results and a modified constitutive equation is established for more accurate prediction of flow behavior of 7055 aluminium alloy.The effects of temperature and strain rate on power dissipation and instability are analyzed to establish a processing map of 7055 aluminium alloy.The dominant deformation mechanism for microstructure evolution at different deformation conditions can be determined and high efficiency of power dissipation may be achieved from power dissipation map.Meanwhile,proper processing parameters to avoid flow instability can be easily acquired in instability map.According to the processing map,optimized processing parameters of 7055 aluminium alloy are temperature of 673?723 K and strain rate of 0.01?0.4 s^?1,during which its efficiency of power dissipation is over 30%.Finite element method(FEM)is used to obtain optimized parameter in hot rolling process on the basis of processing map.展开更多
采用天然沸石、NaCl改性沸石和氯化十六烷基吡啶(CPC)改性沸石吸附沼液中的氨氮,考察了沸石投加量、沼液pH和吸附时间等因素对沼液中氨氮吸附效果,分析了3种沸石对沼液中氨氮的吸附动力学过程。结果表明,对100 m L沼液,NaCl改性沸石对...采用天然沸石、NaCl改性沸石和氯化十六烷基吡啶(CPC)改性沸石吸附沼液中的氨氮,考察了沸石投加量、沼液pH和吸附时间等因素对沼液中氨氮吸附效果,分析了3种沸石对沼液中氨氮的吸附动力学过程。结果表明,对100 m L沼液,NaCl改性沸石对沼液氨氮的吸附性能大于天然沸石和CPC改性沸石,在投加量为20 g、沼液pH为6~8、吸附时间为120 min时,吸附效果为佳;天然沸石投加量为25 g、沼液pH为8、吸附时间为180 min时效果为佳;而CPC改性沸石一直处于较低的吸附水平,不适用于沼液氨氮的吸附。准1级反应动力学方程模型能较好的描述3种沸石吸附沼液中氨氮的过程。展开更多
为了探索沥青路面常用的AC-20沥青混合料的动态模量规律,采用相同料源的粗集料、细集料和矿粉配制了AC-20级配矿质混合料。以马歇尔试验方法确定的最佳油石比,配制了湖沥青改性沥青、SBS改性沥青以及70#基质沥青等3种沥青混合料。采用...为了探索沥青路面常用的AC-20沥青混合料的动态模量规律,采用相同料源的粗集料、细集料和矿粉配制了AC-20级配矿质混合料。以马歇尔试验方法确定的最佳油石比,配制了湖沥青改性沥青、SBS改性沥青以及70#基质沥青等3种沥青混合料。采用基本性能试验仪的沥青混合料单轴压缩动态模量试验方法进行了动态模量试验,并在此基础上运用时间-温度等效原理,采用NCHRP09-29提供的Mastersolver Version 2.2对阿伦尼乌斯方程中的参数进行拟合,建立了参考温度为20℃的3种沥青混合料动态模量主曲线。研究结果表明,湖沥青改性沥青AC-20和SBS改性沥青AC-20的动态模量主曲线始终位于基质沥青AC-20上方,说明沥青改性剂对混合料性能改善作用显著;湖沥青改性沥青AC-20和SBS改性沥青AC-20的动态模量主曲线存在逼近、交叉现象,说明不同改性沥青混合料性能表现出不同的适用范围。展开更多
An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu&#...An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.展开更多
The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With th...The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.展开更多
In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial condit...In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial conditions to show capability of this method.The goveming equation for motion of a nigid rod on the circular surface without slipping have been solved using MHPM.The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks.Outcomes reveal that MHPM has an excellent agreement with numerical solution.The results show that by decreasing the oscillation amplitude,the velocity of rigid rod decreases and for A=w3 the velocity profile is maximum.展开更多
This paper mainly introduces the parallel physics-informed neural networks(PPINNs)method with regularization strategies to solve the data-driven forward-inverse problems of the variable coefficient modified Korteweg-d...This paper mainly introduces the parallel physics-informed neural networks(PPINNs)method with regularization strategies to solve the data-driven forward-inverse problems of the variable coefficient modified Korteweg-de Vries(VC-MKdV)equation.For the forward problem of the VC-MKdV equation,the authors use the traditional PINN method to obtain satisfactory data-driven soliton solutions and provide a detailed analysis of the impact of network width and depth on solving accuracy and speed.Furthermore,the author finds that the traditional PINN method outperforms the one with locally adaptive activation functions in solving the data-driven forward problems of the VC-MKdV equation.As for the data-driven inverse problem of the VC-MKdV equation,the author introduces a parallel neural networks to separately train the solution function and coefficient function,successfully addressing the function discovery problem of the VC-MKdV equation.To further enhance the network’s generalization ability and noise robustness,the author incorporates two regularization strategies into the PPINNs.An amount of numerical experimental data in this paper demonstrates that the PPINNs method can effectively address the function discovery problem of the VC-MKdV equation,and the inclusion of appropriate regularization strategies in the PPINNs can improves its performance.展开更多
The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling w...The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.展开更多
