Summary
We review recent progress in the analysis of mean-field models for Ostwald ripening with particular emphasis on their regime of validity and their large-time dynamics.
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References
N. Alikakos, G. Fusco: The equations of Ostwald ripening for dilute systems. J. Stat. Phys., 95, 5/6:851–866, 1999
N. Alikakos, G. Fusco: Ostwald ripening for dilute systems under quasistationary dynamics. Commun. Math. Phys., to appear
A. D. Brailsford, P. Wynblatt: The dependence of Ostwald ripening kinetics on particle volume fraction. Acta met., 27, 489–497, 1979
J. Carr, O. Penrose: Asymptotic behaviour in a simplified Lifshitz-Slyozov equation. Physica D, 124, 166–176, 1998
J. Carrillo, T. Goudon: A numerical study on large-time asymptotics of the Lifshitz-Slyozov system. 2001. preprint.
J.-F. Collet, T. Goudon: On solutions to the Lifshitz-Slyozov model. Nonlinearity, 13, 1239–1262, 2000
J.-F. Collet, T. Goudon, A. Vasseur: Some remarks on large-time asymptotics of the Lifshitz-Slyozov equations. 2001. preprint.
V. E. Fradkov, M. E. Glicksman, S. P. Marsh: Coarsening kinetics in finite clusters. Phys. Rev. E, 53, 3925–3932, 1996
Peter Fratzl, Oliver Penrose, Joel L. Lebowitz: Modeling of phase separation in alloys with coherent elastic misfit. J. Statist. Phys., 95(5-6), 1429–1503, 1999
A. Garroni, B. Niethammer: Correctors and error-estimates in the homogenization of a Mullins-Sekerka problem. IHP Analyse nonlinéaire, 2001. To appear.
B. Giron, B. Meerson, P. V. Sasorov: Weak selection and stability of localized distributions in Ostwald ripening. Phys. Rev. E, 58, 4213–4216, 1998
A. Hönig, B. Niethammer, F. Otto: On first-order corrections to the LSW-theory. 2001. preprint.
P. Laurençot: Weak solutions to the Lifshitz-Slyozov-Wagner equation. Indiana Univ. Math. J., 50, 3, 1319–1346, 2001
P. Laurençot: The Lifshitz-Slyozov-Wagner equation with total conserved volume. 2002. To appear.
P. Laurençot, S. Mischler: From the Becker-Döring to the Lifshitz-Slyozov-Wagner equations. 2002. To appear in J. Stat. Phys.
I. M. Lifshitz, V. V. Slyozov: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids, 19:35–50, 1961
M. Marder: Correlations and Ostwald ripening. Phys. Rev. A, 36, 858–874, 1987
J. A. Marqusee, J. Ross: Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction. J. Chem. Phys., 80, 536–543, 1984
B. Meerson: Fluctuations provide strong selection in Ostwald ripening. Phys. Rev. E, 60, 3, 3072–3075, 1999
B. Meerson, P. V. Sasorov: Domain stability, competition, growth and selection in globally constrained bistable systems. Phys. Rev. E, 53, 3491–3494, 1996
B. Niethammer: Derivation of the LS W-theory for Ostwald ripening by homogenization methods. Arch. Rat. Mech. Anal., 147, 2, 119–178, 1999
B. Niethammer: The LSW-model for Ostwald Ripening with kinetic undercooling. Proc. Roy. Soc. Edinb., 130 A, 1337–1361, 2000
B. Niethammer, F. Otto: Domain coarsening in thin films. Comm. Pure Appl. Math., 54, 361–384, 2001
B. Niethammer, F. Otto: Ostwald Ripening: The screening length revisited. Calc. Var. and PDE, 13, 1,33–68,2001
B. Niethammer, R. L. Pego: Non-self-similar behavior in the LSW theory of Ostwald ripening. J. Stat. Phys., 95, 5/6, 867–902, 1999
B. Niethammer, R. L. Pego: On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald ripening. SIAM J. Math. Anal., 31,3, 457–485, 2000
B. Niethammer, R. L. Pego: The LSW-model for domain coarsening: Asymptotic behavior for total conserved mass. J. Stat. Phys., 104, 5/6, 1113–1144, 2001
B. Niethammer, J. J. L. Velázquez: Exponential screening and homogenization in coarsening systems. 2001. Preprint.
B. Niethammer, J. J. L. Velázquez: Well-posedness for an inhomogeneous LSW-model in unbounded domains. 2001. Preprint
R. L. Pego: Front migration in the nonlinear Cahn-Hilliard equation. Proc. R. Soc. Lond. A, 422, 261–278, 1989
O. Penrose: The Becker-Döring Equations at Large Times and Their Connection with the LSW Theory of Coarsening. J. Stat. Phys., 89, 1/2, 305–320, 1997
E. Seneta: Regular Varying Functions. Springer-Verlag, New York, 1976. Lec. Note in Math. Vol. 508
K. Thornton, N. Akaiwa, P. W. Voorhees: Dynamics of Late-Stage Phase Separation in Crystalline Solids. Phys. Rev. Let., 86, 7, 1259–1262, 2001
M. Tokuhama, K. Kawasaki: Statistical-mechanical theory of coarsening of spherical droplets. Physica A, 123, 386–411, 1984
J. J. L. Velázquez: The Becker-Döring equations and the Lifshitz-Slyozov theory of coarsening. J. Stat. Phys., 92, 195–236, 1998
J. J. L. Velázquez: On the effect of stochastic fluctuations in the dynamics of the Lifshitz-Slyozov-Wagner model. J. Stat. Phys., 99, 57–113, 2000
P. W. Voorhees: The theory of Ostwald ripening. J. Stat. Phys., 38, 231–252, 1985
P. W. Voorhees: Ostwald ripening of two-phase mixtures. Ann. Rev. Mater. Sc, 22, 197–215, 1992
P. W. Voorhees, M. E. Glicksman: Solution to the multi-particle diffustion problem with application to Ostwald Ripening-1. Theory. Acta met., 32, 2001–2011, 1984
C. Wagner: Theorie der Alterung von Niederschlägen durch Umlösen. Z. Elektrochemie, 65,581–594,1961
J. H. Yao, K. R. Elder, H. Guo, M. Grant: Theory and simulation of Ostwald ripening. Phys. Rev. B, 47, 14110–14125, 1993
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Niethammer, B. (2003). The Mathematics of Ostwald Ripening. In: Hildebrandt, S., Karcher, H. (eds) Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55627-2_34
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DOI: https://doi.org/10.1007/978-3-642-55627-2_34
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