High-order Brownian motion observed

A Nov. 17, 2014 news item on ScienceDaily highlights a new technique for observing Brownian motion,

For the first time, scientists have vividly mapped the shapes and textures of high-order modes of Brownian motions–in this case, the collective macroscopic movement of molecules in microdisk resonators–researchers at Case Western Reserve University report.

To do this, they used a record-setting scanning optical interferometry technique, described in a study published today in the journal Nature Communications.

The new technology holds promise for multimodal sensing and signal processing, and to develop optical coding for computing and other information-processing functions by exploiting the spatially resolved multimode Brownian resonances and their splitting pairs of modes.

A Nov. 17, 2014 Case Western Reserve University news release on EurekAlert, which originated the news item, provides more information about the technique and the research,

Interferometry uses the interference of light waves reflected off a surface to measure distances, a technique invented by Case School of Applied Science physicist Albert A. Michelson (who won the Nobel prize in science in 1907). Michelson and Western Reserve University chemist Edward Morley used the instrument to famously disprove that light traveled through “luminous ether” in 1887, setting the groundwork for Albert Einstein’s theory of relativity.

The technology has evolved since then. The keys to Feng’s new interferometry technique are focusing a tighter-than-standard laser spot on the surface of novel silicon carbide microdisks.

The microdisks, which sit atop pedestals of silicon oxide like cymbals on stands, are extremely sensitive to the smallest fluctuations arising from Brownian motions, even at thermodynamic equilibrium. Hence, they exhibit very small oscillations without external driving forces. These oscillations include fundamental and higher modes, called thermomechanical resonances.

Some of the light from the laser reflects back to a sensor after striking the top surface of the silicon dioxide film. And some of the light is refracted through the film and reflected back on a different path, causing interference in the light waves.

The narrow laser spot scans the disk surface and measures movement, or displacement, of the disk with a sensitivity of about 7 femtometers per square-root of a hertz at room temperature, which researchers believe is a record for interferometric systems. To put that in perspective, the width of a hair is about 40 microns, and a femtometer is 100 million times smaller than a micron.

Although higher frequency modes have small motion amplitudes, the technology enabled the group to spatially map and clearly visualize the first through ninth Brownian modes in the high frequency band, ranging from 5.78 to 26.41 megahertz.

In addition to detecting the shapes and textures of Brownian motions, multimode mapping identified subtle structural imperfections and defects, which are ubiquitous but otherwise invisible, or can’t be quantified most of the time. This capability may be useful for probing the dynamics and propagation of defects and defect arrays in nanodevices, as well as for future engineering of controllable defects to manipulate information in silicon carbide nanostructures

The high sensitivity and spatial resolution also enabled them to identify mode splitting, crossing and degeneracy, spatial asymmetry and other effects that may be used to encode information with increasing complexity. The researchers are continuing to explore the capabilities of the technology.

Here’s a link to and a citation for the paper,

Spatial mapping of multimode Brownian motions in high-frequency ​silicon carbide microdisk resonators by Zenghui Wang, Jaesung Lee & Philip X. -L. Feng. Nature Communications 5, Article number: 5158 doi:10.1038/ncomms6158 Published 17 November 2014

This paper is behind a paywall.

For those who would like a little more information about Brownian motion, there’s this from its Wikipedia entry,

Brownian motion or pedesis (from Greek: πήδησις /pɛ̌ːdɛːsis/ “leaping”) is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the quick atoms or molecules in the gas or liquid. The term “Brownian motion” can also refer to the mathematical model used to describe such random movements, which is often called a particle theory.

The Wikipedia entry also includes this gif

This is a simulation of Brownian motion of a big particle (dust particle) that collides with a large set of smaller particles (molecules of a gas) which move with different velocities in different random directions. http://weelookang.blogspot.com/2010/06/ejs-open-source-brownian-motion-gas.html Lookang Author of computer model: Francisco Esquembre, Fu-Kwun and lookang - Own work

This is a simulation of Brownian motion of a big particle (dust particle) that collides with a large set of smaller particles (molecules of a gas) which move with different velocities in different random directions. http://weelookang.blogspot.com/2010/06/ejs-open-source-brownian-motion-gas.html
Lookang Author of computer model: Francisco Esquembre, Fu-Kwun and lookang – Own work

On a tangential and amusing note, Brown University celebrating its 250th anniversary this year (2014) commissioned a Brownian Motion composition as part of its commemoration activities (from a Feb. 21, 2014 Brown University news release),

While Brown University and its neighbors celebrate the University’s first 250 years during the Opening Celebration Friday and Saturday, March 7-8, 2014, some new history will be made as well. On Friday night, the Brown University Wind Symphony will present the world premier of Brownian Motion, a piece commissioned for the semiquincentenary.

Written by the composer and saxophonist Patrick Zimmerli, the commission was funded by Edward Guiliano, a 1972 Brown graduate who was president of the Brown Band and founded the Brown Wind Ensemble during his time on College Hill.

Zimmerli admits to feeling excitement when approached with the commission. “I didn’t go to Brown but I have many connections to people who did, and I was really looking forward to the challenge of writing for an undergraduate wind ensemble, something I’d never done before.”

McGarrell [Matthew McGarrell, director of bands at Brown] and Zimmerli met last summer to talk about the commission for the first time. Aside from sending Zimmerli a few pieces to use as models, McGarrell gave the composer free reign over over everything from the feel to the length of the piece.

The resulting composition, which Zimmerli presented to McGarrell at the beginning of January, is dominated by jazz rhythms, with some nods to vernacular musics, including Caribbean and calypso, mixed in.

“The piece has several different moods but overall it is celebratory,” Zimmerli said. “After all it’s a birthday piece. It’s meant to be challenging but fun for the players.”

Listeners with a link to Brown may also find parts of the work familiar. Zimmerli subtly weaves an early melody known as “Araby’s Daughter” — Brown’s Alma Mater — throughout the piece, building on it until it’s played in its full glory by the French horns toward the end.

For inspiration, Zimmerli did extensive research on Brown’s early history and was intrigued to learn that Brown’s founding was initially opposed by a group of preachers who had a mistrust for those who had been formally educated. The result is a theme — “learning is evil,” a nod to those early roots — that winds its way throughout the song.

“Brown is an amazing example of an institution that has been able to evolve and transform itself from within, and I thought that fact should be celebrated,” said Zimmerli.

Other parts of the song inspired the Brownian Motion name.

“There’s a jagged theme toward the beginning of the piece that is a bit cheeky, even subversive. The way it moves and darts around through the instruments unexpectedly is what eventually led me to the actual title of the piece,” Zimmerli said.

“We knew we wanted to make it special concert,” said McGarrell of the program selections. “We wanted to reach both the Brown community in history, through the alumni, through musical representation, and we wanted to reach out to the extended Brown community in Rhode Island and southeastern New England, through history and intercultural outreach.”

The Brown musicians have been hard at work since the end of January learning Brownian Motion. While technically challenging, McGarrell said the students have been appreciating the skill level required and that “morale has remained high within the group.” Zimmerli arrives on campus on Wednesday, March 5, to help put the finishing touches on the performance.

There is a youtube video (over 60 mins.) of the Brownian Motion March 2014 performance.

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