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Equilibrium shapes of crystals in a gravitational field: Crystals on a table

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Abstract

We consider the variational problem associated with the equilibrium shape of crystals resting on a table in a gravitational field. For two-dimensional crystals the shape can be calculated explicitly, i.e., reduced to quadrature. In three dimensions only qualitative results are available. The most interesting new result is that for large crystals, under suitable conditions, the top may be a corrugated facet or curved surface. The motivation for this work comes from lowtemperature experiments on helium crystals in equilibrium with the superfluid.

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Author notes

  1. J. E. Avron

    Present address: Department of Physics, Technion, 32000, Haifa, Israel

Authors and Affiliations

  1. Department of Physics, California Institute of Technology, 91125, Pasadena, California

    J. E. Avron

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey

    J. E. Taylor

  3. Physics Department, Virginia Polytechnic Institute & State University, 24060, Blacksburg, Virginia

    R. K. P. Zia

  4. Sektion Physik der Universitat München, München, West Germany

    R. K. P. Zia

Authors
  1. J. E. Avron
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  2. J. E. Taylor
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  3. R. K. P. Zia
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Additional information

Supported in part by NSF grants Nos. MCS 81-19974, MCS 80-0358302, and the Virginia Tech. Educational Foundation.

Alexander von Humboldt Fellow.

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Avron, J.E., Taylor, J.E. & Zia, R.K.P. Equilibrium shapes of crystals in a gravitational field: Crystals on a table. J Stat Phys 33, 493–522 (1983). https://doi.org/10.1007/BF01018830

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  • DOI: https://doi.org/10.1007/BF01018830

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