We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of ...The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.展开更多
The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is stu...The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.展开更多
The low-temperature measurement of Hall effect of the two-dimensional electron system in a double-layered gated Si-δ-doped GaAs is presented.A complex peculiar nonlinear dependence of the depletion on gate voltage i...The low-temperature measurement of Hall effect of the two-dimensional electron system in a double-layered gated Si-δ-doped GaAs is presented.A complex peculiar nonlinear dependence of the depletion on gate voltage is observed.The nonlinearity is also explained on the basis of the assumption that the double-capacity model consists of two δ-doped two-dimensional electron layers and a metallic gate,and the experimental result that the electron mobility is linear with the electron density on a log-log scale.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 paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of differ...This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions, and to detect the effect of bi- directional loading on the seismic response of this type of bridge. The results showed that some characteristics, such as the variable lateral stiffness, the foundation modelling, and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions. It was found that the soft story failure mechanism ：is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure. The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading： was severely increased compared to the bridge response under unidirectional transverse loading, and out-of-phase movements were triggered between adjacent girders.展开更多
In order to reach a compromise between fast response control and torques matching control in double turboshaft engines,research on nonlinear model predictive control for turboshaft engines based on double engines torq...In order to reach a compromise between fast response control and torques matching control in double turboshaft engines,research on nonlinear model predictive control for turboshaft engines based on double engines torques matching is conducted.Meanwhile,a Nonlinear Model Predictive Control(NMPC)method is proposed,which combines the control index of the power turbine speed with torques matching of double engines creatively.In addition to the control index,the difference of output torques between each engine is also incorporated in the objective function as a penalty term to ensure constant speed control and short torques matching time.Simulation results demonstrate that relative to unilateral torques matching,the settling time of the bidirectional matching method can be reduced by nearly 30.8%.Nevertheless,compared with the bidirectional torques matching method under the cascade PID controller,the NMPC method can decrease the overshoot of the power turbine speed by 65%and reduce the matching time by 15.5%synchronously.Besides fast response control of turboshaft engines,fast torques matching control of double engines is accomplished as well.展开更多
We investigate the mechanics ofa new double chain-model of DNA. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the DNA molecule, connected with each ...We investigate the mechanics ofa new double chain-model of DNA. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the DNA molecule, connected with each other by an elastic membrane (or some linear springs) representing the hydrogen bonds between the base pairs of the two chains. The nonlinear dynamical equations are derived and some solitary wave solutions are discussed. By the way,our model can be regarded as the mechanical model of cubic nonlinear Klein-Gordon equation and 4-field equation.展开更多
A new reaction system to determine nonlinear chemical fingerprint(NCF)and its use in identification method based on double reaction system was researched.Panax ginsengs,such as ginseng,American ginseng and notoginseng...A new reaction system to determine nonlinear chemical fingerprint(NCF)and its use in identification method based on double reaction system was researched.Panax ginsengs,such as ginseng,American ginseng and notoginseng were identified by the method.The NCFs of the three samples of Panax ginsengs were determined through two nonlinear chemical systems,namely system 1 consisting of sample components,H2SO4,MnSO4,NaBrO3,acetone and the new system,system 2 consisting of sample components,H2SO4,(NH4)4Ce(SO4)2,NaBrO3 and citric acid.The comparison between the results determined through systems 1 and 2 shows that the speed to determine NCF through system 2 is much faster than that through system 1;for systems 1 and 2,the system similarities of the same kind of samples are≥98.09%and 99.78%,respectively,while those of different kinds of samples are≤63.04%and 86.34%,respectively.The results to identify the kinds of some samples by system similarity pattern show that both the accuracies of identification methods based on single system 1 and 2 are≥95.6%,and the average values are 97.1%and 96.3%,respectively;the accuracy of the method based on double system is≥97.8%,and the average accuracy is 99.3%.The accuracy of the method based on double system is higher than that based on any single system.展开更多
Aiming at the coupling characteristic between the two groups of electromagnets embedded in the module of the maglev train, a nonlinear decoupling controller is designed. The module is modeled as a double-electromagnet...Aiming at the coupling characteristic between the two groups of electromagnets embedded in the module of the maglev train, a nonlinear decoupling controller is designed. The module is modeled as a double-electromagnet system, and based on some reasonable assumptions its nonlinear mathematical model, a MIMO coupling system, is derived. To realize the linearization and decoupling from the input to the output, the model is linearized exactly by means of feedback linearization, and an equivalent linear decoupling model is obtained. Based on the linear model, a nonlinear suspension controller is designed using state feedback. Simulations and experiments show that the controller can effectually solve the coupling problem in double-electromagnet suspension system.展开更多
