An analytic expression for the electrostatic potential of a point charge within a concentric multilayered dielectric medium is derived in terms of a Legendre expansion. A novel Brownian dynamics algorithm for solving the Poisson equation for the reaction-field potential of charges near dielectric interfaces is presented. To test both the computed and analytic solutions, the reaction-field potential and self-energy of a charge within a liposome are calculated and compared.
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Zaloj et al. (1998) studied this question.
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