[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Busseto, Sant'Agata, 2 mars 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Busseto, Sant'Agata, 8 mai 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Sant'Agata, 30 mai 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Tubbiano, 8 septembre 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Sant'Agata, 13 octobre 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Sant'Agata, 12 novembre 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Sant'Agata, 2 décembre 1868]

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[Lettre autographe signée de Giuseppe Verdi adressée à Du Locle, Sant'Agata, 6 décembre 1868]

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Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

Experiments of periodic forcing of Saffman-Taylor fingers

We report on an experimental study of long normal Saffman-Taylor fingers subject to periodic forcing. The sides of the finger develop a low amplitude, long wavelength instability. We discuss the finger response in stationary and nonstationary situations, as well as the dynamics towards the stationary states. The response frequency of the instability increases with forcing frequency at low forcing frequencies, while, remarkably, it becomes independent of forcing frequency at large forcing frequencies. This implies a process of wavelength selection. These observations are in good agreement with previous numerical results reported in [Ledesma-Aguilar et al., Phys. Rev. E 71, 016312 (2005)]. We also study the average value of the finger width, and its fluctuations, as a function of forcing frequency. The average finger width is always smaller than the width of the steady-state finger. Fluctuations have a nonmonotonic behavior with a maximum at a particular frequency.