In this study we used the deep eutectic solvents (ionic liquids) to investigate the reaction between copper (II) with ethylene diamine (en). Two of the existing methods for analyzing spectrophotometric measurements ha...In this study we used the deep eutectic solvents (ionic liquids) to investigate the reaction between copper (II) with ethylene diamine (en). Two of the existing methods for analyzing spectrophotometric measurements have been applied for establishing, the stoichiometry and whenever possible, the stability constants of the chelates formed. The method of continuous variations was necessary to determine first whether, the metal ion and the ligand ethylene diamine form one or more than one chelate, when more than one chelate formed, the results obtained depend on the wavelength and for meaningful conclusions the wavelengths were carefully selected. The empirical formulae of the chelates were further substantiated by the molar ratio method. The effect of time and temperature on the formation and stability of these chelates in solution is also studied. The stability constants, K1 and K2 for the copper (II) chelates were calculated, though reliable, and are comparable to literature values.展开更多
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
Solidification/stabilization （S/S） is one of the most effective methods of dealing with heavy metal contaminated soils. The effects of cyclic wetting and drying on solidified/stabilized contaminated soils were inves...Solidification/stabilization （S/S） is one of the most effective methods of dealing with heavy metal contaminated soils. The effects of cyclic wetting and drying on solidified/stabilized contaminated soils were investigated. A series of test program, unconfined compressive strength （UCS） test, TCLP leaching test and scanning electron microscopy （SEM） test, were performed on lead and zinc contaminated soils solidified/stabilized by fly ash. Test results show that UCS and the leaching characteristics of heavy metal ions of S/S contaminated soils are significantly improved with the increase of fly ash content. UCS of S/S soils firstly increases with the increase of the times of drying and wetting cycles, after reaching the peak, it decreases with it. When the pollutant content is lower （1 000 mg/kg）, the TCLP concentration first slightly decreases under cyclic drying and wetting, then increases, but the change is minor. The TCLP concentration is higher under a high pollutant content of 5 000 mg/kg, and increases with the increase of the times of drying and wetting cycles. The results of scanning electron microscopy （SEM） test are consistent with UCS tests and TCLP leaching tests, which reveals the micro-mechanism of the variations of engineering properties of stabilized contaminated soils after drying and wetting cycles.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
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
An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global ex...An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global exponential stability for the impulsive control of Liu＇s systems. We also present the estimate of the stable region for the equidistance impulsive interval. Furthermore, an illustrative example is given to show the effectiveness of the proposed results.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
文摘In this study we used the deep eutectic solvents (ionic liquids) to investigate the reaction between copper (II) with ethylene diamine (en). Two of the existing methods for analyzing spectrophotometric measurements have been applied for establishing, the stoichiometry and whenever possible, the stability constants of the chelates formed. The method of continuous variations was necessary to determine first whether, the metal ion and the ligand ethylene diamine form one or more than one chelate, when more than one chelate formed, the results obtained depend on the wavelength and for meaningful conclusions the wavelengths were carefully selected. The empirical formulae of the chelates were further substantiated by the molar ratio method. The effect of time and temperature on the formation and stability of these chelates in solution is also studied. The stability constants, K1 and K2 for the copper (II) chelates were calculated, though reliable, and are comparable to literature values.
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Solidification/stabilization （S/S） is one of the most effective methods of dealing with heavy metal contaminated soils. The effects of cyclic wetting and drying on solidified/stabilized contaminated soils were investigated. A series of test program, unconfined compressive strength （UCS） test, TCLP leaching test and scanning electron microscopy （SEM） test, were performed on lead and zinc contaminated soils solidified/stabilized by fly ash. Test results show that UCS and the leaching characteristics of heavy metal ions of S/S contaminated soils are significantly improved with the increase of fly ash content. UCS of S/S soils firstly increases with the increase of the times of drying and wetting cycles, after reaching the peak, it decreases with it. When the pollutant content is lower （1 000 mg/kg）, the TCLP concentration first slightly decreases under cyclic drying and wetting, then increases, but the change is minor. The TCLP concentration is higher under a high pollutant content of 5 000 mg/kg, and increases with the increase of the times of drying and wetting cycles. The results of scanning electron microscopy （SEM） test are consistent with UCS tests and TCLP leaching tests, which reveals the micro-mechanism of the variations of engineering properties of stabilized contaminated soils after drying and wetting cycles.
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Supported by Foundation of Zhejiang Educational Committee under Grant No. Y200805720
文摘An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global exponential stability for the impulsive control of Liu＇s systems. We also present the estimate of the stable region for the equidistance impulsive interval. Furthermore, an illustrative example is given to show the effectiveness of the proposed results.
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.
