Archive for January, 2008

The mysterious volume of a black hole

Monday, January 21st, 2008

Work out the surface area of a non-spinning black hole and you’ll get the answer:

16π(Gm/c^2) /c^2

But ask what volume this surface contains and you’re in for a surprise. Turns out that the volume depends on how the 3-space within the black hole is defined. Now Brandon DiNunno and Richard Matzner from the University of Texas at Austin have performed the calculations for various definitions of 3-space and show how the volume of black hole can be time-dependent and even, in certain circumstances, zero.

Yep, that’s zero!

Ref: arxiv.org/abs/0801.1734: The Volume Inside a Black Hole

In case ya missed ’em…

Sunday, January 20th, 2008

Oranges ‘n’ lemons

Saturday, January 19th, 2008

The shower temperature problem

Friday, January 18th, 2008

Here’s an interesting problem. Imagine a large hotel in which many people are taking a shower at the same time. There isn’t enough hot water to give everyone the shower temperature they’d like and a change in temperature in one shower effects everyone else’s.

What strategy should individuals use to achieve the same temperature for everyone without large temperature changes?

That’s the question posed by Christina Matzke, an economist at the University of Bonn in Germany and a pal from Fribourg, in a curious paper on the arXiv today. They first show that there is a solution to this problem in which everyone can achieve the same shower temperature (although it may not be as hot as they’d like).

But achieving this aint’ easy. Much depends on the resolution of the taps: whether you can change the amount of hot water you getting by a small enough amount to fine tune the temperature. If you can’t, then the temperature will jump around like a cat on hot tin roof.

There are two strategies. If everyone starts with same tap settings, there is a risk of large temperature deviations as peopel change the settings in the same way. If everyone starts with different tap settings, the deviations are less but individuals are also less likely to get close to the optimal temperature.

Matzke then goes on to show that one formulation of the problem is NP-complete meaning that there ain’t a quick way of finding the solution other than testing all the combinations of tap settings.

So there ain’t a magic answer to this one. Looks like we’re destined to be unhappy showerers.

Ref: arxiv.org/abs/0801.1573: Taking a shower in Youth Hostels: risks and delights of heterogeneity

Mapping the radioactive heat beneath our feet

Thursday, January 17th, 2008

Geochemical bods tell us that the Earth is heated from within by the decay of various isotopes, mainly uranium, thorium and potassium. Knowing the distribution of these elements is crucial for understanding the Earth’s inner dynamics.

Geochemists have penty of ideas about how the Earth’s interior may work but no way of taking measurements to prove their ideas. For example, they think there are far more of these hot elements in the Earth’s crust than its mantle but without data, they can’t prove it.

But the geobods ain’t givin’ up and are a-hopin’ and a-prayin’ that the humble neutrino is gonna come to their rescue. The process of radioactive decay gives off neutrinos that would alert geobods to exactly what’s going on and where, if only they could measure ’em.

Truble is that neutrinos are hard to catch at the best of times. Physicists have recently spotted terrestrial neutrinos for the first time, although only by their energy spectrum, not by their direction which is what will be needed if geochems are to work out the distribution of radioactive stuff down there.

Now Stephen “Live and Let” Dye at the University of Hawaii and a pal have worked out exactly what will be needed to map the radioactive brew within the planet. They reckon a large ocean-based detector plus a smaller land based one should do the trick (both will have to be well away from nuclear power stations which produce unwanted neutrinos that would swamp the signal).

The technology to do this is available now but whether they can drum up the support (and the money) needed to make it happen is another question.

Ref: arxiv.org/abs/0801.2366: Estimating Terrestrial Uranium and Thorium by Antineutrino Flux Measurements

Listening out for neutrinos

Wednesday, January 16th, 2008

A lotta neutrino detectors work by looking for the flares ‘n’ flashes of light generated on the rare occasion a neutrino smashes into something solid, like an atom.  Ya need to do a lotta lookin’ though, which is why neutrino detectors sit in vast pools of water or are dropped into the oceans or buried in ancient Antarctic ice.

