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Published April 1, 1986 | public
Journal Article Open

Selection of steady states in the two-dimensional symmetric model of dendritic growth


Selection of steady needle crystals in the full nonlocal symmetric model of dendritic growth is considered. The diffusion equation and associated kinematic and thermodynamic boundary conditions are recast into a nonlinear integral equation which is solved numerically. For the range of Peclet numbers and capillarity lengths considered it is found that a smooth solution exists only if anisotropy is included in the capillarity term of the Gibbs-Thomson condition. The behavior of the selected velocity and tip radius as a function of undercooling is also examined.

Additional Information

©1986 The American Physical Society. Received 16 September 1985. I would like to thank Jim Langer, Yves Pomeau, Nigel Goldenfeld, Gabi Kotliar, and Alain Karma for stimulating discussions and for making their results available prior to publication. I would also like to acknowledge the hospitality of the Institute for Theoretical Physics, University of California at Santa Barbara, where much of this work was done. This work was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AT03-76ER72012.


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August 22, 2023
October 16, 2023