We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens-Fresnel diffraction integral method. This theoretical model i...We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens-Fresnel diffraction integral method. This theoretical model is not only consistent with the cascade structure model for a small nonlinear phase-shift but also can be used for a large nonlinear phase-shift. It has been verified that it is suitable to characterize the double-sided nonlinear media compared with the cascade structure model. A good agreement between the experimental data and the results from the theoretical model is obtained. It will be useful for the design of multi-sided nonlinear materials.展开更多
We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vec...We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.展开更多
In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the...In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables. It is obvious that the above system is a generalization of the traditional differential systems. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria. As a result, the partial stability of differential equations is widely used both in theory and in practice such as dynamic systems and control systems.展开更多
The new multiple （G＇/G）-expansion method is proposed in this paper to seek the exact double traveling wave solutions of nonlinear partial differential equations. With the aid of symbolic computation, this new metho...The new multiple （G＇/G）-expansion method is proposed in this paper to seek the exact double traveling wave solutions of nonlinear partial differential equations. With the aid of symbolic computation, this new method is applied to construct double traveling wave solutions of the coupled nonlinear Klein-Gordon equations and the coupled SchrSdinger-Boussinesq equation. As a result, abundant double traveling wave solutions including double hyperbolic tangent function solutions, double tangent function solutions, double rational solutions, and a series of complexiton solutions of these two equations are obtained via this new method. The new multiple ＇ （G＇/G-expanslon method not only gets new exact solutions of equations directly and effectively, but also expands the scope of the solution. This new method has a very wide range of application for the study of nonlinear partial differential equations.展开更多
In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-sim...In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.展开更多
Classical chaotic behavior in diatomic molecules is studied when chaos is driven by a circularly polarized resonant electric field and expanding up to fourth order of approximation the Morse’s potential and angular m...Classical chaotic behavior in diatomic molecules is studied when chaos is driven by a circularly polarized resonant electric field and expanding up to fourth order of approximation the Morse’s potential and angular momentum of the system. On this double resonant system, we find a weak and a strong stationary (or critical) points where the chaotic characteristics are different with respect to the initial conditions of the system. Chaotic behavior around the weak critical point appears at much weaker intensity on the electric field than the electric field needed for the chaotic behavior around the strong critical point. This classical chaotic behavior is determined through Lyapunov exponent, separation of two nearby trajectories, and Fourier transformation of the time evolution of the system. The threshold of the amplitude of the electric field for appearing the chaotic behavior near each critical point is different and is found for several molecules.展开更多
The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sag...The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sagdeev technique was employed,and an energy equation was derived.Our findings show that the proposed system reveals the existence of a double-layer solution,periodic,supersoliton,and superperiodic waves.The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves.It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model.Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.展开更多
Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherica...Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.展开更多
When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultan...When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.展开更多
Reducing the error of sensitive parameters by studying the parameters sensitivity can reduce the uncertainty of the model,while simulating double-gyre variation in Regional Ocean Modeling System(ROMS).Conditional Nonl...Reducing the error of sensitive parameters by studying the parameters sensitivity can reduce the uncertainty of the model,while simulating double-gyre variation in Regional Ocean Modeling System(ROMS).Conditional Nonlinear Optimal Perturbation related to Parameter(CNOP-P)is an effective method of studying the parameters sensitivity,which represents a type of parameter error with maximum nonlinear development at the prediction time.Intelligent algorithms have been widely applied to solving Conditional Nonlinear Optimal Perturbation(CNOP).In the paper,we proposed an improved simulated annealing(SA)algorithm to solve CNOP-P to get the optimal parameters error,studied the sensitivity of the single parameter and the combination of multiple parameters and verified the effect of reducing the error of sensitive parameters on reducing the uncertainty of model simulation.Specifically,we firstly found the non-period oscillation of kinetic energy time series of double gyre variation,then extracted two transition periods,which are respectively from high energy to low energy and from low energy to high energy.For every transition period,three parameters,respectively wind amplitude(WD),viscosity coefficient(VC)and linear bottom drag coefficient(RDRG),were studied by CNOP-P solved with SA algorithm.Finally,for sensitive parameters,their effect on model simulation is verified.Experiments results showed that the sensitivity order is WD>VC>>RDRG,the effect of the combination of multiple sensitive parameters is greater than that of single parameter superposition and the reduction of error of sensitive parameters can effectively reduce model prediction error which confirmed the importance of sensitive parameters analysis.展开更多
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013XK03the National Natural Science Foundation of China under Grant No.11371361
文摘The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.
文摘The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.
