2003 -11 -05
10 :15 at ML J 21

The Kinetic Basis of Molecular Individualism and the Difference Between Ellipsoid and Parallelepiped

Alexander Gorban

Institute of Polymers, Polymer Physics, ETH Zurich

>>I think the next century will be the century of complexity<< (Stephen Hawking)

The notion of >Molecular Individualism< is rather young: It was introduced in 1997 by Nobel Prize winner P. G. de Gennes in his comments to the paper of Nobel Prize winner S. Chu et al. In this paper the stretching of individual polymers in a spatially homogeneous velocity gradient was observed. At the highest strain rates, distinct conformational shapes with differing dynamics were observed. Molecules behaviour was much more individual than expected. This type of behaviour was reproduced in computational molecular dynamics.
The problem of molecular individualism can be discussed as a complexity problem: how to understand this phenomenon with models which are not so complex as the observed behaviour?
The kinetic basis of molecular individualism is discussed. Models of linear complexity for phenomenon of exponential complexity are demonstrated. Different approximations for multidimensional Fokker-Planck equations are proposed.
The following issues will be discussed:

1. The challenge of complexity and the problem of molecular individualism.
2. Static and dynamic molecular individualism.
3. Mean-field theory of static molecular individualism.
4. Is it possible to describe an exponential complexity of phenomenon with models of polynomial (or even linear) complexity?
5. FENE-P models. Stability and explosion of Gaussian manifold.
6. Polymodal parallelepiped is a generic model for systems with instabilities.
7. Multidimensional Fokker-Planck equation, neurons and particles.
8. Conclusion and outlook.