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Gizmorama - September 10, 2018

Good Morning,

Today's first story is way above my knowledge of math and science. A new study has shown that prime numbers, much like crystals, have similar structural patterns. You read right. It is science at its very core. Please, check this story out below.

Learn about this and more interesting stories from the scientific community in today's issue.

Until Next Time,

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*-- Prime numbers, crystals share similar structural patterns --*

According to a new study, the distribution of prime numbers is similar to the positioning of atoms inside some crystalline materials.

When scientists at Princeton University compared the pattern of prime numbers along a lengthy line of numbers with the atomic patterns revealed when crystals are blasted with X-rays, they were surprised by the similarities.

"There is much more order in prime numbers than ever previously discovered," Salvatore Torquato, professor of chemistry and the Princeton Institute for the Science and Technology of Materials, said in a news release. "We showed that the primes behave almost like a crystal or, more precisely, similar to a crystal-like material called a 'quasicrystal.'"

Until recently, mathematicians thought prime numbers, numbers divisible only by themselves and one, were scattered sporadically throughout the number line. But new research suggests there are patterns to be found when primes are analyzed at greater scales.

Research suggests prime number patterns resemble "hyperuniformity" patterns found in crystals, quasicrystals and other disordered systems. Hyperuniformity describes patterns that reveal themselves at large scales.

One way to identify hyperuniformity in crystals is to blast them with X-rays, a process known as crystallography. When an X-ray travels through a crystal's 3D atomic lattice, the light produces a pattern of bright spots called Bragg peaks.

When X-rays pass through quasicrystals, the resulting pattern of Brag peaks is more complex. In between the main Bragg peaks are additional Bragg peaks -- patterns within patterns.

When scientists designed a model to convert the pattern of prime numbers into a crystalline atomic structure -- into particles -- they found the theoretical quasicrystal produced Bragg-like peaks similar to the hyperuniformity patterns revealed by real quasicrystals.

The comparison only works if a sufficiently large portion of the number line is translated. Over shorter intervals, the pattern of prime numbers appears random and disordered.

"When you go to that distinguished limit, 'Boom!'" Torquato said. "The ordered structure pops out."

Researchers hope the findings -- detailed this week in the Journal of Statistical Mechanics -- will offer new insights into both mathematics and material science.

"Prime numbers have beautiful structural properties," said Torquato. "The primes teach us about a completely new state of matter."

*-- Scientists study single molecules with terahertz spectroscopy for the first time --*

For the first time, scientists have used terahertz spectroscopy to study a single molecule.

Spectroscopy is the study of the interactions between light and matter. Most frequently, scientists use infrared light or X-rays to investigate atomic and molecular worlds.

Terahertz light lies between infrared and microwaves on the electromagnetic spectrum. Its frequency can excite molecules, causing them to vibrate, but its especially long wavelength makes it near-impossible to be focused onto single molecules.

Scientists at the University of Tokyo's Institute of Industrial Science developed a new method for focusing terahertz light beams. Physicists were able to measure the tunneling of a single electron using terahertz radiation.

To overcome the classical diffraction limit for focusing light beams, scientists deployed a single-molecule transistor, composed of two metal electrodes juxtaposed on a bowtie-shaped silicon wafer. The two electrodes form the transistor's source and drain.

Scientists deposited fullerene molecules in the nanoscale gaps between the two electrodes. The source and drain focus the incoming THz beam onto the fullerene molecules.

"The fullerenes absorb the focused THz radiation, making them oscillate around their center-of-mass," researcher Shaoqing Du said in a news release. "The ultrafast molecular oscillation raises the electric current in the transistor, on top of its inherent conductivity."

The change in current is tiny, but it is measurable. The same electrodes used to trap the THz radiation can be used to measure the slight current shift. The two electrodes picked up the change in fullerene absorption peaks when a single electron was added or subtracted from the transistor.

Scientists think their research -- detailed this week in the journal Nature Photonics -- could be used to develop terahertz technologies that complement visible-light and X-ray spectroscopy.

"This scheme provides an opportunity to investigate the ultrafast THz dynamics of subnanometer-scale systems," researchers wrote.


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