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Award ID contains: 2110767

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  1. ; ; (, Journal of Computational Electronics)
    Abstract An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K$$^+$$ +  ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results. 
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  2. ; ; (, The Journal of Physical Chemistry B)
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