### Wednesday, May 14

3:00 PM -4:40 PM

*Peale B Room*

## MS37

Coarse Graining and Renormalization in Material Diffusion

Renormalization and coarse graining methods have been a crucial tool used by physicists to understand complex phenomena in equilibrium condensed matter problems. The methods have been used in a number
of other problems where the collections of a huge amount of information is neither possible or illuminating about the basic nature of the phenomenon.

The diverse set of methods bear the essential feature of determining the transformation that performs the ''coarse graining'' by averaging the details of the system, and understanding the limiting behavior of
these transformations. In principle, the methodology should be adaptable to many of the most interesting questions that involve differential equations arising from materials science. In complex problems such as sidebranching of dendritic growth and Hele-Shaw patterns, the coarse graining methods may provide a perspective that complements the one obtained from a detailed large scale computation.

The speakers in this minisymposium discuss the applications of this methodology to some basic differential equations of materials science and the understanding of the methodology within an applied mathematical
context. Renormalization techniques have proven to be extremely useful for the theory of equilibrium critical phenomena but have only relatively recently been used in dynamical problems involving differential equations. The speakers will introduce the basic ideas and summarize some recent results in a way that does not require previous knowledge of the subject.

**Organizer: Gunduz Caginalp**

*University of Pittsburgh*

**3:00-3:20 A Renormalization Group Calculation of Anomalous Exponents for Nonlinear Diffusion**
- Gunduz Caginalp, Organizer
**3:25-3:45 Numerical Analysis of a 1-Dimensional Immersed-Boundary Method**
- Michael J. Shelley, Courant Institute of Mathematical Sciences, New York University
**3:50-4:10 Renormalization Group as a Unifying Means of Singular and Reductive Perturbations**
- Nigel Goldenfeld and
*Yoshitsuger Oono*, University of Illinois, Urbana-Champaign
**4:15-4:35 Second Type Scaling and Instability Lubrication-Type Equations**
- Andrea Bertozzi, Duke University

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*MMD, 5/1/97*