| Abstract: |
| The Lennard-Jones (LJ) potential, a well-known mathematical model for the interaction between a pair of ions, has important applications in many fields of biology, chemistry and physics. Using band-limited functions, we obtained a class of approximate LJ (LJ_a) potentials which can be used to derive PNP-steric equations as a model to describe the ion transport through (biological) channels (with B. Eisenberg, 2014). However, due to the strong singularities of LJ potentials, it is difficult to calculate the Fourier transform of LJ_a potentials. In this lecture, a new class of approximate LJ (LJ_na) potentials with precise formulas of Fourier transform will be introduced. Using techniques of complex analysis, we may prove that the energy of ions interacting by the LJ_na potential can approach to the energy of ions interacting by the LJ_a potential. This may provide a new PNP type model for the ion transport through channels. |
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