A Mathematical Model of the Emission and Optimal Control of Photochemical Smog

Friday, October 28, 2011
Hall 1-2 (San Jose Convention Center)
Daniel Burkow , Mathematics, Arizona State University, Tempe, AZ
Christina Duron , Mathematics, Swarthmore College, Swarthmore, PA
Kathryn Heal , Mathematics, University of California, Los Angeles, Los Angeles, CA
Arturo Vargas , Mathematics, University of California, Irvine, Irvine, CA
Luis Melara Jr., PhD , Mathematics, Shippensburg University, Shippensburg, PA

This study considers traffic regulations as a tool for reducing the emis-

sion of NO, NO2, CO, and CO2 from vehicles on a subset of highways in

the Los Angeles basin. We reduce an established chemical network into

two simplified nonautonomous models: a linear, uncoupled set of ordinary

differential equations tracking the emissions and a coupled set of six equa-

tions tracking further process detail. We demonstrate, and prove when

able, the existence of periodic pollutant levels. Furthermore, we imple-

ment an optimal control method to evaluate theoretical pollution control

policies by factoring implementation cost and the cost of adverse health

effects.