Andrew S. Johnson ’09
St. Louis Park, Minnesota
Mathematics, Economics
The work leading to my summer
research project began in late
January as I helped Professor
Chad Topaz build the XMAC lab
and began creating an experiment
in swarm theory.
Swarm theory deals with the process
by which organisms interact
to form a unit that acts as a separate
unit, but is not controlled by
any central authority. A wonderful
example of swarming is seen
in flocks of birds and schools of
fish—no single bird or fish tells
the rest to follow in a specific
pattern. It is possible to create
models that approximate the
motion of swarms using simple
assumptions about interactions.
Did you know?
Swarm intelligence is used to develop
spacecraft for
exploration and to improve business efficiency.
One model I studied assumes
that the organisms interact with
the nearest “x” neighbors, where
x depends on sensory limits of
the specific organism, and it
leads to the formation of a pattern
similar to that of flocking
birds.
After some background research,
it was time to find an organism
suitable for an applied mathematics
laboratory. Lacking space
for flocking of birds in the XMAC
lab, I set out to find something
significantly smaller, settling on
a garden pest, the aphid. Aphids
are tiny, and easily kept alive in
lab conditions, which makes them
perfect for experimentation.
They are essentially
plant vampires; they
suck the juices from
plants for nourishment.
My goal was to model
aphids on a search for
food, as individuals and
in groups, and compare
the two in an attempt
to find some support
for their swarming
tendencies. Data were
gathered by filming
the aphids in a circular
arena, breaking the
film into frames, and
then using a program
that connects the positions
of the aphids in
each frame. With a list
of coordinates for the
aphids, we wrote a program
that plots these
coordinates and finds
the turning angle for
each turn. We worked
on creating a model
for the overall movement,
then comparing
the model for single
aphids with those of
multiple aphids to see if
there was a significant
difference.
This project became my math major capstone
project, so I spent my senior year
working on it, presenting the research in
the spring. The most surprising part of the
research was just how enjoyable it can be
to spend 40 hours a week in the lab, and
how great it feels to take an idea and turn
it into an experiment that carries on for
over a year.
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