We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique. A tensor interaction of Coulomb form ...We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique. A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail. The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included.展开更多
In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equati...In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.展开更多
Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is ...Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.展开更多
In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperature...In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series ¶llel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.展开更多
This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this g...This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.展开更多
Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained thro...Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.展开更多
In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are developed.Unlike the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a chang...In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are developed.Unlike the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons.By using the extended auxiliary equation method,we deduced some new soliton solutions of the fourthorder nonlinear modified Degasperis-Procesi equation with constant coefficient.These solutions include symmetrical,non-symmetrical kink solutions,solitary pattern solutions,weiestrass elliptic function solutions and triangular function solutions.We discuss the stability analysis for these solutions.展开更多
For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. I...For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.展开更多
A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified w...A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.展开更多
基金Project(51175257)supported by National Natural Science Foundation of ChinaProject(BK20170785)supported by the Natural Science Foundation of Jiangsu Province,China+1 种基金Project(BE2016179)supported by Science and Technology Planning Project of Jiangsu Province,ChinaProject(Kfkt2017-08)supported by Open Research Fund of State Key Laboratory for High Performance Complex Manufacturing,Central South University,China
文摘To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy under different conditions are obtained and the flow stress increases with ascending strain rate and descending temperature.For Arrhenius constitutive equation,each material parameter is set as a constant,which will bring forth large error for predicting flow behavior.In this work,material parameters are fitted as a function of temperature or strain rate based on experimental results and a modified constitutive equation is established for more accurate prediction of flow behavior of 7055 aluminium alloy.The effects of temperature and strain rate on power dissipation and instability are analyzed to establish a processing map of 7055 aluminium alloy.The dominant deformation mechanism for microstructure evolution at different deformation conditions can be determined and high efficiency of power dissipation may be achieved from power dissipation map.Meanwhile,proper processing parameters to avoid flow instability can be easily acquired in instability map.According to the processing map,optimized processing parameters of 7055 aluminium alloy are temperature of 673?723 K and strain rate of 0.01?0.4 s^?1,during which its efficiency of power dissipation is over 30%.Finite element method(FEM)is used to obtain optimized parameter in hot rolling process on the basis of processing map.
文摘为了探索沥青路面常用的AC-20沥青混合料的动态模量规律,采用相同料源的粗集料、细集料和矿粉配制了AC-20级配矿质混合料。以马歇尔试验方法确定的最佳油石比,配制了湖沥青改性沥青、SBS改性沥青以及70#基质沥青等3种沥青混合料。采用基本性能试验仪的沥青混合料单轴压缩动态模量试验方法进行了动态模量试验,并在此基础上运用时间-温度等效原理,采用NCHRP09-29提供的Mastersolver Version 2.2对阿伦尼乌斯方程中的参数进行拟合,建立了参考温度为20℃的3种沥青混合料动态模量主曲线。研究结果表明,湖沥青改性沥青AC-20和SBS改性沥青AC-20的动态模量主曲线始终位于基质沥青AC-20上方,说明沥青改性剂对混合料性能改善作用显著;湖沥青改性沥青AC-20和SBS改性沥青AC-20的动态模量主曲线存在逼近、交叉现象,说明不同改性沥青混合料性能表现出不同的适用范围。
文摘An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.
基金Supported by the National Natural Science Foundation of China under Grant No. 60772023by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. BUAA-SKLSDE-09KF-04+2 种基金Beijing University of Aeronautics and Astronautics, by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 200800130006Chinese Ministry of Education, and Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No. KM201010772020
文摘The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.