文摘The low-temperature measurement of Hall effect of the two-dimensional electron system in a double-layered gated Si-δ-doped GaAs is presented.A complex peculiar nonlinear dependence of the depletion on gate voltage is observed.The nonlinearity is also explained on the basis of the assumption that the double-capacity model consists of two δ-doped two-dimensional electron layers and a metallic gate,and the experimental result that the electron mobility is linear with the electron density on a log-log scale.
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.
文摘This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions, and to detect the effect of bi- directional loading on the seismic response of this type of bridge. The results showed that some characteristics, such as the variable lateral stiffness, the foundation modelling, and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions. It was found that the soft story failure mechanism ：is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure. The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading： was severely increased compared to the bridge response under unidirectional transverse loading, and out-of-phase movements were triggered between adjacent girders.
基金co-supported by the National Natural Science Foundation of China(No.51576096)Qing Lan and 333 Project and Research Funds for Central Universities(No.NF2018003).
文摘In order to reach a compromise between fast response control and torques matching control in double turboshaft engines,research on nonlinear model predictive control for turboshaft engines based on double engines torques matching is conducted.Meanwhile,a Nonlinear Model Predictive Control(NMPC)method is proposed,which combines the control index of the power turbine speed with torques matching of double engines creatively.In addition to the control index,the difference of output torques between each engine is also incorporated in the objective function as a penalty term to ensure constant speed control and short torques matching time.Simulation results demonstrate that relative to unilateral torques matching,the settling time of the bidirectional matching method can be reduced by nearly 30.8%.Nevertheless,compared with the bidirectional torques matching method under the cascade PID controller,the NMPC method can decrease the overshoot of the power turbine speed by 65%and reduce the matching time by 15.5%synchronously.Besides fast response control of turboshaft engines,fast torques matching control of double engines is accomplished as well.
文摘We investigate the mechanics ofa new double chain-model of DNA. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the DNA molecule, connected with each other by an elastic membrane (or some linear springs) representing the hydrogen bonds between the base pairs of the two chains. The nonlinear dynamical equations are derived and some solitary wave solutions are discussed. By the way,our model can be regarded as the mechanical model of cubic nonlinear Klein-Gordon equation and 4-field equation.
基金Project(61533021)supported by the National Natural Science Foundation of ChinaProject(R201706)supported by Hunan Food Pharmaceutical,China
文摘A new reaction system to determine nonlinear chemical fingerprint(NCF)and its use in identification method based on double reaction system was researched.Panax ginsengs,such as ginseng,American ginseng and notoginseng were identified by the method.The NCFs of the three samples of Panax ginsengs were determined through two nonlinear chemical systems,namely system 1 consisting of sample components,H2SO4,MnSO4,NaBrO3,acetone and the new system,system 2 consisting of sample components,H2SO4,(NH4)4Ce(SO4)2,NaBrO3 and citric acid.The comparison between the results determined through systems 1 and 2 shows that the speed to determine NCF through system 2 is much faster than that through system 1;for systems 1 and 2,the system similarities of the same kind of samples are≥98.09%and 99.78%,respectively,while those of different kinds of samples are≤63.04%and 86.34%,respectively.The results to identify the kinds of some samples by system similarity pattern show that both the accuracies of identification methods based on single system 1 and 2 are≥95.6%,and the average values are 97.1%and 96.3%,respectively;the accuracy of the method based on double system is≥97.8%,and the average accuracy is 99.3%.The accuracy of the method based on double system is higher than that based on any single system.
基金Supported by National Natural Science Foundation of P. R. China (60404003)the Natural Science Foundation of Hunan Province (03JJY3108)Fok Ying-Tong Education Foundation (94028)
文摘Aiming at the coupling characteristic between the two groups of electromagnets embedded in the module of the maglev train, a nonlinear decoupling controller is designed. The module is modeled as a double-electromagnet system, and based on some reasonable assumptions its nonlinear mathematical model, a MIMO coupling system, is derived. To realize the linearization and decoupling from the input to the output, the model is linearized exactly by means of feedback linearization, and an equivalent linear decoupling model is obtained. Based on the linear model, a nonlinear suspension controller is designed using state feedback. Simulations and experiments show that the controller can effectually solve the coupling problem in double-electromagnet suspension system.
基金Project supported by the Natural National Science Foundation of China （Grant Nos 20131040 and 50172013）, the Heilongjiang Province Science Foundation （Grant No F2004-8）, and the 0utstanding Young Research Foundation of Heilongjiang University （Grant No JC200307）.
