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1999
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Research: Science and Education
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Simulation of One-Dimensional Brownian Motion by Stochastic Differential Equations
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Ken Muranaka
K's Garden Nishioji, Suite 401, Kasuga Hachijo Sagaru, Minami-ku, Kyoto 601-8312, JAPAN
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July 1999
Vol. 76 No. 7
p. 994
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| Abstract |
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Diffusion and transport phenomena can be explained by deterministic models involving ordinary or partial differential equations, and Brownian motion has been a popular model for simulating random physical processes. The real dynamics of Brownian motion, however, can be better presented in terms of stochastic or probabilistic models. A Basic program named RWALK, which stands for "random walk", has been written to simulate diffusion processes by a simple yet powerful mathematical tool known as a stochastic differential equation. By entering the initial value, drift, standard deviation (which is related to diffusion coefficient), and periods to be simulated, a student can generate various sample paths or trajectories with this program. A simple and economical exercise to model a student's wrist pulse has been devised. All suggested activities can be done in one normal laboratory period, and the simulation exercises with RWALK should give students in physical chemistry a concrete command over an abstract topic like Brownian motion as well as some exposure to basic statistical concepts using a spreadsheet or a commercial statistical software.
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| Supplement |
Both the source code and the compiled version of the Quick Basic program RWALK have been supplied as supplementary material. RWALK.EXE will run in the MS-DOS mode of Windows 95 and the regular MS-DOS. The basic programs RWALK.BAS and RWALK.EXE have been compressed into zip (for Windows) and sit (for Macintosh) files. RWALK.BAS can also be viewed as a pdf file using Acrobat Reader.
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| More Information |
Citation |
Muranaka, Ken. J. Chem. Educ. 1999 76 994.
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Keywords |
Physical Chemistry; Teaching / Learning Aids; Computational Chemistry; Theoretical Chemistry
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History |
Created:
Last Updated: |
June 9, 1999
November 22, 2005
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| Home > JCE Print > Journal of Chemical Education > Issues >
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