Visualizzazione post con etichetta Math Puzzles. Mostra tutti i post
Visualizzazione post con etichetta Math Puzzles. Mostra tutti i post

lunedì 22 ottobre 2007

Computer Memory May Leap With Solution To Chemical Mystery


Source:

ScienceDaily (Oct. 22, 2007) — A Florida State University researcher has helped solve a scientific mystery that stumped chemists for nearly seven decades. In so doing, his team's findings may lead to the development of more-powerful computer memories and lasers.
Naresh S. Dalal, the Dirac Professor of Chemistry and Biochemistry at FSU, recently collaborated with three colleagues, Jorge Lasave, Sergio Koval and Ricardo Migoni, all of the Universidad Nacional de Rosario in Argentina, to determine why a certain type of crystal known as ammonium dihydrogen phosphate, or ADP, behaves the way it does.
"ADP was discovered in 1938," Dalal said. "It was observed to have some unusual electrical properties that weren't fully understood -- and for nearly 70 years, scientists have been perplexed by these properties. Using the supercomputer at SCRI (FSU's Supercomputer Computations Research Institute), we were able to perform in-depth computational analyses that explained for the very first time what causes ADP to have these unusual properties."
ADP, like many crystals, exhibits an electrical phenomenon known as ferroelectricity. Ferroelectric materials are analogous to magnets in that they maintain a positively charged and a negatively charged pole below a certain temperature that is characteristic for each compound.
"Ferroelectric materials can stay in a given state of charge for a long time -- they retain their charge after the external electrical source is removed," Dalal said. "This has made ADP and other materials like it very useful for storing and transmitting data.
ADP is commonly used in computer memory devices, fiber optic technology, lasers and other electro-optic applications."
What researchers found perplexing about ADP was that it often displays a very different electrical phase -- one known as antiferroelectricity.
"With antiferroelectricity, one layer of molecules in a crystal has a plus and a minus pole, but in the next layer, the charges are reversed," Dalal said. "You see this reversal of charges, layer by layer, throughout the crystal."
Using the supercomputer at SCRI enabled Dalal and his colleagues to perform numerous highly complex calculations that couldn't be duplicated in a laboratory environment. For example, they were able to theoretically alter the angles of ADP's ammonium ions and then measure the effects on the crystal's electrical charge. That approach ultimately led to their solution to the seven-decade mystery.
"We found that the position of the ammonium ions in the compound, as well as the presence of stresses or defects in the crystal, determine whether it behaves in a ferroelectric or antiferroelectric manner," Dalal said.
The team's research is important for two main reasons, Dalal said: "First, this allows us to further understand how to design new materials with both ferroelectric and antiferroelectric properties. Doing so could open new doors for computer memory technology -- and possibly play a role in the development of quantum computers.
"Second, our research opens up new ways of testing materials," Dalal said. "Using supercomputers, we can quickly perform tests to see how materials would react under a variety of conditions. Many such tests can't even be performed in the lab."
A paper "Origin of Antiferroelectricity in NH4H2PO4 from First Principles,"describing Dalal, Lasave and Migoni's findings was published recently in Physical Review Letters.
Adapted from materials provided by Florida State University.

Fausto Intilla

sabato 13 ottobre 2007

Not Just Science Fiction: 'Electromagnetic Wormhole' Possible, Say Mathematicians


Source:

Science Daily — The team of mathematicians that first created the mathematics behind the "invisibility cloak" announced by physicists last October has now shown that the same technology could be used to generate an "electromagnetic wormhole."
In the study, which is to appear in the Oct. 12 issue of Physical Review Letters, Allan Greenleaf, professor of mathematics at the University of Rochester, and his coauthors lay out a variation on the theme of cloaking. Their results open the possibility of building a sort of invisible tunnel between two points in space.
"Imagine wrapping Harry Potter's invisibility cloak around a tube," says Greenleaf. "If the material is designed according to our specifications, you could pass an object into one end, watch it disappear as it traveled the length of the tunnel, and then see it reappear out the other end."
Current technology can create objects invisible only to microwave radiation, but the mathematical theory allows for the wormhole effect for electromagnetic waves of all frequencies. With this in mind, Greenleaf and his coauthors propose several possible applications. Endoscopic surgeries where the surgeon is guided by MRI imaging are problematical because the intense magnetic fields generated by the MRI scanner affect the surgeon's tools, and the tools can distort the MRI images. Greenleaf says, however, that passing the tools through an EM wormhole could effectively hide them from the fields, allowing only their tips to be "visible" at work.
To create cloaking technology, Greenleaf and his collaborators use theoretical mathematics to design a device to guide the electromagnetic waves in a useful way. Researchers could then use these blueprints to create layers of specially engineered, light-bending, composite materials called metamaterials.
Last year, David R. Smith, professor of electrical and computer engineering at Duke's Pratt School, and his coauthors engineered an invisibility device as a disk, which allowed microwaves to pass around it. Greenleaf and his coauthors have now employed more elaborate geometry to specify exactly what properties are demanded of a wormhole's metamaterial in order to create the "invisible tunnel" effect. They also calculated what additional optical effects would occur if the inside of the wormhole was coated with a variety of hypothetical metamaterials.
Assuming that your vision was limited to the few frequencies at which the wormhole operates, looking in one end, you'd see a distorted view out the other end, according the simulations by Greenleaf and his coauthors. Depending on the length of the tube and how often the light bounced around inside, you might see just a fisheye view out the other end, or you might see an Escher-like jumble.
Greenleaf and his coauthors speculated on one use of the electromagnetic wormhole that sounds like something out of science fiction. If the metamaterials making up the tube were able to bend all wavelengths of visible light, they could be used to make a 3D television display. Imagine thousands of thin wormholes sticking up out of a box like a tuft of long grass in a vase. The wormholes themselves would be invisible, but their ends could transmit light carried up from below. It would be as if thousands of pixels were simply floating in the air.
But that idea, Greenleaf concedes, is a very long way off. Even though the mathematics now says that it's possible, it's up to engineers to apply these results to create a working prototype.
Greenleaf's coauthors are Matti Lassas, professor of mathematics at the Helsinki University of Technology; Yaroslav Kurylev, professor of mathematics at the University College, London; and Gunther Uhlmann, Walker Family Endowed Professor of Mathematics at the University of Washington.
Note: This story has been adapted from material provided by University of Rochester.

Fausto Intilla