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
The coal mine roof rating(CMRR) was developed to bridge the gap between geological variation in underground coal mines and engineering design. The CMRR accounts for the compressive strength of the immediate roof, the ...The coal mine roof rating(CMRR) was developed to bridge the gap between geological variation in underground coal mines and engineering design. The CMRR accounts for the compressive strength of the immediate roof, the shear strength and intensity of any discontinuities present, and the moisture sensitivity of the immediate roof. The CMRR has been widely used and validated in Eastern US coal mines, but it has seen limited application in the Western US. This study focuses on roof behavior at a Western coal mine(Mine A). Mine A shows significant lateral geological variation, along with localized faulting and a laterally extensive sandstone channel network. The CMRR is not used to predict roof instability at the mine. It is, therefore, hypothesized that there are other factors that are correlated with roof instability in underground coal mines that could potentially also be considered in conjunction with the CMRR.This hypothesis was tested by collecting 30 CMRR measurements at Mine A. At each measurement location, a binary record of the roof condition(stable or unstable) was made, and other parameters such as depth of cover, presence of faulting, and sandstone channels were also recorded. ANOVA tests showed that the CMRR values and the roof conditions were not strongly correlated, indicating that the CMRR input criteria are not fully predictive of roof stability at this mine. The CMRR values showed statistically significant correlations(p less than 0.05) with faulting as well as with location at an intersection. For areas that had previously experienced roof fall but were currently stable, faulting was correlated with roof condition(p less than 0.05) only when the condition was classified as unstable.展开更多
The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fat...The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.展开更多
In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interf...In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence (de-stabilizing effects) depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.展开更多
Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of e...Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.展开更多
In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given...In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.展开更多
Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the su...Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.展开更多
The stability constants of Sb^5+with Cl−as well as thermodynamics of the Sb−S−Cl−H2O system were calculated.The stability constants of Sb5+with Cl−were obtained by theoretical calculations of the absorbance of a Sb5+-...The stability constants of Sb^5+with Cl−as well as thermodynamics of the Sb−S−Cl−H2O system were calculated.The stability constants of Sb5+with Cl−were obtained by theoretical calculations of the absorbance of a Sb5+-containing solution at different Cl^−concentrations,which was detected by spectrophotometric analysis at certain wavelengths of light(380 nm).The logarithmic values versus 10 of stability constants of Sb^5+with Cl−were 1.795,3.150,4.191,4.955,5.427 and 5.511,respectively,and partly filled the data gaps in the hydrometallurgy of antimony.The presence and distribution of pentavalent antimony compounds under different conditions were analyzed based on equilibrium calculations.Thermodynamic equilibrium calculations were performed for Sb−S−Cl−H2O system,which included the complex behavior of Sb with Cl,and the equilibrium equations of related reactions in this system were integrated into the potential−pH diagram.展开更多
In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s i...In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.展开更多
In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations,the local stability of each of feasible equilibr...In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the CTL-activated infection equilibrium are established, respectively. By means of comparison arguments, it is verified that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio is less than unity. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the CTL-inactivated infection equilibrium of the system is globally asymptotically stable if the immune response reproduction ratio is less than unity and the basic reproduction ratio is greater than unity. Numerical simulations are carried out to illustrate the theoretical result.展开更多
In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), ...In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.展开更多
The method of stabilizing switched systems based on the optimal control is applied,with all modes unstable,for a typical example of the multi-agent system.First,the optimal control method for stabilizing switched syst...The method of stabilizing switched systems based on the optimal control is applied,with all modes unstable,for a typical example of the multi-agent system.First,the optimal control method for stabilizing switched systems is introduced.For this purpose,a switching table rule procedure is constructed.This procedure is inspired by the optimal control that identifies the optimal trajectory for the switched systems.In the next step,the stability of a multi-agent system is studied,considering different unstable connection topologies.Finally,the optimal control method is successfully applied to an aircraft team,as an example of the multi-agent systems.Simulation results evaluate and confirm the successful application of this method in the aircraft team example.展开更多
In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies....In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.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 a NIOSH Capacity Building grant (No. 200-2016-90154) to Drs. G. Walton and E. Holley and collaborators at the Colorado School of Mines
文摘The coal mine roof rating(CMRR) was developed to bridge the gap between geological variation in underground coal mines and engineering design. The CMRR accounts for the compressive strength of the immediate roof, the shear strength and intensity of any discontinuities present, and the moisture sensitivity of the immediate roof. The CMRR has been widely used and validated in Eastern US coal mines, but it has seen limited application in the Western US. This study focuses on roof behavior at a Western coal mine(Mine A). Mine A shows significant lateral geological variation, along with localized faulting and a laterally extensive sandstone channel network. The CMRR is not used to predict roof instability at the mine. It is, therefore, hypothesized that there are other factors that are correlated with roof instability in underground coal mines that could potentially also be considered in conjunction with the CMRR.This hypothesis was tested by collecting 30 CMRR measurements at Mine A. At each measurement location, a binary record of the roof condition(stable or unstable) was made, and other parameters such as depth of cover, presence of faulting, and sandstone channels were also recorded. ANOVA tests showed that the CMRR values and the roof conditions were not strongly correlated, indicating that the CMRR input criteria are not fully predictive of roof stability at this mine. The CMRR values showed statistically significant correlations(p less than 0.05) with faulting as well as with location at an intersection. For areas that had previously experienced roof fall but were currently stable, faulting was correlated with roof condition(p less than 0.05) only when the condition was classified as unstable.
