The Weighted Mean Curvature Derivative of a SpaceFilling Diagram
Abstract
Representing an atom by a solid sphere in $3$dimensional Euclidean space, we get the spacefilling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [HRC13,RHK06] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the spacefilling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [EdKo03], the weighted area in [BEKL04], and the weighted Gaussian curvature [AkEd19], this yields the derivative of the morphometric expression of the solvation free energy.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.06779
 Bibcode:
 2019arXiv190806779A
 Keywords:

 Computer Science  Computational Geometry;
 Physics  Biological Physics
 EPrint:
 20 pages, 4 figures