Professor Albert Fannjiang, an applied analyst, will enhance the existing group of strong analysts working in fluid dynamics, extending the scope of the group to wider applications and interactions including possible collaboration with the Engineering School.
Professor Alexander Mogilner, a mathematical biologist, is a strong addition to the existing group of excellent mathematical biologists on campus, and is expected to increase interactions between the Department of Mathematics and the Institute of Theoretical Dynamics.
The research area of Professor Fannjiang is applied analysis. He has been working on the theory of homogenization together with applications to particle dispersion and wave propagation in periodic and random media. He, in collaboration with Papanicolaou, turned the variational methods into a powerful tool of studying the large scale behaviors and small diffusion asymptotics for convection diffusion processes. They obtained sharp results for the homogenization condition and for the transport coefficients. Their results not only gave rigorous justification of physical theories but also provide an effective methods of computing physical quantities. The application to diffusions in two dimensional steady periodic or random flows has been quite successful.
The sharp homogenization conditions for time dependent turbulence are not known and the transport and mixing coefficients for chaotic flows are difficult to calculate. Professor Fannjiang expects to extend the variational methods to the former systems. For the latter systems, the numerical computations are a delicate issue. Collaborating with Professor Bill Morokoff at UCLA, he plans to adopt wavelet bases within the variational framework to obtain stable and efficient algorithms.
Currently, he is also studying the asymptotic behaviors of randomly perturbed dynamical systems on various time scales.
Professor Fannjiang is originally from Taiwan. He lives in Davis with his wife and their daughter.
He then jumped into mathematical biology. In 1992, Dr. Mogilner joined the Mathematics Department of the University of British Columbia, Canada, as a graduate student. It was indeed a big transition for him. There he received his Ph.D. Degree in Applied Mathematics this past summer.
In his new research area of mathematical modeling in cell and molecular biology, Dr. Mogilner has published already three papers in Journal of Mathematical Biology and Physica D. The problems treated in these papers concerned a wide variety of biological phenomena of aggregation and alignment of cells and proteins (such as actin) in cytoplasm. The spatio-angular distributions of cells and molecules were described by systems of non-linear integro-differential equations. Apart from the purely mathematical significance of the research the applications to such important event of life as morphogenesis were considered.
Professor Mogilner is on leave for the academic year 1995-96 at the University of California, Berkeley, as a Fellow in the prestigious Program in Mathematics and Molecular Biology (there are only 4 Fellows nationwide). There he will conduct a joint research with Professor G. Oster.
The main project will be to model mathematically motions of cell driven by actin polymerization. The description of these processes leads to some complex equations of Fokker-Planck type and is of vital importance for the understanding of phagocytosis and spreading of some pathogenic bacteria. Another goal will be to create and treat a model of the flagella motor, astonishing device of molecular size which bacteria use to swim.
Professor Mogilner will start his research and teaching in Davis in Fall 1996. He plans to start a number of projects in mathematical biology including modeling of pattern formation in bacterial swarms and dynamics of cytoplasm and cytoskeleton.
(M.M., as the Former Chair of the Search Committee, with
A.F. and A.M.)