Mathematics
and Computer Science Speaker Series
California State University, Stanislaus
Date: Friday, September 24,
2010
Time: 4:00 - 5:00 p.m
Room: TBA
Speaker: Jonathan Sarhad
Title: Applications of Differential Equations in
Advective Ecological Systems
Abstract: There is much interest in modeling population
dynamics in advective ecological systems using differential
equations. A specific example is given by river and stream
ecologies, where the system is greatly affected by a uni-directional
hydrologic flow. Population dynamics at various trophic levels in
a river or stream, such as algae, fly larvae, and fish, are influenced
by flow, individually and as parts of integrated systems.
Kurt Anderson from the University of California, Riverside, and
collaborators have studied effects of flow in one dimensional models of
advective systems. They have identified a parameter, called the response length of the system,
which measures a system's equilibrium response to point source
disturbances in space and more general driving forces. Many
waterways are part of dendritic or `branching' systems and we are
currently working on extending the one dimensional model to branching
systems. A natural setting for this is the theory of quantum
graphs, which pairs a metric graph with a differential operator.
I will review some basic partial differential equations in one spatial
dimension, discuss Kurt Anderson's work, and outline the quantum graph
approach to branching systems.