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Expansion for the superheating field in a semi-infinite film in the weak-κ limit
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 36 / Issue 6 / November 2002
- Published online by Cambridge University Press:
- 15 January 2003, pp. 971-993
- Print publication:
- November 2002
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- Article
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Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-κ limit. These authors deduceda formal expansion for the superheating field in powers of $\kappa^{\frac{1}{2}}$
up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers of $\kappa^{\frac{1}{2}}$ for the superheating field.
