Phys. Math. Seminar, MIT, 2-338, 2:30pm, March 14, 2000
"Collapsing Bacterial Cylinders"
Meredith Betterton
Dept of Physics, Harvard University
Under special conditions bacteria excrete an attractant and aggregate. The
pattern formation is driven by the formation of singularities. The high
density regions initially collapse into cylindrical structures, which
subsequently destabilize and break up into spherical aggregates. This
paper presents a theoretical description of the process. Cylindrical
collapse is marginal, which leads to corrections to the collapse laws
expected from dimensional analysis. The instability of a collapsing
cylinder is composed of two stages: Initially, slow modulations to the
cylinder develop, which correspond to a variation of the collapse time
along the cylinder axis. Ultimately, one point on the cylinder pinches
off. At this final stage of the instability, a front propagates from the
pinch into the remainder of the cylinder. The spacing of the resulting
spherical aggregates is determined by the front propagation.