文摘In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial conditions to show capability of this method.The goveming equation for motion of a nigid rod on the circular surface without slipping have been solved using MHPM.The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks.Outcomes reveal that MHPM has an excellent agreement with numerical solution.The results show that by decreasing the oscillation amplitude,the velocity of rigid rod decreases and for A=w3 the velocity profile is maximum.
文摘This paper mainly introduces the parallel physics-informed neural networks(PPINNs)method with regularization strategies to solve the data-driven forward-inverse problems of the variable coefficient modified Korteweg-de Vries(VC-MKdV)equation.For the forward problem of the VC-MKdV equation,the authors use the traditional PINN method to obtain satisfactory data-driven soliton solutions and provide a detailed analysis of the impact of network width and depth on solving accuracy and speed.Furthermore,the author finds that the traditional PINN method outperforms the one with locally adaptive activation functions in solving the data-driven forward problems of the VC-MKdV equation.As for the data-driven inverse problem of the VC-MKdV equation,the author introduces a parallel neural networks to separately train the solution function and coefficient function,successfully addressing the function discovery problem of the VC-MKdV equation.To further enhance the network’s generalization ability and noise robustness,the author incorporates two regularization strategies into the PPINNs.An amount of numerical experimental data in this paper demonstrates that the PPINNs method can effectively address the function discovery problem of the VC-MKdV equation,and the inclusion of appropriate regularization strategies in the PPINNs can improves its performance.
文摘The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.
文摘We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique. A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail. The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included.
文摘In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.
基金Project supported by the National Key R&D Program of China(Grant Nos.2022YFE03070000 and 2022YFE03070003)the National Natural Science Foundation of China(Grant Nos.12375220 and 12075114)+3 种基金the Hunan Provincial Natural Science Foundation(Grant No.2021JJ30569)the Doctoral Initiation Fund Project of University of South China(Grant No.190XQD114)the Hunan Nuclear Fusion International Science and Technology Innovation Cooperation Base(Grant No.2018WK4009)the Hengyang Key Laboratory of Magnetic Confinement Nuclear Fusion Research(Grant No.2018KJ108)。
文摘Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.
基金Project(51275414)supported by the National Natural Science Foundation of ChinaProject(2015JM5204)supported by the Natural Science Foundation of Shaanxi Province,China+1 种基金Project(Z2015064)supported by the Graduate Starting Seed Fund of the Northwestern Polytechnical University,ChinaProject(130-QP-2015)supported by the Research Fund of the State Key Laboratory of Solidification Processing(NWPU),China
文摘In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series ¶llel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.
基金funded by the National Natural Science Foundation of China (Grant No. 11975145)
文摘This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12161061)the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics (Grant No. NCYWT23036)+2 种基金the Young Innovative and Entrepreneurial Talents of the Inner Mongolia Grassland Talents Project in 2022,Autonomous Region “Five Major Tasks” Research Special Project for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. NCXWD2422)High Quality Research Achievement Cultivation Fund for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. GZCG2426)the Talent Development Fund of Inner Mongolia Autonomous Region, China。
文摘Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.
文摘In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are developed.Unlike the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons.By using the extended auxiliary equation method,we deduced some new soliton solutions of the fourthorder nonlinear modified Degasperis-Procesi equation with constant coefficient.These solutions include symmetrical,non-symmetrical kink solutions,solitary pattern solutions,weiestrass elliptic function solutions and triangular function solutions.We discuss the stability analysis for these solutions.
基金Acknowldgements. The authors would like to express their sincere thanks to the editor and referees for their very helpful comments and suggestions, which greatly improved the quality of this paper. We also would like to thank Dr. Xiu Ye for useful discussions. The first author＇s research is partially supported by the Natural Science Foundation of Shandong Province of China grant ZR2013AM023, the Project Funded by China Postdoctoral Science Foundation no. 2014M560547, the Fundamental Research Funds of Shandong University no. 2015JC019, and NSAF no. U1430101.
文摘For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11032006,11072094,and 11121202)the Ph.D.Program Foundation of Ministry of Education of China(Grant No.20100211110022)+2 种基金the National Key Project of Magneto-Constrained Fusion Energy Development Program(Grant No.2013GB110002)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2013-1)the Scholarship Award for Excellent Doctoral Student granted by the Lanzhou University
文摘A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.
