2015/10/01 20:13 [學術]Poisson-Nernst-Planck and Poisson-Boltzmann type equations

輔 仁 大 學 數 學 系

學 術 演 講

演講人:林太家 教授(國立台灣大學數學系)

講 題:Poisson-Nernst-Planck and Poisson-Boltzmann type equations

日 期:民國104年10月7日(星期三)

時 間:下午4:00~4:50

地 點:輔仁大學數學系MA307教室

茶 會:當日下午4:50於數學系會議室(MA318)

 

Abstract:The Poisson-Nernst-Planck (PNP) system is a well-known model of ion transport, which belongs to Keller-Segel type systems and plays a crucial role in the study of many physical and biological phenomena. Due to the size effect of crowded ions, we derive extra diffusion terms from the energy functional with hard-sphere repulsion and get PNP-steric equations. Symmetry and non-symmetry breaking conditions are represented by their coupling coefficients. When symmetry breaking condition holds true, two steady state solutions can be found and the excess currents (due to steric effects) associated with these two steady state solutions are derived and expressed as two distinct formulas. Our results indicate that PNP-steric equations may become a useful model to study spontaneous gating of ion channels. On the other hand, when non-symmetry breaking condition holds true, steady state PNP-steric equations may become a Poisson-Boltzmann (PB) type equation called the PB_{ns} equation (new Poisson-Boltzmann equation with steric effects). Under specific parameter regimes, the PB_{ns} equation may be reduced to the PB type models of D. Andelman (1997) and B. Li (2009). It would be expected that the PB_{ns} equation may have more applications on electrolytes with high concentrations of ions.

 

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民國104年9月30日

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