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Multiscale methods

People:  Yuen Au Yeung
  Marco Cicalese
  Gero Friesecke
  Alice Mikikits-Leitner
  Sarah Rathbauer

Mechanical examples of truly multiscale systems include bulk solids, polymers, biological membranes, proteins. Their large-scale mechanical response is governed by a small number of active "modes", but both these modes and the constitutive parameters driving their behaviour depend crucially on the details of the underlying microstructure at a large spectrum of length- and timescales (e.g., in case of a bulk alloy, positions and energy barriers of the individual atoms, crystallographic phases, grains, dislocations, and cracks). A key challenge, which in complex examples lies well beyond current mathematical understanding, is to relate or couple the relevant mathematical models at the different scales.

Our own research concerns carefully chosen model systems which exhibit central difficulties appearing in more complex systems. In particular, we study

Recent workshop

Development and Analysis of Multiscale Methods Pfeil
IMA Annual Program Year Workshop,
University of Minnesota, USA, November 3-7, 2008
Organizers:
Frank L. H. Brown, Chemistry and Biochemistry, University of California
Anne M. Chaka, National Institute of Standards and Technology
Gero Friesecke, Mathematics, TU Munich
Kurt Kremer, Max Planck Institute for Polymer Research, Mainz
Yousef Saad, Computer Science and Engineering, University of Minnesota
Gregory A. Voth, Theoretical and Physical Chemistry, University of Utah

Publications