P. Gujrati
University of Akron, Physics and Polymer Science
Recursive Approach for Incorporating Local Correlations in Homogenization
Puru Gujrati
Department of Physics, Department of Polymer Science
The University of Akron
Homogenization is a common technique used in all branches of theoretical physics, ranging from thermodynamics and fluid mechanics to nuclear and particle physics, where there are many length or time scales present. Homogenization is an averaging process over some length scale, and results in a model in terms of an average field with weak correlation. The standard techniques then allow us to solve
the coarse-grained model. In some cases, and that is the focal interest in this
talk, the average field has crucial local correlations that are important such as in superconductivity, gauge theories, polymers, spin glasses, regular glasses, surface effects, etc. In these cases, new techniques have to be developed to make progress. We have developed one such technique, which is recursive in nature
that has been applied successfully to study spin glasses, gauge theories and, in particular, polymeric systems. We will consider two of these problems (polymer
crystallization and glass transition and polymers next to surfaces), describe the nature of the new method and present analytical and numerical results.