文摘We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens-Fresnel diffraction integral method. This theoretical model is not only consistent with the cascade structure model for a small nonlinear phase-shift but also can be used for a large nonlinear phase-shift. It has been verified that it is suitable to characterize the double-sided nonlinear media compared with the cascade structure model. A good agreement between the experimental data and the results from the theoretical model is obtained. It will be useful for the design of multi-sided nonlinear materials.
文摘We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.
文摘In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables. It is obvious that the above system is a generalization of the traditional differential systems. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria. As a result, the partial stability of differential equations is widely used both in theory and in practice such as dynamic systems and control systems.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11202106、61201444)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20123228120005)+4 种基金the Jiangsu Information and Communication Engineering Preponderant Discipline Platformthe Natural Science Foundation of Jiangsu Province(Grant No.BK20131005)the Jiangsu Qing Lan Projectthe Natural Sciences Fundation of the Universities of Jiangsu Province(Grant No.13KJB170016)the Fundamental Research Funds for the Southeast University(Grant No.CDLS-2016-03)
文摘The new multiple （G＇/G）-expansion method is proposed in this paper to seek the exact double traveling wave solutions of nonlinear partial differential equations. With the aid of symbolic computation, this new method is applied to construct double traveling wave solutions of the coupled nonlinear Klein-Gordon equations and the coupled SchrSdinger-Boussinesq equation. As a result, abundant double traveling wave solutions including double hyperbolic tangent function solutions, double tangent function solutions, double rational solutions, and a series of complexiton solutions of these two equations are obtained via this new method. The new multiple ＇ （G＇/G-expanslon method not only gets new exact solutions of equations directly and effectively, but also expands the scope of the solution. This new method has a very wide range of application for the study of nonlinear partial differential equations.
文摘In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.
文摘Classical chaotic behavior in diatomic molecules is studied when chaos is driven by a circularly polarized resonant electric field and expanding up to fourth order of approximation the Morse’s potential and angular momentum of the system. On this double resonant system, we find a weak and a strong stationary (or critical) points where the chaotic characteristics are different with respect to the initial conditions of the system. Chaotic behavior around the weak critical point appears at much weaker intensity on the electric field than the electric field needed for the chaotic behavior around the strong critical point. This classical chaotic behavior is determined through Lyapunov exponent, separation of two nearby trajectories, and Fourier transformation of the time evolution of the system. The threshold of the amplitude of the electric field for appearing the chaotic behavior near each critical point is different and is found for several molecules.
文摘The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sagdeev technique was employed,and an energy equation was derived.Our findings show that the proposed system reveals the existence of a double-layer solution,periodic,supersoliton,and superperiodic waves.The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves.It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model.Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.
基金Project supported by the National Natural Science Foundation of China (No. 19972024)the Key Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of Chinathe Key Laboratory of Diagnosis of Fault in Engineering Structures of Guangdong Province of China
文摘Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.
基金funded by the National Natural Science Foundation of China (Grant No. 51608541)the Postdoctoral Science Foundation of China (Grant No. 2015M580702)the Guizhou Provincial Department of Transportation of China (Grant No. 2014122006)
文摘When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.
基金Supported by the National Natural Science Foundation of China(No.41405097)the Fundamental Research Funds for the Central Universities of China in 2017
文摘Reducing the error of sensitive parameters by studying the parameters sensitivity can reduce the uncertainty of the model,while simulating double-gyre variation in Regional Ocean Modeling System(ROMS).Conditional Nonlinear Optimal Perturbation related to Parameter(CNOP-P)is an effective method of studying the parameters sensitivity,which represents a type of parameter error with maximum nonlinear development at the prediction time.Intelligent algorithms have been widely applied to solving Conditional Nonlinear Optimal Perturbation(CNOP).In the paper,we proposed an improved simulated annealing(SA)algorithm to solve CNOP-P to get the optimal parameters error,studied the sensitivity of the single parameter and the combination of multiple parameters and verified the effect of reducing the error of sensitive parameters on reducing the uncertainty of model simulation.Specifically,we firstly found the non-period oscillation of kinetic energy time series of double gyre variation,then extracted two transition periods,which are respectively from high energy to low energy and from low energy to high energy.For every transition period,three parameters,respectively wind amplitude(WD),viscosity coefficient(VC)and linear bottom drag coefficient(RDRG),were studied by CNOP-P solved with SA algorithm.Finally,for sensitive parameters,their effect on model simulation is verified.Experiments results showed that the sensitivity order is WD>VC>>RDRG,the effect of the combination of multiple sensitive parameters is greater than that of single parameter superposition and the reduction of error of sensitive parameters can effectively reduce model prediction error which confirmed the importance of sensitive parameters analysis.
