In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied...In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied.The quasi-fractional dynamics model here refers to the variational problem based on the definition of RiemannLiouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL).First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained.Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved.The Pfaff-Birkhoff principles,Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article.Finally,some examples are given.展开更多
In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system inv...In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system involving multiple parameters was carried out,and a new type oscillation heat transfer dynamic model of the CLOHP was set up based on conservation laws of mass,momentum and energy.Application results indicate that its oscillation heat transfer dynamics features depend largely on the filling rate,pipe diameter and difference in temperature.Besides,oscillation intensity and transfer performance can be improved to a large extent by increasing the temperature difference properly and enlarging the pipe diameter within a certain range under a certain filling rate.展开更多
基金supported by the National Natural Science Foundation of China (Nos.11972241,11572212 and 11272227)the Natural Science Foundation of Jiangsu Province(No. BK20191454)。
文摘In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied.The quasi-fractional dynamics model here refers to the variational problem based on the definition of RiemannLiouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL).First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained.Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved.The Pfaff-Birkhoff principles,Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article.Finally,some examples are given.
基金Project(531107040300)supported by the Fundamental Research Funds for the Central Universities in ChinaProject(51176045)supported by the National Natural Science Foundation of China
文摘In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system involving multiple parameters was carried out,and a new type oscillation heat transfer dynamic model of the CLOHP was set up based on conservation laws of mass,momentum and energy.Application results indicate that its oscillation heat transfer dynamics features depend largely on the filling rate,pipe diameter and difference in temperature.Besides,oscillation intensity and transfer performance can be improved to a large extent by increasing the temperature difference properly and enlarging the pipe diameter within a certain range under a certain filling rate.
