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Analytic solution of emden-fowler equation and critical adsorption in spherical geometry

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Zeitschrift für Physik B Condensed Matter

Abstract

In the framework of mean-field theory the equation for the order-parameter profile in a spherically-symmetric geometry at the bulk critical point reduces to an Emden-Fowler problem. We obtain analytic solutions for the surface universality class of extraordinary transitions ind=4 for a spherical shell, which may serve as a starting point for a pertubative calculation. It is demonstrated that the solution correctly reproduces the Fisherde Gennes effect in the limit of the parallel-plate geometry.

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Authors and Affiliations

  1. Fachbereich Physik, Universität GH Essen, D-45117, Essen, Germany

    S. Gnutzmann & U. Ritschel

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  1. S. Gnutzmann
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  2. U. Ritschel
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Gnutzmann, S., Ritschel, U. Analytic solution of emden-fowler equation and critical adsorption in spherical geometry. Z. Physik B - Condensed Matter 96, 391–393 (1995). https://doi.org/10.1007/BF01313061

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  • DOI: https://doi.org/10.1007/BF01313061

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