In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bo...In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.展开更多
Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical proper...Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical properties of as-produced thin sheets.Although many works focusing mainly on controlling fields of thermal,concentration and convection have been reported,how to control artificially and quantitatively the segregation using a theoretical connection between processing parameters and solidification models,has not been realized,yet.Regarding it,a systematical framework integrating non-equilibrium dendritic growth and overall solidification kinetics with the TRC parameters,was constructed applying a general-ized stability(GS)conception deduced from transient thermodynamic driving force△G^(t)and transient ki-netic energy barrier Q_(eff)^(t)evolving upon solidification.Departing from this framework considering synergy of thermodynamics and kinetics(i.e.,thermo-kinetic synergy),a criterion of high△G^(t)-high GS guaranteed that the macro(i.e.,the centerline)and the micro(i.e.,the edge)segregation can be suppressed by in-creasing△G^(t)and GS at the beginning and the ending stage of sub-rapid solidification,respectively.This typical thermo-kinetic combination producing the microstructure can be inherited into the plastic de-formation,as reflected by corresponding strength-ductility combinations.This work realized quantitative controlling of TRC by a theoretical connection between processing parameters and solidification models,where,an optimization for sub-rapid solidification segregation using the GS conception including△G^(t)and Q_(eff)^(t)has been performed.展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic ...Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic deformations(PDs).Both PTs and PDs follow inherent trade-off relation between thermodynamic driving force ΔG and kinetic energy barrier Q,i.e.,so-called thermo-kinetic correlation.By analyzing nucleation and growth and proposing a conception of negative driving force integrating strain energy,interface energy and any kind of energy that equivalently inhibits the PT itself,ΔG^(S),unified expressions for the thermo-kinetic correlation and generalized stability(GS)were derived for three kinds of PTs,i.e.,diffusive PTs with simultaneously decreasedΔG and increased Q,diffusive PTs with simultaneously increasedΔG and decreased Q,and displacive PTs with simultaneously increased ΔG and decreased Q.This leads to so-called thermo-kinetic connectivity by integrating the thermo-kinetic correlation and the GS,where,by application in typical PTs,it was clearly shown,a criterion of high ΔG-high GS can be predicted by modulating chemical driving force,negative driving force and kinetic energy barrier for diffusion or nucleation.Following thermo-kinetic connectivity,analogous procedure for dislocation evolution upon PDs was performed,and materials design in terms of the highΔG-high GS criterion was discussed and prospected.展开更多
In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property i...In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.展开更多
Generalized short circuit ratio(g SCR)for grid strength assessment of multi-infeed high-voltage direct current(MIDC)systems is a rigorous theoretical extension of the traditional SCR,which enables SCR to be extended t...Generalized short circuit ratio(g SCR)for grid strength assessment of multi-infeed high-voltage direct current(MIDC)systems is a rigorous theoretical extension of the traditional SCR,which enables SCR to be extended to MIDC systems.However,g SCR is originally based on the assumption of homogeneous MIDC systems,in which all high-voltage direct current(HVDC)converters have an identical control configuration,thus presenting challenges to applications of g SCR to inhomogeneous MIDC systems.To weaken this assumption,this paper applies matrix perturbation theory to explore the possibility of utilization of g SCR into inhomogeneous MIDC systems.Results of numerical experiments show that in inhomogeneous MIDC systems,the previously proposed g SCR can still be used without modification.However,critical g SCR(Cg SCR)must be redefined by considering the characteristics of control configurations of HVDC converter.Accordingly,the difference between g SCR and redefined Cg SCR can effectively quantify the pertinent AC grid strength in terms of the static-voltage stability margin.The performance of the proposed method is demonstrated in a triple-infeed inhomogeneous line commutated converter based high-voltage direct current(LCC-HVDC)system.展开更多
基金Supported partly by the National Natural Science Foundation of China (Grant Nos. 60474011 and 60274007)the National Natural Science Foun-dation of China for Excellent Youth (Grant No. 60325310)+2 种基金the Guangdong Province Science Foundation for Program of Research Team (Grant No. 04205783)the Natural Science Fund of Guangdong Province, China (Grant No. 05006508)the Natural Science and Engineering Re-search Council of Canada (Grant No. R2686A02)
文摘In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.
