In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic ...In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.展开更多
The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage....The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.展开更多
To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with ...To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term,which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems.By the same approach,the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered.On the other hand,in order to enhance the design flexibility,a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed,which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model.By the numerical examples,the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains.For instance,when the allowable time-delay increases from 7.3s to 12s for an uncertain T-S fuzzy control system with time-delay,the norm of the feedback gains decreases from(34.299 2,38.560 3)to(10.073 3,11.349 0),respectively.Meanwhile,the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition ofx(0)=[3-1].展开更多
This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model ...This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
Accelerated crucible rotation technique(ACRT) has been used for the directional solidification of Al-4.5wt% Cu binary alloy.By rotating the crucible at varying rate and direction,forced liquid flows are aroused These ...Accelerated crucible rotation technique(ACRT) has been used for the directional solidification of Al-4.5wt% Cu binary alloy.By rotating the crucible at varying rate and direction,forced liquid flows are aroused These flows include Ekman flow,Couette flow and Spiral Shear flow.Especially,Ekman flow acts directly at the L/S interface,changes diffusion and heat exchange conditions and has strong influences on the morphology of L/S interface.Experimental results show that,compared with normal Bridgman specimens,the solidification region is much narrower and the cell spacing is much smaller in ACRT specimens.These influences become much stronger when the accelerating rate is increased.展开更多
Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive an...Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua's circuit.展开更多
The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal over...The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal overlapped-rules group(MORG),a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function(CLKF) approach and the fuzzy Lyapunov-Krasovskii function(FLKF) approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.展开更多
The austenite medium Mn steel modified with controlled additions of Ca, Y, Si were directionally solidified using the vertical Bridgman method to study the effects of Ca(Y)-Si modifier on the solid-liquid (S-L) in...The austenite medium Mn steel modified with controlled additions of Ca, Y, Si were directionally solidified using the vertical Bridgman method to study the effects of Ca(Y)-Si modifier on the solid-liquid (S-L) interface morphology and solute segregation. The interface morphology and the C and Mn segregation of the steel directionally solidified at 6.9 μtrn/s were investigated with an image analysis and a scanning electron microscope equipped with energy dispersive X-ray analysis. The 0.5wt% Ca-Si modified steel is solidified with a planar S-L interface. The interface of the 1.0wt% Ca-Si modified steel is similar to that of the 0.5wt% Ca-Si modified steel, but with larger nodes. The 1.5wt% Ca-Si modified steel displays a cellular growth parttern. The S-L interface morphology of the 0.5wt% Ca-Si+1.0wt% Y-Si modified Mn steel appears as dendritic interface, and primary austenite dendrites reveal developed lateral branching at the quenched liquid. In the meantime, the independent austenite colonies are formed ahead of the S-L interface. A mechanism involving constitutional supercooling explains the S-L interface evolution. It depends mainly on the difference in the contents of Ca, Y, and Si ahead of the S-L interface. The segregation of C and Mn ahead of the S-L interface enhanced by the modifiers is observed.展开更多
The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to...The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.展开更多
A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constrain...A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper.展开更多
基金supported by China Postdoctoral Science Foundation grant 2020TQ0344the NSFC grants 11871139 and 12101597the NSF grants DMS-1720116,DMS-2012882,DMS-2011838,DMS-1719942,DMS-1913072.
文摘In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.
基金Foundation item: Projects(41172273, 40802079, 51108288) supported by the National Natural Science Foundation of China Project(KLE-TJGE-B1106) supported by the Opening Fund of Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education (Tongji University), China
文摘The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.
基金Project(61273095)supported by the National Natural Science Foundation of ChinaProject(135225)supported by the Academy of Finland
文摘To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term,which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems.By the same approach,the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered.On the other hand,in order to enhance the design flexibility,a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed,which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model.By the numerical examples,the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains.For instance,when the allowable time-delay increases from 7.3s to 12s for an uncertain T-S fuzzy control system with time-delay,the norm of the feedback gains decreases from(34.299 2,38.560 3)to(10.073 3,11.349 0),respectively.Meanwhile,the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition ofx(0)=[3-1].
基金Supported by National Natural Science Foundation of China (50977008, 60904017, 60774048, 60728307), the Funds for Creative Research Groups of China (60521003), the Program for Cheung Kong Scholars and Innovative Research Team in University (IRT0421), and the 111 Project (B08015), National High Technology Research and Development Program of China (863 Program) (2006AA04Z183)
文摘This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
文摘Accelerated crucible rotation technique(ACRT) has been used for the directional solidification of Al-4.5wt% Cu binary alloy.By rotating the crucible at varying rate and direction,forced liquid flows are aroused These flows include Ekman flow,Couette flow and Spiral Shear flow.Especially,Ekman flow acts directly at the L/S interface,changes diffusion and heat exchange conditions and has strong influences on the morphology of L/S interface.Experimental results show that,compared with normal Bridgman specimens,the solidification region is much narrower and the cell spacing is much smaller in ACRT specimens.These influences become much stronger when the accelerating rate is increased.
基金Project supported by the Major State Basic Research Development Program of China(Grant No.2012CB215202)the National Natural Science Foundation of China(Grant Nos.61104080 and 61134001)the Fundamental Research Funds for the Central Universities(Grant No.CDJZR13 175501)
文摘Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua's circuit.
基金supported in part by the Scientific Research Project of Heilongjiang Province Education Bureau(12541200)
文摘The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal overlapped-rules group(MORG),a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function(CLKF) approach and the fuzzy Lyapunov-Krasovskii function(FLKF) approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.
基金This work is financially supported by the National Natural Science Foundation of China (No.50001008 and No. 50271042).
文摘The austenite medium Mn steel modified with controlled additions of Ca, Y, Si were directionally solidified using the vertical Bridgman method to study the effects of Ca(Y)-Si modifier on the solid-liquid (S-L) interface morphology and solute segregation. The interface morphology and the C and Mn segregation of the steel directionally solidified at 6.9 μtrn/s were investigated with an image analysis and a scanning electron microscope equipped with energy dispersive X-ray analysis. The 0.5wt% Ca-Si modified steel is solidified with a planar S-L interface. The interface of the 1.0wt% Ca-Si modified steel is similar to that of the 0.5wt% Ca-Si modified steel, but with larger nodes. The 1.5wt% Ca-Si modified steel displays a cellular growth parttern. The S-L interface morphology of the 0.5wt% Ca-Si+1.0wt% Y-Si modified Mn steel appears as dendritic interface, and primary austenite dendrites reveal developed lateral branching at the quenched liquid. In the meantime, the independent austenite colonies are formed ahead of the S-L interface. A mechanism involving constitutional supercooling explains the S-L interface evolution. It depends mainly on the difference in the contents of Ca, Y, and Si ahead of the S-L interface. The segregation of C and Mn ahead of the S-L interface enhanced by the modifiers is observed.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61004038)
文摘The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.
基金the National Natural Science Foundation of China (No. 60504024)the Specialized Research Fund for the Doc-toral Program of Higher Education, China (No. 20060335022)+1 种基金the Natural Science Foundation of Zhejiang Province, China (No. Y106010)the "151 Talent Project" of Zhejiang Province (Nos. 05-3-1013 and 06-2-034), China
文摘A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper.