Brownian motion, the tiny random movements of small objects suspended in a fluid, has served as a paradigm for concepts of randomness ranging from noise in light detectors to fluctuations in the stock market. Penn MRSEC researchers, Yodh, Lubensky and their collaborators, have used digital video microscopy to reveal for the first time the twisty "walk" arising from the effects of random rotations and displacements of a micrometer sized plastic ellipsoid in water.
Interestingly, the ellipsoid's rotational diffusion is independent of its translational diffusion but not vice versa; the friction tensor for translation depends on the orientation of the ellipsoid relative to its velocity, producing a â€Ëœcross-talk' between particle translation and rotation. The theoretical consequences of translational-rotational coupling for this fundamental problem were first analyzed and then investigated using state-of-the-art digital imaging and computer image analysis to record the orientations and positions of the plastic ellipsoid in water at a sequence of times (see figure). Curious non-Gaussian effects were found: see Han et al Science (2006).
figure caption: A typical 20 second experimental trajectory of an ellipsoid in water. The rainbow color represents orientation of the ellipsoid, purple indicating alignment along the vertical axis, and red for alignment along the horizontal axis.