Annual Report 2008.pdf - SAMSI

Purdue University
Center for Computational & Applied Mathematics
mdehoop@math.purdue.edu
"Analysis of Field-Field Cross Correlations in Random Media and Seismic Interferometry in SE
Tibet"
Weinan E
Princeton University
Department of Mathematics
weinan@math.princeton.edu
"Some Representative Issues in Multiscale Modeling"
This talk will focus on the methodologies for efficiently capturing the macroscale behavior of a
system using microscopic models. I will try to give a candid assessment of the current status of
the field, discussing both the main successes and the major difficulties. I will start by reviewing
some of the classical methodologies. I will then discuss the attempts that have been made to
construct general frameworks. I will present a relatively new strategy for constructing seamless
techniques that do not require going back and forth between the macro and micro states of the
system. If time permits, I will also discuss some typical instabilities and inconsistencies that can
arise in multiscale methods. Finally, I will discuss what can be done for systems that do not have
scale separation or any other special features.
Bjorn Engquist
University of Texas-Austin
Department of Mathematics
engquist@math.utexas.edu
“Interface Tracking in Connection to Multiscale Processes”
Lisa Fauci
Tulane University
Department of Mathematics
fauci@tulane.edu
“Interface Problems Inspired by the Biofluidmechanics of Reproduction”
Complex fluid-structure interactions are central to mammalian fertilization. Motile spermatozoa,
muscular contractions of the uterus and oviduct, as well as ciliary beating generate forces that
drive fluid motion. At the same time, the dynamic shapes of these biostructures are determined
by the fluid mechanics. In many of these systems, the fluid exhibits non-Newtonian
characteristics. While much progress has been made in the development of mathematical models
and numerical methods for fluid-structure interactions in a Newtonian fluid, much work needs to
be done in the case of complex fluids. In this talk we will give an overview of the classical work
in fluid dynamics that has been applied to reproduction. We will also present recent