Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and ...Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and that a stable limitt cycle existsaround the singularity (1/2, 2) when K∈(9-δ, 9).展开更多
A modified mathematical model is used to study the effects of various forces on the stability of cavitation bubbles within a diesel droplet. The principal finding of the work is that viscous forces of fluids stabilize...A modified mathematical model is used to study the effects of various forces on the stability of cavitation bubbles within a diesel droplet. The principal finding of the work is that viscous forces of fluids stabilize the cavitation bubble, while inertial force destabilizes the cavitation bubble. The droplet viscosity plays a dominant role on the stability of cavitation bubbles compared with that of air and bubble. Bubble–droplet radius ratio is a key factor to control the bubble stability, especially in the high radius ratio range. Internal hydrodynamic and surface tension forces are found to stabilize the cavitation bubble, while bubble stability has little relationship with the external hydrodynamic force. Inertia makes bubble breakup easily, however, the breakup time is only slightly changed when bubble growth speed reaches a certain value(50 m·s-1). In contrast, viscous force makes bubble hard to break. With the increasing initial bubble–droplet radius ratio, the bubble growth rate increases, the bubble breakup radius decreases, and the bubble breakup time becomes shorter.展开更多
This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incr...This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.展开更多
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional...Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.展开更多
This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-...This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-hydraulic proportional valve is established,and the friction characteristics are described based on the LuGre model.The global asymptotic stability of the control system with the adaptive friction compensation controller is guaranteed over Lyapunov theorem.The adaptive compensation of the friction on LuGre friction model is verified by simulation and experiment.The steady-state error is about [-4.23 × 10^(-5)m,5.91 × 10^(-5)m]and[-2.5 × 10^(-4)m,2.6 ×10^(-4) m] on simulation and experiment,the position tracking accuracy is higher,and the lag time of the main valve through the dead zone is shorter.The result proves that the adaptive friction compensation method can effectively compensate for the negative effects of nonlinear friction.展开更多
Centrifugal forces are commonly created when ships turn, which may cause a ship to capsize in a critical situation. A mathematical model has been developed to optimize the stability coefficients for ship, with the aim...Centrifugal forces are commonly created when ships turn, which may cause a ship to capsize in a critical situation. A mathematical model has been developed to optimize the stability coefficients for ship, with the aim to prevent capsizing and to increase ship maneuverability in high-speed water craft. This model can be used to develop algorithms for control system improvement. The mathematical model presented in this paper optimized the use of multipurpose hydrofoils to reduce heeling and the trimming moment, maintaining an upright ship’s position and lessening the resistance via transverse force. Conventionally, the trimming and heeling of a ship are controlled using ballast water;however, under variable sea conditions it is sometimes difficult to control a ship’s motion using ballast water. In this case, a hydrofoil would be more stable and maneuverable than a ballast tank controlled vessel. A movable hydrofoil could theoretically be adapted from moveable aerofoil technology. This study proves the merit of further investigation into this possibility.展开更多
The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In t...The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.展开更多
In this note, we present some detail estimates for the integral with general integer k, as well as a singular integral formed from it, which would be useful for some nonlinear additive problems of primes.
A highly efficient three-dimensional （31）） Lattice Boltzmann （LB） model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 （200...A highly efficient three-dimensional （31）） Lattice Boltzmann （LB） model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 （2004） 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative （NND） scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, （i） Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; （ii） reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.展开更多
We investigate the formation of optical bistability （OB） in a crystal of molecular magnets contained in a unidirectional ring cavity. The crystal is subjected to one dc magnetic field and two （probe and coupling） ...We investigate the formation of optical bistability （OB） in a crystal of molecular magnets contained in a unidirectional ring cavity. The crystal is subjected to one dc magnetic field and two （probe and coupling） ac resonant magnetic field. The results show that OB can be controlled efficiently by adjusting the intensity of the control field, the detuning of probe magnetic field and the cooperation parameter, Furthermore, within certain parameter range, the optical multistablity （OM） can also be observed in the crystal medimn. This＇ investigation can be used for designing new types of nonelectronic devices for realizing switching process.展开更多
Described the outcomes of a comprehensive numerical modeling on the rock bolting performance for preventing the deformation of stratified, composite roof structure of drift in a coal mine. The investigation was undert...Described the outcomes of a comprehensive numerical modeling on the rock bolting performance for preventing the deformation of stratified, composite roof structure of drift in a coal mine. The investigation was undertaken in the adverse geological condi- tions, with variation of bolt parameters, including length, density, distribution, pretension, as well as the geometry of opening,so as to determine the effect of bolting parameter variation on roof deformation and stability. The outcomes clearly demonstrated that a sig- nificant improvement of roof stability can be achieved associating with bolting parameters optimization, and indicated the importance of flexible geotechnical designation of rock bolting reinforcement in mining practice.展开更多
The stability and the sequential dynamics of the sixteen-state Hamiltnn neural network model have been discussed with the energy function. The optical implementation scheme about Hamilton number vector-matrix multipli...The stability and the sequential dynamics of the sixteen-state Hamiltnn neural network model have been discussed with the energy function. The optical implementation scheme about Hamilton number vector-matrix multiplication is simply discussed.展开更多
文摘Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and that a stable limitt cycle existsaround the singularity (1/2, 2) when K∈(9-δ, 9).
