Course Outline:

This semester the Capstone (M451H) course first considered the BZ reaction in a closed reactor (glass beaker) with continuous stirring (spatially homogeneous reaction). The experiments are performed for each of the six groups (two students per group) with their own recipes for the chemical oscillation. Thanks for Prof. Nadim's kind assistance and generosity, we are able to utilize some equipments in their neurobiology labs at Rutgers to make sure the toxic chemicals do not cause any hazards during and after the experiments. The chemical reactions are modeled by a system of ordinary differential equations. Before the experiments, students learn how to use the Law of Mass Action to derive ordinary differential equation models of chemical reactions. Students learn linear stability analysis by conducting a local analysis on the ODEs. Several nonlinear dynamics system approaches have been adopted in this semester. The first is the relaxed oscillation method, allowing students to estimate the period of chemical oscillations in their experiments. The second is the numerical approach to determine the period of chemical oscillation. In the experiments students employed potentiometric methods to directly measure the concentrations of the important components in this reaction using special electrodes and the LabPro equipment; the experimental  results were compared to the  theoretical model result.

Also, the BZ reaction in Petri dishes (spatially inhomogeneous reaction) was considered. Students performed the experiment and modeled it with a system of parabolic partial differential equations. Some theoretical tools for the analysis of the resulting infinite-dimensional dynamical system comprised of reaction-diffusion partial differential equations were presented, and some numerical tools to solve such models of the experiment were employed. Also, a video camera was used to record the evolution of target patterns and spiral waves in an attempt to compare the observed chemical wave speed with that obtained through theory and computational experiments.

Course Objectives: 
 

• To learn how differential equations arise in the modeling of chemical reactions.
   
• To learn how to measure quantities of interest while a chemical reaction is occuring.
   
• To learn how useful the Belousov-Zhabotinskii reaction is in diverse scientific areas.
   
• To see how one can employ mathematical models to simulate experiments.
   
• To see how one can employ mathematical analysis to guide experiments.
   
• To gain more experience in writing a scientific report and constructing a public presentation of scientific results.