The area derivative of a space-filling diagram

R. Bryant, H. Edelsbrunner, P. Koehl, M. Levitt, Discrete & Computational Geometry 32 (2004) 293–308.

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Abstract
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 of these weighted areas contribute to the force that drives the motion. In this paper we give formulas for the weighted and unweighted area derivatives of a molecule modeled as a space-filling diagram made up of balls in motion. Other than the radii and the centers of the balls, the formulas are given in terms of the sizes of circular arcs of the boundary and edges of the power diagram. We also give inclusion-exclusion formulas for these sizes.
Publishing Year
Date Published
2004-09-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
Partially supported by NSF under grant CCR-00-86013 and NSF under grant CCR-97-12088.
Volume
32
Issue
3
Page
293 - 308
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Bryant R, Edelsbrunner H, Koehl P, Levitt M. The area derivative of a space-filling diagram. Discrete & Computational Geometry. 2004;32(3):293-308. doi:10.1007/s00454-004-1099-1
Bryant, R., Edelsbrunner, H., Koehl, P., & Levitt, M. (2004). The area derivative of a space-filling diagram. Discrete & Computational Geometry, 32(3), 293–308. https://doi.org/10.1007/s00454-004-1099-1
Bryant, Robert, Herbert Edelsbrunner, Patrice Koehl, and Michael Levitt. “The Area Derivative of a Space-Filling Diagram.” Discrete & Computational Geometry 32, no. 3 (2004): 293–308. https://doi.org/10.1007/s00454-004-1099-1.
R. Bryant, H. Edelsbrunner, P. Koehl, and M. Levitt, “The area derivative of a space-filling diagram,” Discrete & Computational Geometry, vol. 32, no. 3, pp. 293–308, 2004.
Bryant R, Edelsbrunner H, Koehl P, Levitt M. 2004. The area derivative of a space-filling diagram. Discrete & Computational Geometry. 32(3), 293–308.
Bryant, Robert, et al. “The Area Derivative of a Space-Filling Diagram.” Discrete & Computational Geometry, vol. 32, no. 3, Springer, 2004, pp. 293–308, doi:10.1007/s00454-004-1099-1.

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