The mathematical modelling of matter can take place on at least three
different scales: On the quantum mechanical level via
the Schr\"odinger equation, on an ab-initio level by means
of HF or DFT and on the classical level using
molecular dynamics methods. The arising numerical problems
can efficiently be treated also by multi-scale methods.
We discuss these techniques and show our results from numerical
simulations for applications from the field of nano-technology and biophysics
with special emphasis on the numerical simulation of carbon nanotubes.
Copyright. All Rights Reserved.