Poisson-Nernst-Planck systems are basic models for electrodiffusion process,particularly,for ionic flows through ion channels embedded in cell membranes.In this article,we present a brief review on a geometric singula...Poisson-Nernst-Planck systems are basic models for electrodiffusion process,particularly,for ionic flows through ion channels embedded in cell membranes.In this article,we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model.The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and,most crucially,on the reveal of two specific structures of Poisson-Nernst-Planck systems.As a result of the geometric framework,one obtains a governing system-an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions,and hence,provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties.As an illustration,we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.展开更多
A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin i...A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.展开更多
基金supported by Simons Foundation Mathematics and Physical Sciences-Collaboration Grants for Mathematicians 581822。
文摘Poisson-Nernst-Planck systems are basic models for electrodiffusion process,particularly,for ionic flows through ion channels embedded in cell membranes.In this article,we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model.The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and,most crucially,on the reveal of two specific structures of Poisson-Nernst-Planck systems.As a result of the geometric framework,one obtains a governing system-an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions,and hence,provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties.As an illustration,we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.
基金Project supported by the National Natural Science Foundation of China(Nos.11672265,11202182,and 11621062)the Fundamental Research Funds for the Central Universities(Nos.2016QNA4026 and2016XZZX001-05)the Open Foundation of Zhejiang Provincial Top Key Discipline of Mechanical Engineering
文摘A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.
