Prev. Article Next Article Table of Contents

Article

Simulation of One-Dimensional Brownian Motion by Stochastic Differential Equations

Supporting Info

Your current credentials do not allow retrieval of the full text.

Purchase the full-text

PDF/HTML,
figures/images,
references and tables,
(where available)

Ken Muranaka

K''s Garden Nishioji, Suite 401, Kasuga Hachijo Sagaru, Minami-ku, Kyoto 601-8312, JAPAN

J. Chem. Educ., 1999, 76 (7), p 994

DOI: 10.1021/ed076p994

Publication Date (Web): July 1, 1999

Section:

History, Education, and Documentation

Abstract

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.