The Physics Of Ponytails

I kid you not! They even came up with something called the "Rapunzel Number"!

It turns out that there is an important-enough research being done on the physics of ponytails that it warrants a publication in the Physical Review Letters, no less!

He and two other physicists have been trying to determine whether the shape of a ponytail can be deduced from the properties of a single hair. After all, a head with 100,000 strands is a complex physical system, as anyone with a copious coiffure can attest. 

And it turns out that there is a simple theory. The crucial characteristics are elasticity, density and curliness, which essentially tell how springy a piece of hair is, plus the length of the ponytail. The researchers came up with a simple formula that describes the ponytail shape when the hair is bundled together.

They called it the Rapunzel number. “We couldn’t resist,” Dr. Goldstein said. 

Oh dear!

I'll try to find the exact reference to this one when it appears and post it here. I wish they explain why this is important and what other implications this involved. Maybe it's written in the actual paper. The only thing I can find in the news article is the sentence "...  Dr. Goldstein said the findings could also be applied to bundles of other long filaments, including fiberglass and wool...", which doesn't say much.

Another news report on this story mention quite a bit more, but it is still unclear what properties actually that is so important.

Scientists said the work has implications for understanding the structure of materials made up of random fibers, such as wool and fur and will have resonance with the computer graphics and animation industry, where the representation of hair has been a challenging problem.

"Our findings extend some central paradigms in statistical physics and show how they can be used to solve a problem that has puzzled scientists and artists ever since Leonardo da Vinci remarked on the fluid-like streamlines of hair in his notebooks 500 years ago," Goldstein said.

So maybe this won't be nominated for an Ig Nobel after all! :)

Edit: the Ponytail physics is getting a Synopsis coverage! Click that link for the exact reference.

Zz.

Experimental Test of Airplane Boarding Methods

Back in 2008, I reported a rather interesting (at least, to me) use of some of the techniques from statistics and physics to find the most optimum boarding method onto an airplane. This study was done purely via mathematical modeling. Of course, being physicists/scientists, just having a model isn't enough. One has to verify it.

Now come a report whereby the author of that original paper and others have done an experimental study various methods of boarding an airplane.

Abstract: We report the results of an experimental comparison of different airplane boarding methods. This test was conducted in a mock 757 fuselage, located on a Southern California soundstage, with 12 rows of six seats and a single aisle. Five methods were tested using 72 passengers of various ages. We found a significant reduction in the boarding times of optimized methods over traditional methods. These improved methods, if properly implemented, could result in a significant savings to airline companies.

I would say that airlines such as Southwest could learn quite a bit from this study, since they have such a short turn-around time for their airplanes.

And I love it when there's a follow up to a study such as this.

Zz.

Mean Free Path In Soccer And Gasses

An interesting title on a familiar topic. This paper presents an intro to students on the concept of kinetic theory of ideal gas, and explains the concept of mean free path in gasses using an analogous approach to the "mean free path" of a soccer ball during a soccer match.

J. Luzuriaga, Eur. J. Phys. v.31, p.1071 (2010).

Abstract:

The trajectories of the molecules in an ideal gas and of the ball in a soccer game are compared. The great difference between these motions and some similarities are discussed. This example could be suitable for discussing many concepts in kinetic theory in a way that can be pictured by students for getting a more intuitive understanding. It could be suitable for an introductory course in vacuum techniques or undergraduate courses in kinetic theory of gases. Without going into the slightly harder quantitative results, the analysis presented might be used for introducing some ideas of kinetic theory qualitatively to high school students.

Published 21 July 2010

Note that you could get a free copy of the paper within 30 days of online publication.

Zz.

Sterioid Use in Baseball

The recent admission of steroid use by Mark McGwire brings another black chapter in baseball. This news report cited a paper by Roger Tobin, which I mentioned already a while back. The AJP paper[1] examines the correlation between increase in batted speed (presumably due to increase in muscle mass) and the ability to hit long balls.

Note also that statistical evidence has also been used to show that there's a likelihood of the use of performance enhancing drugs in baseball.

Zz.

[1] R. Tobin, Am. J. Phys. v.76, p. 15 (2008).

More is the Same; Phase Transitions and Mean Field Theories

This is a clear and concise treatise on phase transition, written by Leo Kadanoff, one of the leading figures today in condensed matter physics. Even if you don't understand the mathematics, the written description of phase transition is very well presented, so I highly recommend this for everyone to read.

Abstract: This paper Looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method".
In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s.
A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.

Zz.