Math Colloquia: Alexander Khapalov (Washington State University)
Thursday, January 26 2012 at 3:30 PM
Location: TLC 032
TITLE: Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid
ABSTRACT: The swimming phenomenon has been a source of great interest and inspiration for many researchers for a long time, with formal publications traced as far back as to the works of G. Borelli in 1680--1681.
The goal of this particular lecture is to discuss how the geometric shape of a swimmer affects the forces acting upon it in a 3-D incompressible fluid, such as governed by the nonstationary Stokes or Navier-Stokes equations.
Namely, we are interested in the following question: How will the swimmer's internal forces (i.e., not moving the center of swimmer's mass when it is not inside a fluid) ``transform'' their actions when the swimmer is placed
inside a fluid (thus, possibly, creating its self-propelling motion)?
We focus on the case when the swimmer's body consists of either small parallelepipeds or balls. Such problems are of interest in biology and engineering application, as well as in mathematical control theory, dealing with propulsion systems in fluids.
This is a joint work with Giangbang Trinh.