Department of Mathematics Colloquium

University of Idaho

 Spring 2012 

Thursday,  January 26, 3:30-4:20 pm, room TLC 032

Refreshments in Brink 305 at 3:00 pm

Geometric aspects of  transformations of forces acting
upon a swimmer in a 3-D incompressible fluid


Alexander  Khapalov

Department of Mathematics

Washington State University


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.