03-492 Pierre Del Castillo

Proof of the Parr Formula for the superheating field (276K, Poscript) Nov 7, 03

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Abstract. In \cite{BoHe4}, in order to prove the De Gennes Formula \cite{Ge1966}, C. Bolley and B. Helffer have obtained an upper bound for the superheating field $h^{sh}(\ka)$ in a semi-infinite film in the weak-$\kappa$ limit. Precisely, they have proved that $\ka \left(h^{sh}(\ka)\right)^2\leq 2^{-\frac{3}{2}}+\mathcal{O}(\ka^{\frac{1}{2}}).$ In this paper, we improve this result and get the upper bound $$ \ka \left(h^{sh}(\ka)\right)^2\leq 2^{-\frac{3}{2}}+\frac{15}{32}\ka+\mathcal{O}(\ka^{1+\rho}),\;\;\;\rho>0. $$ Combining this result with the lower bound for $h^{sh}(\ka)$ obtained in \cite{Ca1}, we deduce the Parr Formula~\cite{parr}.

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