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Journal article
MINIMAL SURFACE WITH A CAVITY OF GIVEN PERIMETER
Journal of geometry and symmetry in physics, v 28
01 Jan 2012
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Abstract
We pose a variant of the classical minimum surface problem inspired by a simple experiment with soap films: to find the surface of least area containing a cavity of given perimeter. We show that the equilibrium surface is governed by a system of two equations one of which is the zero mean curvature condition. The other equation states that the curvature of the cavity's contour is constant and that its principal normal lies in the plane tangential to the surface. A gradient descent simulation confirms the analytical equilibrium conditions and yields configurations qualitatively consistent with experiment.
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Details
- Title
- MINIMAL SURFACE WITH A CAVITY OF GIVEN PERIMETER
- Creators
- Alex Benjamin - Drexel Univ, Mech Engn, Philadelphia, PA 19104 USARishon Benjamin - Drexel Univ, Chem Engn, Philadelphia, PA 19104 USAPavel Grinfeld - Drexel University
- Publication Details
- Journal of geometry and symmetry in physics, v 28
- Publisher
- Inst Biophysics & Biomedical Engineering, Bulgarian Acad Sciences
- Number of pages
- 8
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000436564300003
- Scopus ID
- 2-s2.0-84874071953
- Other Identifier
- 991019312385004721
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- Web of Science research areas
- Physics, Mathematical