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.