Brownian Motion in 1828 Robert Brown, Investigating Pollen in Water Through a Microscope, Observed Particles Moving Irregularly

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Brownian Motion In 1828 Robert Brown, investigating pollen in water through a microscope, observed particles moving irregularly. 2 micron spheres 2 micron spheres in water in goo (DNA solution) (Movies from Eric Weeks) Theories of Brownian Motion • Wrong theories proposed (irregular heating by incident light; electrical forces) • In 1877 Delsaux proposed Brownian motion due to impacts of liquid molecules on the observed particles. (Right idea) • Between 1905 and 1908, Einstein published papers laying out the theory of Brownian motion. Simulation of Brownian Motion brownianSimulation.html Einstein’s Theory of Brownian Motion • Smaller particles move faster. • Particles move faster at higher temperature. • Larger particles move less than smaller particles. • Particles move less in high viscosity solutions. • Particles diffuse rather than move ballistically. start Random Walk end • The trajectory of the diffusing particle is a random walk. brownianSimulation.html • Drunk starts from a lamp post and has equal probability of taking a step to the right or the left. • Don’t know where to go for dinner? Flip a coin at every intersection to decide whether to go right or left. Your route will be a random walk. Displacement r is distance traveled as the crow flies start Displacement r end Diffusion • Perfume particles diffuse through the air to your nose from an open perfume bottle • Milk in coffee diffuses • Drop of ink in water diffuses • Particles undergo Brownian motion • Particles perform random walk Diffusion vs. Ballistic Motion • Ballistic motion: Distance traveled increases linearly with time. • When particles diffuse, they don’t go as far as when they move ballistically in a straight line in one direction. • Average diffusive displacement < r> goes as start end diffusion Einstein’s Legacy • Brownian motion, diffusion, random walks are still used today in science (physics, biology, chemistry, etc.), engineering and economics. .

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