The thermodynamics of Tetris - May 07, 2009
How do molecules, or nanoparticles, of many different shapes jostle together while nestling against a surface? Scientists from the University of Washington, St Louis Washington University in St Louis [press release], simulated such a situation using the seven tetrominoes of Tetris - an analogy that has been suggested before (F Cicoira and F Rosei, Surface Science Perspectives, doi:10.1016/j.susc.2005.10.063).
In the simulations (B C Barnes, D W Siderius and L D Gelb, Langmuir, doi:10.1021/la900196b) pieces from an infinite store were allowed to drop onto a flat board and shift around, but not to interact with each other (unlike real molecules). So the patterns generated simply reflect the system increasing its entropy (a measure of disorder). Even so, the scientists noted complicated clustering and that particular pieces fitted preferentially around each other - which they summarise by the old maxim "like attracts like".
Testing a number of combinations of shapes - from 'pure fluids' all the way up to a 7 component system - the researchers found that squares are easiest to surround (most 'soluble'), while rods are the hardest. "The results obtained to date may have some relevance to successful strategies for playing the Tetris computer game, but this has not been considered in detail," they say.
Ars Technica has more on this research. "Thermodynamically, how do they explain the spontaneous disappearance of a row once it has been completely, and continuously, assembled?" asks 'Vibedog'.
The researchers have been promised a show of Cossack dancing on completing their work.
Image: A four-component mixture of squares, rods, S shapes and Z shapes shows the pieces make little clusters rather than completely mixing together. Credit: Washington University, St Louis.
Comments
This comment is from one of the authors (D.W. Siderius). We noticed a small error in the blog post: our affiliate university is "Washington University in St Louis," not "University of Washington St Louis."
Posted by: Daniel Siderius | May 11, 2009 04:38 PM