基金supported by the National High Technology Development Program of China(863Program,Grant No.2008AA092301)the Fundamental Research Foundation of Harbin Engineering University(Grant No.HEUFT08001)the Postdoctoral Science Foundation of China(Grant No.20080440838)
文摘The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.
文摘In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence (de-stabilizing effects) depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.
基金supported by the National Natural Science Fundation of China(No.10972143)
文摘Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.
基金supported by the National Natural Science Foundation of China (No. 10871063)Scientific Research Fund of Hunan Provincial Education Department (No. 07A038)
文摘In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.
基金Supported by the National Natural Science Founda-tion of China (19531070) and the Major Project Foundation of HubeiProvince Education Department (2004Z001)
文摘Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.
基金Projects(51904048,51922108)supported by the National Natural Science Foundation of ChinaProject(2019JJ20031)supported by the Hunan Natural Science Foundation,ChinaProject(gjj170507)supported by the Scientific Research Foundation of Jiangxi Provincial Department of Education,China。
文摘The stability constants of Sb^5+with Cl−as well as thermodynamics of the Sb−S−Cl−H2O system were calculated.The stability constants of Sb5+with Cl−were obtained by theoretical calculations of the absorbance of a Sb5+-containing solution at different Cl^−concentrations,which was detected by spectrophotometric analysis at certain wavelengths of light(380 nm).The logarithmic values versus 10 of stability constants of Sb^5+with Cl−were 1.795,3.150,4.191,4.955,5.427 and 5.511,respectively,and partly filled the data gaps in the hydrometallurgy of antimony.The presence and distribution of pentavalent antimony compounds under different conditions were analyzed based on equilibrium calculations.Thermodynamic equilibrium calculations were performed for Sb−S−Cl−H2O system,which included the complex behavior of Sb with Cl,and the equilibrium equations of related reactions in this system were integrated into the potential−pH diagram.
基金This work was supported by the National Natural Science Foundation of China(No.11371368)and(No.11871316)。
文摘In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.
基金Supported by the NNSF of China(11371368,11071254)Supported by the NSF of Hebei Province(A2014506015)Supported by the NSF for Young Scientists of Hebei Province(A2013506012)
文摘In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the CTL-activated infection equilibrium are established, respectively. By means of comparison arguments, it is verified that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio is less than unity. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the CTL-inactivated infection equilibrium of the system is globally asymptotically stable if the immune response reproduction ratio is less than unity and the basic reproduction ratio is greater than unity. Numerical simulations are carried out to illustrate the theoretical result.
文摘In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.
文摘The method of stabilizing switched systems based on the optimal control is applied,with all modes unstable,for a typical example of the multi-agent system.First,the optimal control method for stabilizing switched systems is introduced.For this purpose,a switching table rule procedure is constructed.This procedure is inspired by the optimal control that identifies the optimal trajectory for the switched systems.In the next step,the stability of a multi-agent system is studied,considering different unstable connection topologies.Finally,the optimal control method is successfully applied to an aircraft team,as an example of the multi-agent systems.Simulation results evaluate and confirm the successful application of this method in the aircraft team example.
文摘In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.