Hyon, YunkyongEisenberg, BobLiu, Chun2016-06-062016-06-062010-06https://hdl.handle.net/11299/1809051 online resource (PDF, 14 pages, includes illustrations)enFinite size effectsEnergetic variational approachPoisson-Nernst-Planck equationsHard sphereLennard-Jones repulsive potentialHard sphere potential in density functional theoryIon channels(MSC2010)76A05(MSC2010)76M99(MSC2010)65C30A mathematical model for the hard sphere repulsion in ionic solutionsPreprint