Program

The following is a tentative schedule, still subject to change.

Friday March 9th

  • 6:30-8:30pm Registration Reception (Hampton Inn)
    • light hors d’oeuvres

Saturday March 10th

Sunday March 11th

Plenary Talks

New Methods for Tracking Evolving Interfaces: Voronoi Implicit Interface Methods with Applications to Industrial Foams, Biological Cell Clusters, and Domain Decomposition

J.A. Sethian
Dept. of Mathematics
University of California, Berkeley

Many scientific and engineering problems involve interconnected moving interfaces separating different regions, including dry foams, crystal grain growth,  and multi-cellular structures in man-made and biological materials. Producing consistent and well-posed mathematical models that capture the motion of these interfaces, especially at degeneracies, such as triple points and triple lines where multiple interfaces meet, is challenging.

Joint with Robert Saye of UC Berkeley, we have built the Voronoi Implicit Interface Method (VIIM), which is an efficient and robust mathematical and computational methodology for computing the solution to two and three-dimensional multi-interface problems involving complex junctions and topological changes in an evolving general multiphase system. We demonstrate the method on a collection of problems, including geometric coarsening flows under curvature, incompressible flow coupled to multi-fluid interface problems, and biological cell cluster growth under competing effects of geometry, fluid dynamics, and elasticity.

Finally, we compute the dynamics of unstable foams, such as soap bubbles, evolving under the combined effects of gas-fluid interactions, thin-film lamella drainage, and topological bursting.

A model of collective motion of self-propelled organisms

Ricardo Cortez
Tulane University, New Orleans

We consider the motion and interaction of self-propelled microscopic swimmers, such as bacteria, immersed in a viscous fluid. Their motion is coupled through the fluid, producing complex flow structures such as wakes and eddies that are important to investigate due to their application in transport and mixing. In order to study collective motion, it is convenient to develop a reduced model for each organism so that computations are feasible. I will present a new reduced model of self propelled organisms in low Reynolds number viscous incompressible flows. The model is based on a particular limit of regularized Stokeslets (the fundamental solution of Stokes equation in free space) with built-in asymmetry in order to produce a swimming direction. The result is a single-particle model of a swimmer that does not require special treatment of the self velocity due to the regularization.  Modeling “pusher” and “puller” organisms is straightforward and the model can also be extended to flows bounded by a plane wall using a method of images. I will show numerical examples characterizing the particle dynamics and discuss the diffusion of these particles as a function of the concentration density.