Abstract
In the last chapter we derived the steady asymptotic solution which we called the RPE solution. However, so far we have not specified the steady state solution itself. How to specify the steady state solution in dendrite growth is an important subject which must be approached with great caution. In the literature, many researchers have looked for the classic, steady needle solution for dendrite growth. Such efforts have not been successful for the case of isotropic surface tension.
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References
G. E. Nash, and M. E. Glicksman, “Capillarity-limited Steady-State Dendritic Growth I. Theoretical Development”, Acta Metall. 22, pp. 1283–1299, (1974).
M. Kruskal and H. Segur, “Asymptotics Beyond All Orders in a Model of Crystal Growth”, Stud. in Appl. Math. No. 85, pp. 129–181, (1991).
J. S. Langer, ‘Lectures in the Theory of Pattern Formation’ USMG NATO AS Les Houches Session XLVI 1986 - Le hasard et la matiere/ chance and matter. Ed. by J. Souletie, J. Vannimenus and R. Stora, (Elsevier Science, Amsterdam 1986)
D. A. Kessler, J. Koplik and H. Levine, “Pattern Formation Far from Equilibrium: the free space dendritic crystal”, in ‘Proc. NATO A.R. W. on Patterns, Defects and Microstructures in Non-equilibrium Systems’ Austin, TX, March 1986.
P. Peke, ‘Dynamics of Curved Front’ (Academic, New York 1988).
E. A. Brener and V. L. Melnikov, “Pattern Selection in Two Dimensional Dendritic Growth”, Adv. Phys. 40, pp. 53–97, (1991).
H. Segur, S. Tanveer and H. Levine (Eds.), ‘Asymptotics Beyond All Orders’ NATO ASI Series, Series B: Physics, Vol. 284, (Plenum, New York 1991).
Y. Pomeau, M. Ben Amer, “Dendrite Growth and Related Topics” in ‘Solids Far Prom Equilibrium’ Ed. by C. Godreche, (Cambridge University Press, Cambridge, New York 1991).
J. J. Xu, “Interfacial Wave Theory of Solidification - Dendritic Pattern Formation and Selection of Tip Velocity”, Phys. Rev. A15 43, No: 2, pp. 930–947, (1991).
J. Kevorkian, J. D. Cole, ‘Multiple Scale and Singular Perturbation Methods’ Applied Mathematical Sciences, Vol. 114, (Springer, Berlin, Heidelberg 1996).
J. K. Hale, L. T. Magalhaes and W. M. Oliva ‘An Introduction to Infinite Dimensional Dynamical Systems- Geometric Theory’ Series of Applied Mathematical Sciences, Vol. 47, Ed. by F. John, J. E. Marsden, L. Sirovich, (Springer, New York 1984).
S. Wiggins, ‘Global Bifurcations and Chaos: Analytical Methods’ Series of Applied Mathematical Sciences, Vol. 73, Ed. by F. John, J. E. Marsden, L. Sirovich, (Springer, New York 1988).
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© 1998 Springer-Verlag Berlin Heidelberg
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Xu, JJ. (1998). The Steady State for Dendrite Growth with Nonzero Surface Tension. In: Interfacial Wave Theory of Pattern Formation. Springer Series in Synergetics, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80435-9_5
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DOI: https://doi.org/10.1007/978-3-642-80435-9_5
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