Abstract
During the last two years, important Improvements have been made in the understanding of hydrodynamical instabilities leading to formation of patterns as the Saffman-Taylor fingers, directionnal solidification and free dendrites. Among those instabilities, some lead to a continuous family of steady states as shown some time ago, under the condition that the effects of surface tension are neglected (Gibbs-Thomson effect). When they are included, they are usually believed to be responsible of the velocity selection observed in experiments.
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References
Nash G. C. and GlicksmanM. E., Acta Metal. 22, 1283(1974)
Langer J.S, Rev. Mod. Phys. 52, 1 (1980)
Pelcé P. and Pomeau Y., Studies in App. Math. 74, 245 (1986)
Langer J.S., Phys. Rev. A33, 435 (1986);
Caroli B., Caroli C., Langer J.S. and Roulet B., Phys. Rev. A33,442 (1986)
Kruskal M. and Segur H., “Asymptotics Beyond all Orders In a Model of dendritic Crystals” Aero. Res. Ass. of Princeton Tech. Memo. (1985)
Ben Amar M. and B. Moussallam, “Numerical Results on Two Dimensionnal Dendritic solidification”, to appear in Physica D
Ben Amar M. and Pomeau Y. Euro. Lett., 2(4) 307(1986)
Caginalp G., “The Role of Microscopic Anisotropy in the Macroscopic Behavior of a Phase Boundary”, University of Pittsburgh preprint (1986)
Vanden Broeck J.M., Phys. Fluids 26, 2033 (1983)
Shraiman B., Phys. Rev. lett., 56 2028 (1986);
Hong D.C. and Langer J.S. Phys. Rev. Lett., 56 2032 (1986);
Combescot R., Dombre T., Hakim V., Pumir A. and Pomeau Y., Phys. Rev. Lett. 56 2036 (1986)
Bender C..M. and Orzag S. A., “Advanced Mathematical Methods For Scientists And Engineers ” (McGraw-Hill Co., new York, N.Y.) 1979
Ben-Jacob E., Goldenfeld N.D., Kotliar G., Langer J.S. Phys. Rev. Lett. 53, 2110 (1984)
Gradshteyn I.S. and Ryzhik I. M., “Table of Integrals, Series And Products”, (Academic Press) 1980
Kessler D.A., Koplik J. and Levine H, Phys. Rev. A33, 3352 (1986); Kessler D.A., Koplik J., Levine H., Proceedings of Nato A.R.W on “Patterns, Defects and Microstructures in Non equilibrium Systems”, (Austin, Texas, March 1986)
Caroli B., Caroli C, Roulet B., “On Velocity Selection for 2-d Needle-Crystals in a Fully non Local Model of Solidification”, Ecole Normale Superieure Preprint (1986)
Barbieri A., Hong D.C. and Langer J.S.,“Velocity Selection in the Symmetric model of Dendritic crystal growth”, Preprint (1986)
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© 1988 Plenum Press, New York
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Amar, M.B., Pomeau, Y. (1988). Theory of the Needle Crystal. In: Velarde, M.G. (eds) Physicochemical Hydrodynamics. NATO ASI Series, vol 174. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0707-5_37
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DOI: https://doi.org/10.1007/978-1-4613-0707-5_37
Publisher Name: Springer, Boston, MA
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