基金Supported by the National Natural Science Foundation of China(51276011)the National High Technology Research and Development Program of China(2013AA065303)+1 种基金Beijing Municipal Natural Science Foundation of China(3132016)the Opening Foundation of State Key Laboratory of Engines(K2013-3)
文摘A modified mathematical model is used to study the effects of various forces on the stability of cavitation bubbles within a diesel droplet. The principal finding of the work is that viscous forces of fluids stabilize the cavitation bubble, while inertial force destabilizes the cavitation bubble. The droplet viscosity plays a dominant role on the stability of cavitation bubbles compared with that of air and bubble. Bubble–droplet radius ratio is a key factor to control the bubble stability, especially in the high radius ratio range. Internal hydrodynamic and surface tension forces are found to stabilize the cavitation bubble, while bubble stability has little relationship with the external hydrodynamic force. Inertia makes bubble breakup easily, however, the breakup time is only slightly changed when bubble growth speed reaches a certain value(50 m·s-1). In contrast, viscous force makes bubble hard to break. With the increasing initial bubble–droplet radius ratio, the bubble growth rate increases, the bubble breakup radius decreases, and the bubble breakup time becomes shorter.
文摘This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
基金The National Natural Science Foundation of China(No70271039)
文摘Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
基金Supported by the National Key Basic Research Program of China(No.2014CB046405)Key Projects in the National Science&Technology Pillar Program during the Twelfth Five-year Plan of China(No.2014BAF02B00,2011BAF09B04)
文摘This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-hydraulic proportional valve is established,and the friction characteristics are described based on the LuGre model.The global asymptotic stability of the control system with the adaptive friction compensation controller is guaranteed over Lyapunov theorem.The adaptive compensation of the friction on LuGre friction model is verified by simulation and experiment.The steady-state error is about [-4.23 × 10^(-5)m,5.91 × 10^(-5)m]and[-2.5 × 10^(-4)m,2.6 ×10^(-4) m] on simulation and experiment,the position tracking accuracy is higher,and the lag time of the main valve through the dead zone is shorter.The result proves that the adaptive friction compensation method can effectively compensate for the negative effects of nonlinear friction.
文摘Centrifugal forces are commonly created when ships turn, which may cause a ship to capsize in a critical situation. A mathematical model has been developed to optimize the stability coefficients for ship, with the aim to prevent capsizing and to increase ship maneuverability in high-speed water craft. This model can be used to develop algorithms for control system improvement. The mathematical model presented in this paper optimized the use of multipurpose hydrofoils to reduce heeling and the trimming moment, maintaining an upright ship’s position and lessening the resistance via transverse force. Conventionally, the trimming and heeling of a ship are controlled using ballast water;however, under variable sea conditions it is sometimes difficult to control a ship’s motion using ballast water. In this case, a hydrofoil would be more stable and maneuverable than a ballast tank controlled vessel. A movable hydrofoil could theoretically be adapted from moveable aerofoil technology. This study proves the merit of further investigation into this possibility.
基金the National Natural Science Foundation of China (Nos. 10725210 and 10432030) the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20060335107)the Program for New Century Excellent Talents in University, MOE, China (No. NCET-05-05010)
文摘The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.
文摘In this note, we present some detail estimates for the integral with general integer k, as well as a singular integral formed from it, which would be useful for some nonlinear additive problems of primes.
基金Supported by the Science Foundations of Laboratory of Computational PhysicalScience Foundation of China Academy of Engineering Physics under Grant Nos. 2009A0102005, 2009B0101012National Natural Science Foundation under Grant Nos. 10775018, 11074300, and 1107521 of China
文摘A highly efficient three-dimensional （31）） Lattice Boltzmann （LB） model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 （2004） 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative （NND） scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, （i） Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; （ii） reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.
基金National Natural Science Foundation of China under Grant Nos.10575040,90503010,and 10747133
文摘We investigate the formation of optical bistability （OB） in a crystal of molecular magnets contained in a unidirectional ring cavity. The crystal is subjected to one dc magnetic field and two （probe and coupling） ac resonant magnetic field. The results show that OB can be controlled efficiently by adjusting the intensity of the control field, the detuning of probe magnetic field and the cooperation parameter, Furthermore, within certain parameter range, the optical multistablity （OM） can also be observed in the crystal medimn. This＇ investigation can be used for designing new types of nonelectronic devices for realizing switching process.
文摘Described the outcomes of a comprehensive numerical modeling on the rock bolting performance for preventing the deformation of stratified, composite roof structure of drift in a coal mine. The investigation was undertaken in the adverse geological condi- tions, with variation of bolt parameters, including length, density, distribution, pretension, as well as the geometry of opening,so as to determine the effect of bolting parameter variation on roof deformation and stability. The outcomes clearly demonstrated that a sig- nificant improvement of roof stability can be achieved associating with bolting parameters optimization, and indicated the importance of flexible geotechnical designation of rock bolting reinforcement in mining practice.
文摘The stability and the sequential dynamics of the sixteen-state Hamiltnn neural network model have been discussed with the energy function. The optical implementation scheme about Hamilton number vector-matrix multiplication is simply discussed.
