This program is broadly concerned with fundamental challenges
of modeling, analysis and computation for (mostly)
incompressible fluid dynamics. Much attention will be focused
on non-Newtonian fluids in which complex material constitutions
produce nonlinear and/or nonlocal relationships between
stresses and rates-of-strain (and sometimes strains) leading to
unique and often unforeseen flow phenomena. Complex fluids are
ubiquitous in engineering applications and the applied sciences
from biology to geology. They serve as the focus of active
areas of research within the larger fluid dynamics community.
Complex flows include those of both simple and complex fluids
in simple and complex domains, in the presence of moving
boundaries, and turbulent flows. Key questions for such flows
include transport and mixing properties, and flow-structure
interactions generating motions including swimming, flying,
sliding and crawling. Recent research has revealed new
connections between fluid characteristics, flow complexity and
transport properties that will in part serve as a unifying
theme throughout the program.
The year will be organized around specific themes highlighted by
six week-long workshops encompassing the following topics:
Rheology of complex fluids
Dynamics of complex fluids
Microfluidics and electrokinetic and interfacial
phenomena
Analysis and computation of simple and complex fluids
Transport and mixing in complex and turbulent flows
Fluid-structure interactions and locomotion
The mathematical scope of this program will be very broad,
ranging from fundamental modeling questions through issues of
computation, simulation, approximation and analysis. Program
participants will include researchers from the engineering and
applied sciences, including both theorists and
experimentalists, numerical analysis and scientific
computation, and both
applied and abstract analysts. A central goal of the program
will be to bring these interdisciplinary perspectives together
and facilitate productive engagement. Toward this end, each
focused week-long workshop will be preceded by introductory
tutorials aimed at researchers from neighboring areas.
