Brownian Motion of Ellipsoidal Particles

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. One hundred years ago, Einstein first described rotational Brownian motion for spheres in water. In his 1906 paper, Einstein predicted that the rotation of spherical particles does not affect their translation.

On average, particles undergoing Brownian motion do not move very far. For example, in one second, the largest number of particles will stay very close, say within one micron, of their starting point; a smaller number will move between one micron and two microns; a still smaller number will move between two microns and three microns, and so on. A plot of the number of particles traveling specific distances yields the famous bell-shaped or Gaussian curve from statistics.

Jean Perrin

On the other hand, the rotation of non-spherical particles may affect their translation. Since most Brownian particles are not spherical, they may experience cross-talk between translation and rotation. This idea of such a coupling was first published by French physicist Francis Perrin in the 1930s but were apparently "forgotten" by the science community. Perrin's father, Jean Perrin won the Nobel Prize in 1926 for the first experimental observations confirming Einstein's theories about Brownian motion.

In a recent research paper published in Science, a research team led by Arjun G. Yodh of University of Pennsylvania confirmed the theory's curious description of how an ellipsoid's random motions are different from those of spherical particles. They reported definitive measurement of the Brownian motion of an isolated ellipsoidal particle. UPenn researchers employed state-of-art digital imaging technology and computer image analysis for their experiments. Using a charge-couple device (CCD) camera, they recorded the orientations and positions of a single, micrometer-sized plastic ellipsoid particle suspended in water at a sequence of times. Their study of the motion produced a curve that is not Gaussian -- thus directly confirming ideas about rotational-translational coupling.

Reference: "Brownian Motion of an Ellipsoid" by Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 27 October 2006: pp626-630. Abstract.

Ken Libbrecht & Physics of Snowflakes

Last week, the U.S. Postal Service issued a set of four commemorative stamps featuring images of snowflakes based on photographs taken by Ken Libbrecht, a professor of physics at the California Institute of Technology.

For several years Libbrecht has been investigating the basic physics of how patterns are created during crystal growth and other simple physical processes. He has delved particularly deeply into a case study of the formation of snowflakes. His research is aimed at better understanding how structures arise in material systems, but it is also visually compelling and, from the start, has been a hit with the public. His snowflake website, snowcrystals.com, is getting about two million hits a year. He is also the author of a new book, Ken Libbrecht's Field Guide to Snowflakes, a 112-page guide for anyone who wants to know more about the many different types of snow crystals and how to find them.

Libbrecht began his research by growing synthetic snowflakes in his lab, where they can be created and studied under well-controlled conditions. Precision micro-photography was necessary for this work, and over several years Libbrecht developed some specialized techniques for capturing images of snow crystals. Starting in 2001, he expanded his range to photographing natural snowflakes as well.

This interesting research project was aimed essentially as a case study of the growth of ice crystals from the vapor phase, the purpose of which is to better understanding pattern formation in nonlinear nonequilibrim systems. The diverse morphologies seen in snow crystals are largely due to the bizarre temperature dependence of ice crystal growth rates, a phenomenon that was discovered 75 years ago and remains unexplained to this day. Libbrecht has been making precise measurements of the growth rates of the different facets of ice crystals under controlled conditions to gain insights into the temperature dependent molecular structure of the ice surface and how it affects crystal growth.

Libbrecht can grow many different snowflake forms at will in his lab, but says there are still many subtle mysteries in crystal growth that are of interest to physicists who are trying to understand and control the formation of various materials. A real-world application of research on crystals is the growth of semiconductors for our electronic gadgets. These semiconductors are made possible in part by painstakingly controlling how certain substances condense into solid structures.

Libbrecht's research activities are not limited to snowflakes. He is also involved in the Laser Interferometer Gravitational-Wave Observatory (LIGO), an NSF-funded project that seeks to confirm the existence of gravitational waves from exotic cosmic sources such as colliding black holes. In LIGO, Libbrecht has lots of professional company; in fact, the field was essentially founded by Albert Einstein, who first predicted the existence of gravitational waves as a consequence of general relativity. Kip Thorne and Ron Drever at Caltech, along with Rai Weiss at MIT, were instrumental in initiating the LIGO project in the 1980s.

Physics Nobel 2006: Mather & Smoot

George F Smoot

John C Mather and George F Smoot have been jointly awarded the 2006 Nobel Prize in physics for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation. John C. Mather is a Senior Astrophysicist at NASA's Goddard Space Flight Center and George F Smoot is Physics Professor at University of California at Berkeley.

Their work looks back into the infancy of the Universe and attempts to gain some understanding of the origin of galaxies and stars. Their work is based on measurements made with the help of the COBE satellite launched by the NASA on November 18, 1989. The COBE results provided increased support for the Big Bang scenario for the origin of the Universe. The measurements also marked the inception of cosmology as a precise science. It was not long before it was followed up, for instance by the WMAP satellite, which yielded even clearer images of the background radiation. Soon, the European Planck satellite will be launched in order to study the radiation in even greater detail.

John C Mather

According to the Big Bang scenario, the cosmic microwave background radiation is a relic of the earliest phase of the Universe. Immediately after the big bang itself, the Universe can be compared to a glowing body emitting radiation in which the distribution across different wavelengths depends solely on its temperature. The shape of the spectrum of this kind of radiation has a special form known as blackbody radiation. When it was emitted, the temperature of the Universe was almost 3,000 degrees Centigrade. Since then, according to the Big Bang scenario, radiation has gradually cooled as the Universe has expanded. The background radiation we can measure today corresponds to a temperature that is barely 2.7 degrees above absolute zero.

The background radiation was first measured in 1965 by Arno Penzias and Robert Woodrow Wilson with their radio antenna at Bell Telephone Laboratories. They received Nobel Prize for their work in 1978. Smooth and Mather's work led to more precise measurements of various characteristics of this radiation with COBE satellite.

WMAP has produced a detailed picture of the infant universe. Colors indicate "warmer" (red) and "cooler" (blue) spots. The white bars show the "polarization" direction of the oldest light [Photo credit: NASA/WMAP Science Team]

COBE also had the task of seeking small variations of temperature in different directions (anisotropy). Extremely small differences of this kind in the temperature of the cosmic background radiation -- in the range of a hundred-thousandth of a degree -- offer an important clue to how the galaxies came into being. The variations in temperature show us how the matter in the Universe began to 'aggregate.' This was necessary if the galaxies, stars and ultimately life like us were to be able to develop. Without this mechanism, matter would have taken a completely different form, spread evenly throughout the Universe.

Further Study:
WMAP's introductory page on Cosmic Microwave background
Wikipedia page on Cosmic Microwave Background