Densest dice packing and computing with molecules

May 3, 2010
Tetrahedral dice have four triangular faces. When the dice are randomly poured into a container, they pack themselves more tightly than any other shape studied so far. Credit: Alexander Jaoshvili, Andria Esakia, Massimo Porrati, and Paul M. Chaikin

Physicists have made two new breakthroughs -- discovering a shape that packs more efficiently than any other known, and completing a high speed quantum calculation thousands of times faster than possible with conventional computation.

Dice Packing Record

Tetrahedral dice, which have four triangular sides, pack more densely than any other shape yet tested, according to research performed by a collaboration of New York University and Virginia Tech physicists. The revelation is the result of a series of experiments that involved pouring tetrahedral dice into containers, shaking them, and adding more dice until the containers were completely filled. After adding water to measure the open space between the dice, the researchers confirmed that the tetrahedrons fill roughly 76% of the available space in a large container. Similar experiments with spheres typically only fill containers to about 64% of the total volume. The researchers were able to get an inside view of the packed tetrahedral dice by imaging the containers with an MRI machine. The images are vital in helping them check and refine their die packing models.

The experiment, which is reported in the May 3 issue of , confirms recent calculations predicting efficient packing. Such packing problems are related to understanding many other problems including liquids seeping through soils, the flow of granular materials like sand and gravel, dense storage of information in digital memory, and even determining the best shapes for packaging consumer products like medicine tablets and candies. Daan Frankel of the University of Cambridge discusses the tetrahedral packing experiment and related research in a Viewpoint article appearing in the current edition of APS Physics.

Molecular Computations

An of a quantum calculation has shown that a single molecule can perform operations thousands of times faster than any conventional computer. In a paper published in the May 3 issue of Physical Review Letters, researchers in Japan describe a proof-of-principle calculation they performed with an iodine molecule. The calculation involved that computation of a discrete Fourier transform, a common algorithm that's particularly handy for analyzing certain types of signals.

Although the calculation was extraordinary swift, the methods for handling and manipulating the iodine molecule are complex and challenging. In addition, it's not entirely clear how such computational components would have to be connected to make something resembling a conventional PC. Nevertheless, in a Viewpoint in the current edition of APS Physics, Ian Walmsley (University of Oxford) points out that the demonstration of such an astonishingly high-speed calculation shows that there is a great deal to be gained if physicists can overcome the difficulties in putting single-molecule computation to practical use.

Explore further: Algorithm Advance Produces Quantum Calculation Record

More information:
-- Experiments on the Random Packing of Tetrahedral Dice, Alexander Jaoshvili, Andria Esakia, Massimo Porrati, and Paul M. Chaikin, Phys. Rev. Lett. 104, 185501 (2010) - Published May 03, 2010, Download PDF (free)

-- Ultrafast Fourier Transform with a Femtosecond-Laser-Driven Molecule, Kouichi Hosaka, Hiroyuki Shimada, Hisashi Chiba, Hiroyuki Katsuki, Yoshiaki Teranishi, Yukiyoshi Ohtsuki, and Kenji Ohmori, Phys. Rev. Lett. 104, 180501 (2010) - Published May 03, 2010. Download PDF (free)

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May 03, 2010
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5 / 5 (1) May 03, 2010
Cubical dice can indeed be packed with 100% density. However, this experiment was about randomly-oriented dice. Using cubical dice, randomly oriented, I'm sure you would get less than 76% density. Somehow tetrahedral dice, randomly oriented, pack tightly.

Alejo Hausner
May 03, 2010
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1 / 5 (2) May 07, 2010
The answer lies in the ratio of the angle of the join of the sides of the given shape, and that calculated against the number of sides. This, expressed as comparison of to the ratio of a cube to a sphere. the subset is the 2-d comparison of similar, with respect to the packing of triangles to circles. Ie, Pythagorean issues in relation to pi. (4 sides/3=1.333, closest to 4/pi=1.27)

This takes you directly to the issue of molecular packing and overall appearances of what is actually the wave particle duality and atomic shape equivalents, which hit the same highlights.

Which, of course, heads straight into mass, density, elasticity, conductivity,dielectrics, etc.

This Predicative model, once grokked, can be taken quite far with regard to creating plausibility (hypothesis) and then that can be tested.

What I'm saying is that it took a very long time for 'mainstream' science to get back to Sacred Geometry, as it was dumb enough to throw it out in the first place.

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