# The Weighted Mean Curvature Derivative of a Space-Filling Diagram

@article{Akopyan2020TheWM, title={The Weighted Mean Curvature Derivative of a Space-Filling Diagram}, author={Arseniy V. Akopyan and Herbert Edelsbrunner}, journal={Computational and Mathematical Biophysics}, year={2020}, volume={8}, pages={51 - 67} }

Abstract Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling 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 [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the…

## 2 Citations

The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

- MathematicsComputational and Mathematical Biophysics
- 2020

The morphometric approach to solvation free energy is rewritten as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram and a formula is given for the derivative of the weighted GaRussian curvature.

On M-theory on real toric fibrations

- Mathematics
- 2021

Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory…

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