This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a n...This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.展开更多
This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is...This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.展开更多
The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are...The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.展开更多
The Poisson–Boltzmann(PB)theory is one of the most important theoretical models describing charged systems continuously.However,it suffers from neglecting ion correlations,which hinders its applicability to more gene...The Poisson–Boltzmann(PB)theory is one of the most important theoretical models describing charged systems continuously.However,it suffers from neglecting ion correlations,which hinders its applicability to more general charged systems other than extremely dilute ones.Therefore,some modified versions of the PB theory are developed to effectively include ion correlations.Focused on their applications to ionic solutions,the original PB theory and its variances,including the field-theoretic approach,the correlation-enhanced PB model,the Outhwaite–Bhuiyan modified PB theory and the mean field theories,are briefly reviewed in this paper with the diagnosis of their advantages and limitations.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)
文摘This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China(12272248,11972241)。
文摘The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA17010504)the National Natural Science Foundation of China(Nos.11774357 and 11947302)the CAS Biophysics Interdisciplinary Innovation Team Project(No.2060299)。
文摘The Poisson–Boltzmann(PB)theory is one of the most important theoretical models describing charged systems continuously.However,it suffers from neglecting ion correlations,which hinders its applicability to more general charged systems other than extremely dilute ones.Therefore,some modified versions of the PB theory are developed to effectively include ion correlations.Focused on their applications to ionic solutions,the original PB theory and its variances,including the field-theoretic approach,the correlation-enhanced PB model,the Outhwaite–Bhuiyan modified PB theory and the mean field theories,are briefly reviewed in this paper with the diagnosis of their advantages and limitations.
