Many multiphysics problems in fluids, materials and biosystems involve time-dependent free boundaries where the boundary motion is mediated by the competition among stabilizing microscopic forces (e.g. surface tension) and destabilizing macroscopic driving forces (e.g. undercooling in crystals, pumping rate in Hele-Shaw flows and external flow for multiphase fluids and biomembranes). In a variety of circumstances, the resulting instabilities that the boundaries experience can be controlled and redirected such that the shapes can be prescribed giving the potential to design materials uniquely targeted to specific technologically important applications.

In this talk, I will focus on the Mullins-Sekerka instability in crystal growth and the Saffman-Taylor instability in Hele-Shaw flows. I will demonstrate that there exist critical conditions such that these instabilities may be suppressed and instead yield attractive, compact self-similarly evolving shapes (universal shapes). We then design protocols by which compact growth with desired symmetries can be achieved. We present both 2D and 3D results using adaptive boundary integral methods. Preliminary experimental results are presented that suggest the confirmation of the theory.

Bio sketch of the speaker

Dr. Li received his B.S. degree from Tongji University, Shanghai, China and M.S. and Ph.D. from the University of Minnesota (UMN), Twin Cities. He is a Doctoral Dissertation Fellow of UMN 2004-2005. Since Fall 2005, he has been a visiting assistant professor in the Math Department, University of California, Irvine. His research interests include computational and applied mathematics, multi-physics problems with applications in materials science and biology.