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  3. Discrete Variational Problems with Interfaces
  • Cited by 11
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2024
      December 2023
      ISBN:
      9781009298766
      9781009298780
      DOI:
      https://doi.org/10.1017/9781009298766
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.533kg, 295 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Computational Science, Physics and Astronomy, Condensed Matter Physics, Nanoscience and Mesoscopic Physics, Real and Complex Analysis
      Series:
      Cambridge Monographs on Applied and Computational Mathematics (40)
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    Subjects:
    Mathematics, Computational Science, Physics and Astronomy, Condensed Matter Physics, Nanoscience and Mesoscopic Physics, Real and Complex Analysis
    Series:
    Cambridge Monographs on Applied and Computational Mathematics (40)
    Information

    Book description

    Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.

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