1. Motivation and aims The Belousov-Zhabotinsky system The Java applet References 1.Stochastic Modelling Web Module: http://www.cheng.cam.ac.uk/c4e/WebModule/ 2.Web site of the Computational Modelling Group: http://www.cheng.cam.ac.uk/research/groups/como/ 3.M. Kraft, S. Mosbach, and W. Wagner. Teaching Stochastic Modeling to Chemical Engineers Using a Web Module, 2005. (to appear in Chemical Engineering Education) Conclusions The stochastic algorithm System of ordinary differential equations in dimensionless form: A Web Teaching Module for Stochastic Modelling in Chemical Engineering M. Kraft, S. Mosbach, A. Selmer, Department of Chemical Engineering, University of Cambridge, United Kingdom W. Wagner, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany Acknowledgement The authors gratefully acknowledge financial support from the EPSRC. Phase space evolution Time evolution of species concentrations In order to support the lecture course “Stochastic Modelling in Chemical Engineering” at Cambridge University, an interactive web module simulating chemical reactions has been developed. It aims to enable students without knowledge of a programming language to gain hands-on experience with a Monte Carlo method. Two sets of reactions in a batch reactor are studied, one of which is the Belousov-Zhabotinsky system, which shows oscillating behaviour. Nullclines Output window for results of computations Parameters for simulation control (physical and numerical) Field, Körös, Noyes mechanism: Initialize the number of particles for each species, i.e.,,, and, set the time, and fix the stopping time. Calculate the reaction rate functions, the waiting time parameter, and the reaction probabilities. Advance the current time to. If then stop. Generate an exponentially distributed waiting time, where the decay parameter of the exponential is given by, and a reaction index according to the probabilities. Perform the reaction chosen in the previous step, i.e.: ●If then increase by 1 and decrease by 1. ●If then decrease by 2. ●If then decrease and each by 1. ●If then increase by 1 and by 2. ●If then increase by f/2 and decrease by 1. X-Z-Phase space evolution: Oscillatory case:Non-oscillatory cases: The parameters ε, ε’, and q, which are functions of the rate constants and A and B, determine the qualitative dynamical behaviour of the system. Species of interest: X, Y, Z Abundant supply of species A and B Product: P Model parameter: f f=0.25 f=3 f=1 Nullclines are curves in phase space for steady state of species. 1.Introduction explaining the subject and the aims of the module 2.Theoretical background on the considered systems, local stability analysis, and dynamical systems in general 3.Direct Simulation Monte Carlo Algorithms 4.Numerical experiments involving a Java applet, and a set of problems 5.Videos of actual experiments 6.A questionnaire to provide feedback 7.A short survey of web-based teaching 8.References and suggested reading 1 2 3 4 5 6 We regard this as a first step towards web-based teaching: We plan to increase the number of web modules. A virtual laboratory has been set up within the Cambridge-MIT Institute (CMI) The web module was well received by students: Most students enjoyed completing the module and the hands-on experience. The aspect of modelling real reactions as seen in an experiment was appreciated. Students welcomed the fact that they could concentrate on the material rather than technicalities of computer programming. However, there were complaints about the wealth of material. Structure of the web module © G. Dupuis, N. Berland, Lycée Faidherbe Lille After having completed the web module, students have to hand in an essay for marking, including answers to the set of problem given on the web pages. Rate constants:,,,, 1.To provide a numerical tool based on a Monte Carlo method simulating chemical reactions 2.To study a chemical system analytically using linear stability analysis 3.To present an example for oscillating reactions and chemical feedback