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An Application of the Modular Function in Nonlocal Variational Problems

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Abstract

Using the modular function and its invariance under the action of a modular group and an heuristic reduction of a mathematical model, we present a mathematical account of a hexagonal pattern selection observed in di-block copolymer melts.

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Author notes

  1. Yoshihito Oshita

    Present address: Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushimanaka, Okayama, 700-8530, Japan

Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Xinfu Chen

  2. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan

    Yoshihito Oshita

Authors
  1. Xinfu Chen
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  2. Yoshihito Oshita
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Correspondence to Yoshihito Oshita.

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Communicated by F. Otto

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Chen, X., Oshita, Y. An Application of the Modular Function in Nonlocal Variational Problems. Arch Rational Mech Anal 186, 109–132 (2007). https://doi.org/10.1007/s00205-007-0050-z

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  • DOI: https://doi.org/10.1007/s00205-007-0050-z

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