The Steady State for Dendrite Growth with Nonzero Surface Tension
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.
KeywordsDendrite Growth Needle Crystal Composite Solution Expansion Solution Root Condition
Unable to display preview. Download preview PDF.
- 5.2M. Kruskal and H. Segur, “Asymptotics Beyond All Orders in a Model of Crystal Growth”, Stud. in Appl. Math. No. 85, pp. 129–181, (1991).Google Scholar
- 5.3J. 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)Google Scholar
- 5.4D. 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.Google Scholar
- 5.5P. Peke, ‘Dynamics of Curved Front’ (Academic, New York 1988).Google Scholar
- 5.7H. Segur, S. Tanveer and H. Levine (Eds.), ‘Asymptotics Beyond All Orders’ NATO ASI Series, Series B: Physics, Vol. 284, (Plenum, New York 1991).Google Scholar
- 5.8Y. 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).Google Scholar
- 5.10J. Kevorkian, J. D. Cole, ‘Multiple Scale and Singular Perturbation Methods’ Applied Mathematical Sciences, Vol. 114, (Springer, Berlin, Heidelberg 1996).Google Scholar
- 5.11J. 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).Google Scholar
- 5.12S. 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).Google Scholar