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Discrete Variational Problems with Interfaces by Roberto Alicandro

Discrete Variational Problems with Interfaces

by Roberto Alicandro , Andrea Braides , Marco Cicalese
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Book cover type: Hardcover
  • ISBN13: 9781009298780
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 295
  • Original Price: GBP 94.0
  • Language: English
  • Edition: N/A
  • Item Weight: 577 grams
  • BISAC Subject(s): Mathematical Analysis

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.

Alicandro, Roberto: - Roberto Alicandro is Full Professor at the University of Naples. He works in the calculus of variations and homogenization. His results have applications in different fields, including atomistic-to-continuum limits for nonlinear models in materials science, topological singularities and defects in materials. He co-authored the monograph 'A Variational Theory of Convolution-type Functionals' (2022).

Braides, Andrea: - Andrea Braides is Full Professor at SISSA (International School for Advanced Studies), Trieste. He was an Invited Speaker at the 2014 International Congress of Mathematicians and received the Levi-Civita prize in 2015. He is the author of five books including 'Gamma-convergence for Beginners' (2002 ), 'Local Minimization, Variational Evolution and Gamma-convergence' (2014) and 'Geometric Flows on Planar Lattices' (2021).

Cicalese, Marco: - Marco Cicalese is Professor of Mathematical Continuum Mechanics at the Technical University of Munich. He works in the calculus of variations and its applications to materials science.

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