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.