The Weighted Mean Curvature Derivative of a Space-Filling Diagram

The Weighted Volume Derivative of a Space Filling Diagram

Figure 1: Computing geometric properties of a molecule. As common in biology, atoms are treated as intersecting balls, whose union forms the space-filling diagram. Richards and others proposed to study this union using the Voronoi diagram (or more exactly the power diagram since the balls have different radii). That diagram divides the space into convex cells, one per atom. In the two-dimension...

The weighted-volume derivative of a space-filling diagram.

Computing the volume occupied by individual atoms in macromolecular structures has been the subject of research for several decades. This interest has grown in the recent years, because weighted volumes are widely used in implicit solvent models. Applications of the latter in molecular mechanics simulations require that the derivatives of these weighted volumes be known. In this article, we giv...

The Area Derivative of a Space-Filling Diagram

The motion of a biomolecule greatly depends on the engulfing solution, which is mostly water. Instead of representing individual water molecules, it is desirable to develop implicit solvent models that nevertheless accurately represent the contribution of the solvent interaction to the motion. In such models, hydrophobicity is expressed as a weighted sum of atomic surface areas. The derivatives...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form