Monotonicity theorems for two-phase solids
- 46 Downloads
Certain alloys, such as gold-copper, have two solid phases. We establish a general mathematical framework in which we show that the fraction in one phase and the compositions within each phase are in some sense decreasing in the overall composition. The tools used include useful new lemmas on minima of functions of several variables and parameters.
KeywordsNeural Network Complex System Nonlinear Dynamics Electromagnetism Mathematical Framework
Unable to display preview. Download preview PDF.
- [CL]J. W. Cahn & F. Larché, A simple model for coherent equilibrium, Acta Metall. 32 (1984), 1915–1923.Google Scholar
- [FP]R. Fosdick & J. Patiño, On the Gibbsian thermostatics of mixtures, Arch. Rational Mech. Anal. 93 (1986), 203–221.Google Scholar
- [JV]W. C. Johnson & P. W. Voorhees, Phase equilibrium in two-phase coherent solids, Metal. Trans. A 18A (1987), 1213–1228.Google Scholar
- [Kes]J. Kestin, A Course in Thermodynamics, Blaisdell, 1966, II: 303–304.Google Scholar
- [Koh]R. V. Kohn, The relationship between linear and nonlinear variational models of coherent phase transitions, in Trans. 7th Army Conf. on Appl. Math. and Computing, ARO Report 90-1, 1990.Google Scholar
- [LC]H. Le Chatelier, Sur un énoncé des lois des équilibres chimiques, C. R. Acad. Sci. Paris 99 (1884), 786.Google Scholar
- [LMS]F. Larché, F. Morgan & J. M. Sullivan, Phase behavior in coherent equilibria, Scripta Metall. Mater. 24 (1990), 491–493.Google Scholar
- [R]R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.Google Scholar