Starting from nonlinear equations on the F-plane containing frictional dissipation under the Boussinesq approximation, a new kind of generalized energy is proposed as the Lyapunov function, and averages are taken as a...Starting from nonlinear equations on the F-plane containing frictional dissipation under the Boussinesq approximation, a new kind of generalized energy is proposed as the Lyapunov function, and averages are taken as any functions of (x, z) instead of the commonly-used means of bilinear functions of (x, z), thereby resulting in a new criterion of generalized nonlinear symmetric stability. It shows that not only must the dissipative coefficient be greater than a certain critical value but the initial disturbance amplitude must be synchronously smaller than another marginal value as well. It follows that the latter imposes a crucial constraint on the former, thus leading to the fact that when the amplitude is bigger compared to another critical value, generalized nonlinear subcritical symmetrical instability may occur. The new criterion contributes greatly to the improvement of the previous results of its kind.展开更多
In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hys...In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.展开更多
The symmetric stability problems in the mesoscale synoptic dynamics have been studied. Without the assumption of the existence of some needed Casimir, the nonlinear stability criterion has been got, which satisfies al...The symmetric stability problems in the mesoscale synoptic dynamics have been studied. Without the assumption of the existence of some needed Casimir, the nonlinear stability criterion has been got, which satisfies all the needed properties. This result fills the gap between the conditions needed by the energy_Casimir method and by the energy_Lagrange method.展开更多
The fractional quadric-cubic coupled nonlinear Schrodinger equation is concerned,and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method.The relationship between the Lé...The fractional quadric-cubic coupled nonlinear Schrodinger equation is concerned,and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method.The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated.Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index,respectively.The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied.Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.展开更多
The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simu...The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.展开更多
文摘Starting from nonlinear equations on the F-plane containing frictional dissipation under the Boussinesq approximation, a new kind of generalized energy is proposed as the Lyapunov function, and averages are taken as any functions of (x, z) instead of the commonly-used means of bilinear functions of (x, z), thereby resulting in a new criterion of generalized nonlinear symmetric stability. It shows that not only must the dissipative coefficient be greater than a certain critical value but the initial disturbance amplitude must be synchronously smaller than another marginal value as well. It follows that the latter imposes a crucial constraint on the former, thus leading to the fact that when the amplitude is bigger compared to another critical value, generalized nonlinear subcritical symmetrical instability may occur. The new criterion contributes greatly to the improvement of the previous results of its kind.
文摘In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.
文摘The symmetric stability problems in the mesoscale synoptic dynamics have been studied. Without the assumption of the existence of some needed Casimir, the nonlinear stability criterion has been got, which satisfies all the needed properties. This result fills the gap between the conditions needed by the energy_Casimir method and by the energy_Lagrange method.
基金supported by Zhejiang Provincial Natural Science Foundation of China(No.LR20A050001)National Natural Science Foundation of China(No.12075210)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘The fractional quadric-cubic coupled nonlinear Schrodinger equation is concerned,and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method.The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated.Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index,respectively.The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied.Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.
基金supported by the Iraqi ministry of higher education and scientific research
文摘The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.
