# Math Colloquium

*January 13, 2011*

Our first math colloquium of the semester will be **Wednesday, January 19,** from **3:30-4:30**. Chad Williamson, a Truman Student, will be speaking on *Understanding how fronts propagate through flowing fluids – the search for a new model. *As usual,** refreshments will be provided**.

ABSTRACT

Advection-reaction-diffusions systems – systems consisting of a fluid

flow in which a front (perhaps a chemical reaction) is propagating

through a flow – are common in nature and range from cellular-level

processes to plankton blooms in the oceans. Reaction dynamics without

a flow present (reaction-diffusion systems) are well understood, as

are the dynamics of laminar, nonreactive fluid flows (chaotic mixing;

advection-diffusion systems). Extensions of the established theory for

reaction-diffusion systems (the so-called

Fisher–Kolmogorov–Petrowskii–Piscounov Theory), which attempt to

account for the addition of a flow, show major disagreements with

recent experimental observations. Roads the quest for a new theory may

take will be discussed, with an emphasis on the role of coherent

structures in flows (such as vortices) and tools adapted from chaotic

mixing (manifolds and lobes). The discussion will highlight both

computational and experimental research conducted in the Physics

Department at Bucknell University under Tom Solomon during the summer

of 2010, the computational component of which is ongoing here at

Truman. The work is sponsored by National Science Foundation grants

DMR-0703635 and PHY-0552790.