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Science 1 August 1986:
Vol. 233. no. 4763, pp. 548 - 551
DOI: 10.1126/science.233.4763.548
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Articles

A Cusp Singularity in Surfaces That Minimize an Anisotropic Surface Energy

JEAN E. TAYLOR 1 and JOHN W. CAHN 2

1 Mathematics Department, Rutgers, the State University of New Jersey, New Brunswick, NJ 08903.
2 Center for Materials Science, National Bureau of Standards, Gaithersburg, MD 20899.

A mathematical proof shows that a surface with a cusp-shaped singularity can arise from minimizing an anisotropic surface free energy for a portion of a crystal surface. Such cusps have been seen on crystal surfaces but usually have been interpreted as being the result of defects or nonequilibrium crystal growth. Our result predicts that they can occur as equilibrium or near-equilibrium phenomena. It also enriches the mathematical theory of minimal surfaces.

Submitted on December 19, 1985
Accepted on March 13, 1986

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Science. ISSN 0036-8075 (print), 1095-9203 (online)