The phenomenon of Brownian motion (after botanist Robert Brown, who discovered it 1828) was described by Albert Einstein in 1905, when he published his statistical molecular theory of liquids. Brownian motion is basically the random movement of particles within a fluid.  
  As a new study by University of Illinois scientists shows, Brownian motion is, perhaps, not as mathematically applicable as previously thought.  Einstein thought if the motions of many particles were watched, and the distance each moved in a certain time were recorded, the distribution would resemble the familiar Gaussian, bell-shaped curve used to assign grades in a science class.  But was Einstein right?
   "Like Einstein, we used to think we could describe Brownian motion with a standard bell-shaped curve. But now, with the ability to measure very small distances much more precisely than was possible 100 years ago, we have found that we can have extremes much farther than previously imagined," says Steve Granick, Founder Professor of Engineering, and professor of materials science and engineering, of chemistry, of chemical and biomolecular engineering, and of physics at the U. of Illinois.

   Thanks to a century's worth of technological advances, researchers designed two experiments that tested Einstein's theory.

 In the first experiment, beads were moved up and down tiny tubes of lipid molecules by Brownian motion, as researchers observed.   In the second experiment, the researchers watched as the beads diffused through a porous membrane of entangled macromolecule filaments. This, too, followed Brownian motion but Einstein's bell-shaped curve didn't budge in nearly all features of both experiments; there were also features in significant disagreement. The beads moved much farther than predicted by the bell curve in some cases.

Contrary to expectations of Gaussian diffusion behavior, researches witnessed behavior that was exponential.      These new findings mean that we may have rethink the bell curve when addressing future problems.