Now Jonathan Perkin, a  fresh-faced physicist at the University of Sheffield suggests that it might also be possible to listen for the sound that neutrinos make when they whizz through water. The thinkin is that an ultra high energy neutrino smashing into an atom rapidly raises the temperature of the water nearby producing an acoustic pulse which could be picked up by an off-the-shelf hydrophone.

Neat idea, except that Perkin goes on to to say that to have a realistic chance of picking up the sound of neutrinos you’d need a detector that is over a thousand cubic kilometres in size with over 100 hydrophones in each cubic kilometre. That’s big enough to be a nonstarter in most people’s books.

Where neutrino noise might turn out to be useful, however, is for filtering data from the big neutrino telescopes such as IceCube under the South Pole.

Pick up both the light and sound signatures of a neutrino hit and that’s pretty good evidence that it ain’t no false alarm. So the sound of neutrinos zipping past might turn out to be useful after all.

Ref: arxiv.org/abs/0801.0991: The Acoustic Detection of Ultra High Energy Neutrinos

Four letter wordistics

Tuesday, January 15th, 2008

Ah know many of ya have a penchant for four letter words judging by the comments ya leave, so this post will be of interest.

There are a possible (26)^4 = 456,976 possible four letter words although we English speakers have only got round to using a tiny fraction of ’em.

It’s fairly easy to tell which combinations are real, legal words and which are plain nonsense but only if ya are a fluent speaker who is steeped in the arcane rules of the language (i before e except after c etc). If ya don’t know them rules, forget it.

Now Bill Bialek and a buddy at Princeton University in New Jersey reckons there is another way to spot legal four letter words using a particular kind of statistical analysis. He’s taken the entire corpus of four letter words used in the novels of Jane Austen (and a colorful collection it ain’t) and studied the statistical relationship between the letters. He’s looked, not just at consecutive letters but all pairwise correlations within the words.

He’s then worked out the information content of these letter combinations, their entropy, and created a kinda map of this information landscape.Within this landscape there are local energy minima, words in which any single letter change will increase the energy. Turns out that almost two thirds of legal words lie at these local minima.

So a pretty good way of determining whether a four letter word is legal or not is to see whether its sits at a local mininum.

These “stable” words, says Bialek, have the property that any single letter spelling error can be corrected by relaxing to the nearest local energy minima. A handy kinda spell checker.

But Bialek’s most interesting speculation is that if it were possible to construct the energy landscape of legal sentences, they would all lie at local energy minima.

So grammar checkers in future could work without any knowledge of the rules of English but simply by relaxing to the local minima.

Ref: arxiv.org/abs/0801.0253: Toward a Statistical Mechanics of Four Letter Words

Cooling with sound

Monday, January 14th, 2008

The next generation of chips are gonna need some major coolin’, perhaps as much as 1000 Watts of cold per square centimetre. We’re talkin’ high-speed microprocessors, optoelectronics, micro- and millimeter-wave power electronics and power conditioning transistors for electronic motor control in hybrid vehicles power converters etc. These are machines that will generate significant heat.

Ordinary coolin fans ain’t gonna work for those kindsa fluxes so alotta engineers have been thinkin’ about phase change systems in which a liquid absorbs heat, boils into a gas and carries the energy away.

The trouble is that  a vapor layer tends to form over the surface of a chip and this acts as an insulator preventing further heat transfer.

So Ari Glezer and pals at the Georgia Institue of Technology in Atlanta have come up with a way of dislodging the vapor by bombarding it with sound. It’s just a pump for pushing the liquid round with a piezovibrator to create an acoustic field.

They reckon it works well and at relatively low power. In their set up, they achieve a colling rate of 165W per square cm. But with acoustic zapping they can raise this to 338 W per square cm. That’s an improvement of 150%.

Ref: arxiv.org/abs/0801.0785: Acoustically Enhanced Boiling Heat Transfer

In case ya missed ’em

Sunday, January 13th, 2008

This week’s posts on the physics arxiv blog:

How to spot a wormhole

The puzzle of flyby anomolies

The Turing alternatives

Information and evolution

The bar at the heart of the galaxy

Clouds ‘n’ cottonwool

Saturday, January 12th, 2008