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IMA Annual Program Year Tutorial
Physics and Mathematics of Multiscale Modeling for Chemistry and Materials
November 2, 2008

  Organizers
Weinan E Mathematics and Program in Applied and Computational Mathematics, Princeton University
Burkhard Dünweg Max-Planck-Institut für Polymerforschung
Richard D. James Aerospace Engineering and Mechanics, University of Minnesota
  Description

Macroscopic properties of materials and whole systems are the consequence of specific local interactions and cooperative effects on many different length and time scales ranging from truly microscopic, i.e. on the level of individual atoms, to the meso- and macrosopic regime. Physics and chemsitry over many years have tried to elucidate the underlying mechanisms and to then use them for artificial, synthetic materials and systems. Theory has played a pivotal role in identifying general principles and providing general guidelines or looking at some specific details. With modern computational methods now it becomes more and more possible to go beyond the isolated approaches mentioned above and link the different prviously well separated studies. This provides a potential route for truly quantitative structure property relations. This however also requires new ways of thinking and poses many computational and mathematical challenges. The tutorial will provide an introduction into this world of multiscale modelling. Starting from materials, often named ''hard matter'' such as crystals or glasses made of inividual atoms or small molecules basic principles and the physical motivation will be explained (R.D. James). In a next step towards polymers systems of very large molecules with many internal degrees of freedom in contrast to the previous case will be introduced (B. Duenweg). These two cases provide the physical motivation, questions and already some first answers to the mathamatical aspects of multiscale modelling, which will be introduced in the last lecture by E. Vanden Eijnden and W. E.

  Schedule
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