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Resonance

March 2005
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Paul Langevin

Paul Langevin was the first person to write the ‘Newton’s equation’ for a Brownian particle. This equation is now called the Langevin equation and is often the starting equation required for understanding systems where microscopic fluctuations play an important role.

Brownian motion is the observed random motion of a small particle immersed in a fluid. For example if a very dilute mixture of milk in water is seen under the microscope one would see the micron-sized fat droplets executing a random motion.
In 1905 Albert Einstein presented the first detailed mathematical analysis of Brownian
motion. Einstein’s derivation basically involved looking at the diffusion of a large number of Brownian particles in the presence of a density gradient. Using arguments from statistical mechanics and thermodynamics he related the diffusion constant D to: (I) the mean square displacement D2, in time t, of individual particles by the formula D2 = 2 Dt and (II) the macroscopic properties of the fluid such as its viscosity h and absolute temperature T by the famous Einstein relation 6 ph a D=R T/N, where N is the avogadro number, R is the gas constant and a is the radius of the particle. Einstein's achievement was in proposing a definite quantitative measurement on the motion of a Brownian particle that could provide a direct proof of the atomistic nature of matter. Indeed this led to one of the first accurate experimental measurements of the Avogadro number. An important aspect of Einstein's analysis of the problem involved looking at a collection of Brownian particles.

 

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