Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvationmodel proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvationmodel is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.