Brownian Motion

In 1827, botanist Robert Brown noticed that while studying plant pollen under a microscope, these pieces of pollen jiggled about randomly. This motion is due to collusions of the particle with molecules of the immersion fluid. In a landmark 1905 paper, Albert Einstein predicted the existence of this microscopically-visible motion based on kinetic theory, and calculated the diffusion constant in terms of properties of the particle and the fluid in which it is immersed. Brownian motion has applications ranging from manufacturing to stock market analysis.

Some links to various Brownian motion websites:

• Brownian motion applet allows one to "see" Brownian motion occur.
• Another Brownian motion applet One of the ubiquitous Brownian motion applets--this one in one or two dimensions.
• Derivation of the diffusion constant A derivation of the diffusion constant and mean squared displacement for Brownian motion.
• The real Brown Some remarks by Robert Brown himself, after discovering the motion named after him.
• Brownian motor A Java applet simulating a Brownian motor and a discussion of why it does not violate thermodynamics.
• Brownian motion and Avogadro's number Figuring out Avogadro's number by observing particles undergoing Brownian motion.
• Introduction to Brownian motion This is an introduction for people interested in Brownian motion from a very mathematical perspective.
• Robert Brown A brief bio of Robert Brown, with a picture.
• Fractals Mostly an introduction to fractals, with a short section on the relation of Brownian motion.
• Fractional Brownian motion An introduction to fractional Brownian motion, with applications.
• Backgammon and Brownian motion A model of features of the game using Brownian motion.