Tag Archives: Brownian motion

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.

Computer simulation errors and corrections

In addition to being a news release, this is a really good piece of science writing by Paul Preuss for the Lawrence Berkeley National Laboratory (Berkeley Lab), from the Jan. 3, 2013 Berkeley Lab news release,

Because modern computers have to depict the real world with digital representations of numbers instead of physical analogues, to simulate the continuous passage of time they have to digitize time into small slices. This kind of simulation is essential in disciplines from medical and biological research, to new materials, to fundamental considerations of quantum mechanics, and the fact that it inevitably introduces errors is an ongoing problem for scientists.

Scientists at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) have now identified and characterized the source of tenacious errors and come up with a way to separate the realistic aspects of a simulation from the artifacts of the computer method. …

Here’s more detail about the problem and solution,

How biological molecules move is hardly the only field where computer simulations of molecular-scale motion are essential. The need to use computers to test theories and model experiments that can’t be done on a lab bench is ubiquitous, and the problems that Sivak and his colleagues encountered weren’t new.

“A simulation of a physical process on a computer cannot use the exact, continuous equations of motion; the calculations must use approximations over discrete intervals of time,” says Sivak. “It’s well known that standard algorithms that use discrete time steps don’t conserve energy exactly in these calculations.”

One workhorse method for modeling molecular systems is Langevin dynamics, based on equations first developed by the French physicist Paul Langevin over a century ago to model Brownian motion. Brownian motion is the random movement of particles in a fluid (originally pollen grains on water) as they collide with the fluid’s molecules – particle paths resembling a “drunkard’s walk,” which Albert Einstein had used just a few years earlier to establish the reality of atoms and molecules. Instead of impractical-to-calculate velocity, momentum, and acceleration for every molecule in the fluid, Langevin’s method substituted an effective friction to damp the motion of the particle, plus a series of random jolts.

When Sivak and his colleagues used Langevin dynamics to model the behavior of molecular machines, they saw significant differences between what their exact theories predicted and what their simulations produced. They tried to come up with a physical picture of what it would take to produce these wrong answers.

“It was as if extra work were being done to push our molecules around,” Sivak says. “In the real world, this would be a driven physical process, but it existed only in the simulation, so we called it ‘shadow work.’ It took exactly the form of a nonequilibrium driving force.”

They first tested this insight with “toy” models having only a single degree of freedom, and found that when they ignored the shadow work, the calculations were systematically biased. But when they accounted for the shadow work, accurate calculations could be recovered.

“Next we looked at systems with hundreds or thousands of simple molecules,” says Sivak. Using models of water molecules in a box, they simulated the state of the system over time, starting from a given thermal energy but with no “pushing” from outside. “We wanted to know how far the water simulation would be pushed by the shadow work alone.”

The result confirmed that even in the absence of an explicit driving force, the finite-time-step Langevin dynamics simulation acted by itself as a driving nonequilibrium process. Systematic errors resulted from failing to separate this shadow work from the actual “protocol work” that they explicitly modeled in their simulations. For the first time, Sivak and his colleagues were able to quantify the magnitude of the deviations in various test systems.

Such simulation errors can be reduced in several ways, for example by dividing the evolution of the system into ever-finer time steps, because the shadow work is larger when the discrete time steps are larger. But doing so increases the computational expense.

The better approach is to use a correction factor that isolates the shadow work from the physically meaningful work, says Sivak. “We can apply results from our calculation in a meaningful way to characterize the error and correct for it, separating the physically realistic aspects of the simulation from the artifacts of the computer method.”

You can find out more in the Berkeley Lab news release, or (H/T)  in the Jan. 3, 2013 news item on Nanowerk, or you can read the paper,

“Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium discrete Langevin dynamics simulations,” by David A. Sivak, John D. Chodera, and Gavin E. Crooks, will appear in Physical Review X (http://prx.aps.org/) and is now available as an arXiv preprint at http://arxiv.org/abs/1107.2967.

This casts a new light on the SPAUN (Semantic Pointer Architecture Unified Network) project, from Chris Eliasmith’s team at the University of Waterloo, which announced the most  successful attempt (my Nov. 29, 2012 posting) yet to simulate a brain using virtual neurons. Given the probability that Eliasmith’s team was not aware of this work from the Berkeley Lab, one imagines that once it has been integrated that SPAUN will be capable of even more extraordinary feats.

Teaching nano the haptic way; Brownian motion ain’t what we thought; EPA issues final new rules for carbon nanotubes

In keeping with my interest in the multimodal communication of science, I have found a slide show about teaching nanotechnology using haptics here. The technique is intended for the visually impaired but as the authors point out visual contact at the nano scale is impossible. So, everyone, visually impaired or not, makes haptic contact with material at the nano scale with the consequence that the teaching technique is suitable for everybody.

As suggested in my July 27, 2009 blog posting (part 4 of the robots and human enhancement series), developments such as these suggest that the notion of physical impairment may change significantly or disappear.

In a media release, on the Azonano site, detailing new revelations about Brownian motion,  Steve Granick, Founder Professor of Engineering at the University of Illinois, describes how many of us are taught about Brownian motion,

“In high school science classes, students are often assigned the task of using a microscope to watch a particle of dust sitting in a drop of water,” Granick said. “The dust particle seems alive, moving back and forth, never in the same way. The motion of the dust particle is caused by the random ‘kicks’ of surrounding water molecules.”

Granick goes on to describe what he and his researchers have observed,

“Like Einstein, we used to think we could describe Brownian motion with a standard bell-shaped curve,” Granick said. “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.”

Please do take a look at the story on the Azonano site for more about the significance of this discovery.

Nanowerk News has posted a media release from the US Environmental Protection Agency (EPA) about new rules which allow for commercialization of carbon nanotubes under limited conditions.  The EPA document is here and pages 9 (multi-walled carbon nanotubes) and 10 (single-walled nanotubes) are the relevant pages.