本文作者：小红猪小分队

Source:http://www.newscientist.com/article/mg21528832.000-big-bangs-theory-unlocking-the-secrets-of-great-hair.html?full=true&print=true

【Time to pay a visit to a physicist (Image: Image Source/Getty Images)】

The physics of what happens on the top of our heads is surprisingly complex

EITAN GRINSPUN’S curling locks provide him with the perfect excuse for a spot of mirror-gazing in the name of science. “There are all these crazy forces between hairs,” he muses.

Anyone who has ever encountered an unmanageable mane in the glass first thing in the morning would give that statement the nod. But some researchers find unimagined complexity nestling in our crowning glory. Our hairs constantly rub up against one another, creating friction and static electricity. Minuscule scales on their surfaces cause some to lock together and tiny pockets of air get trapped between others, while natural lubricating oils engulf them all in a sticky surface tension.

Grinspun is a computer scientist at Columbia University in New York who works with the likes of Disney and Pixar to develop more realistic computer animations of, among other things, hair. He is not the only person with an unexpected interest in a good ‘do. “I have a couple of graduate students with very nice ponytails,” says Raymond Goldstein, a complex-systems physicist at the University of Cambridge. “I’m always measuring them.”

Since 2008, Goldstein has been collaborating with the cosmetics arm of the consumer-goods multinational Unilever, which has a multimillion-dollar interest in understanding what makes hair frizz or hang lank in a ponytail. But not only shampoo-makers and Hollywood animators could profit from this particular strand of research.

At a basic level, human hairs are just chains of interlocking proteins. Their various adhesive, frictional and electrostatic interactions are computationally problematic, but the real challenge comes from sheer weight of numbers. “You have about 100,000 hairs on your head and each one has about 10,000 interactions with other hairs,” says computer scientist Andreas Weber of the University of Bonn, Germany, who has been examining hair for a decade.

And wet hair and dry hair interact differently. As it dries, or ambient humidity decreases, each strand undergoes a “glass transition”, suddenly locking into a particular curvature that is determined by the precise structure of its protein chains. This change is instinctively understood by a good hairdresser. The reverse process can wreak havoc with even the most carefully styled coiffure on a humid day.

To a physicist such as Goldstein, grappling with such issues hair by hair is a shortcut to madness. Following initial discussions with Unilever, he and his team decided to tackle the problem with a mathematical modelling method known as density functional theory that is more often used to sum up the interactions of many electrons within solids.

Their first stop was the basic question of what makes a ponytail take a particular shape. Density functional theory allowed the researchers to represent this agglomeration as a single strand acted on by gravity, with all the interactions between hairs summed into a single force field acting outwards from the centre. The resulting “ponytail shape equation” successfully predicts the form a ponytail of different lengths takes, once factors such as hair elasticity, density and curl – bundled into a constant dubbed the “Rapunzel number” – are taken into account (Physical Review Letters, vol 108, p 078101).

It would be easy to give the brush-off to this sort of research. Indeed, this week Goldstein and his collaborators were awarded one of 10 “Ig Nobel” prizes, which honour scientific achievements that “first make people laugh, and then make them think”. For Unilever, it has provoked much more of the second. Consumers are always looking for things like sustained volume control, says Patrick Warren, who works at the company’s research facility in Port Sunlight, UK, and was part of Goldstein’s team. “Hair volume translates to expanded ponytails, and we now have a deep understanding of how this derives from the properties of individual hair fibres.”

Tangle, swish and bounce

Factors such as the average curvature and elastic properties vary dramatically across the globe, and until now it has been hard to tailor products to take account of that. “There could be a way of putting a number on that – you’ve got type 4.2 hair and here’s the optimum conditioner for that waviness, that kind of thing,” says Goldstein.

A similar drive for whole-head understanding motivates Grinspun, Weber and their ilk, if for very different reasons. It is down to their work that the monolithic hair slab of the first Lara Croft, feisty heroine of the Tomb Raider video games, has given way in the past decade to more differentiated tresses in which, for example, light seems to scatter realistically off individual hairs.

Grinspun sharpened his modelling scissors helping Adobe to develop their Bristle Tips tool, a brush for its Photoshop software that splays and flexes realistically as you paint, and he has since contributed his expertise to such heavyweight hirsute films as Avatar and the 2005 remake of King Kong. But Hollywood has some way to go before its computer-generated hair matches the lustrous locks of its human stars – and it’s all down to that same lack of understanding of the fundamentals, says Grinspun. “We want to capture physics at the level we need in order to get the hair to sit and fly and bounce and lift in same way as actual physical hair.” That involves him and his team in a lot of computational heavy lifting to work out what exactly goes on when hairs collide, for example.

If talk of better shampoos and digital animations makes all this work sound rather superficial, it is worth bearing in mind that there is a lot out there that resembles hair and can be characterised by the same equations. Together with Pedro Reis of the Massachusetts Institute of Technology, Grinspun is using the same physics to investigate how cooked spaghetti strands coil up when they are dropped, as an analogue for what happens to communications cables when they are spooled onto the ocean floor – and thus perhaps find a way to optimise their final resting place. Reis himself is working with oil and gas companies to investigate how pipelines bend under their own weight like human hair, and he and MIT colleague Roman Stocker are researching how similar processes influence the propulsive efficiency of the bacterial flagellum, a curved tail that rotates and propels microbes through fluids. “The mechanics is universal,” says Reis.

That’s not to deny where the real money lies: after all, a lot of us have an interest in great hair. “If you get 50 cents from half the people on Earth you can fund a lot of research,” says Weber. Only a tiny fraction of that sum is flowing into Goldstein’s work, and with his balding pate he has little to gain personally. But it is a problem he still wants to get to the root of. Having solved the ponytail puzzle, he has moved on to the knottier question of what makes hair tangle. He expects “significant progress” on that in the next few months, and also has his sights on some fundamental investigations of what makes hair swishy.

“We’re going to put hair in a wind tunnel and see what we find,” he says. It might sound like a lot of time and money to develop a product that makes you look good in a hurricane. But, then, you’re worth it.

Michael Brooks is a consultant forNew Scientist, and author of The Secret Anarchy of Science(Profile/Overlook)