EAN: 9789462391536

MEAN FIELD THEORIES AND DUAL VARIATION - MATHEM...

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic
overviews. It is still in progress  fluid mechanics  gauge theory  plasma physics  quantum
chemistry  mathematical oncology  non-equilibirum thermodynamics. spite of such a wide range of
scientific areas that are concerned with the mean field theory  a unified study of its
mathematical structure has not been discussed explicitly in the open literature. The benefit of
this point of view on nonlinear problems should have significant impact on future research  as
will be seen from the underlying features of self-assembly or bottom-up self-organization which
is to be illustrated in a unified way. The aim of this book is to formulate the variational and
hierarchical aspects of the equations that arise in the mean field theory from macroscopic
profiles to microscopic principles  from dynamics to equilibrium  and from biological models to
models that arise from chemistry and physics.

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