基金Natural Science Foundation of China(Nos.51790481,51790483,52130110,51901182)Natural Science Foundation of Shaanxi Province,China(No.2020JQ-157)Research Fund of the State Key Laboratory of Solidification Processing,China(No.2022-TS-01)。
基金support of the Natural Science Foundation of China(Nos.51790481,51790483,52130110,51901182)the Natural Science Foundation of Shaanxi Province(No.2020JQ-157)+1 种基金the Foundation of State Key Laboratory of Rolling and Automation(No.2020RALKFKT001)the Research Fund of the State Key Laboratory of Solidification Processing(No.2022-TS-01).
文摘Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical properties of as-produced thin sheets.Although many works focusing mainly on controlling fields of thermal,concentration and convection have been reported,how to control artificially and quantitatively the segregation using a theoretical connection between processing parameters and solidification models,has not been realized,yet.Regarding it,a systematical framework integrating non-equilibrium dendritic growth and overall solidification kinetics with the TRC parameters,was constructed applying a general-ized stability(GS)conception deduced from transient thermodynamic driving force△G^(t)and transient ki-netic energy barrier Q_(eff)^(t)evolving upon solidification.Departing from this framework considering synergy of thermodynamics and kinetics(i.e.,thermo-kinetic synergy),a criterion of high△G^(t)-high GS guaranteed that the macro(i.e.,the centerline)and the micro(i.e.,the edge)segregation can be suppressed by in-creasing△G^(t)and GS at the beginning and the ending stage of sub-rapid solidification,respectively.This typical thermo-kinetic combination producing the microstructure can be inherited into the plastic de-formation,as reflected by corresponding strength-ductility combinations.This work realized quantitative controlling of TRC by a theoretical connection between processing parameters and solidification models,where,an optimization for sub-rapid solidification segregation using the GS conception including△G^(t)and Q_(eff)^(t)has been performed.
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金the National Key R&D Program of China(No.2017YFB0703001)the National Natural Science Foundation of China(Nos.52130110,51790481,51901182 and 51901185)the Natural Science Foundation of Shaanxi Province(Nos.2020JQ-157 and 2020JQ-153)。
文摘Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic deformations(PDs).Both PTs and PDs follow inherent trade-off relation between thermodynamic driving force ΔG and kinetic energy barrier Q,i.e.,so-called thermo-kinetic correlation.By analyzing nucleation and growth and proposing a conception of negative driving force integrating strain energy,interface energy and any kind of energy that equivalently inhibits the PT itself,ΔG^(S),unified expressions for the thermo-kinetic correlation and generalized stability(GS)were derived for three kinds of PTs,i.e.,diffusive PTs with simultaneously decreasedΔG and increased Q,diffusive PTs with simultaneously increasedΔG and decreased Q,and displacive PTs with simultaneously increased ΔG and decreased Q.This leads to so-called thermo-kinetic connectivity by integrating the thermo-kinetic correlation and the GS,where,by application in typical PTs,it was clearly shown,a criterion of high ΔG-high GS can be predicted by modulating chemical driving force,negative driving force and kinetic energy barrier for diffusion or nucleation.Following thermo-kinetic connectivity,analogous procedure for dislocation evolution upon PDs was performed,and materials design in terms of the highΔG-high GS criterion was discussed and prospected.
基金supported by National Natural Science Foundation of China(12071018)Fundamental Research Funds for the Central Universitiessupported by the National Research Foundation of Korea(NRF)funded by the Korea government(MIST)(2020R1F1A1A01051370)。
文摘In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.
基金jointly supported by the National Natural Science Foundation of China(No.52007163)China Postdoctoral Science Foundation(No.2020M671718)。
文摘Generalized short circuit ratio(g SCR)for grid strength assessment of multi-infeed high-voltage direct current(MIDC)systems is a rigorous theoretical extension of the traditional SCR,which enables SCR to be extended to MIDC systems.However,g SCR is originally based on the assumption of homogeneous MIDC systems,in which all high-voltage direct current(HVDC)converters have an identical control configuration,thus presenting challenges to applications of g SCR to inhomogeneous MIDC systems.To weaken this assumption,this paper applies matrix perturbation theory to explore the possibility of utilization of g SCR into inhomogeneous MIDC systems.Results of numerical experiments show that in inhomogeneous MIDC systems,the previously proposed g SCR can still be used without modification.However,critical g SCR(Cg SCR)must be redefined by considering the characteristics of control configurations of HVDC converter.Accordingly,the difference between g SCR and redefined Cg SCR can effectively quantify the pertinent AC grid strength in terms of the static-voltage stability margin.The performance of the proposed method is demonstrated in a triple-infeed inhomogeneous line commutated converter based high-voltage direct current(LCC-HVDC)system.
