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Contact: Mary Ann Leung
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Fellow’s paper cracks quantum force riddle

A Department of Energy Computational Science Graduate Fellowship recipient is lead author of a paper outlining a way to calculate the effects of a quantum mechanical force.

The method described by fourth-year fellow Alejandro Rodriguez and his Massachusetts Institute of Technology colleagues could have implications for microelectromechanical systems (MEMS), microscopic machines with potential applications in medicine, microelectronics and other areas.

Jointly funded by the Department of Energy’s Office of Science and the National Nuclear Security Administration, the DOE CSGF provides up to four years of support to students pursuing a doctoral degree in areas of study that focus on the use of high-performance computing to solve complex problems in science and engineering. As part of the program Rodriguez completed a practicum at Lawrence Livermore National Laboratory in summer 2008.

In the paper published this month in the Proceedings of the National Academies of Sciences (PNAS), Rodriguez, fellow graduate student Alexander McCauley and professors John Joannopoulos and Steven Johnson describe the theoretical ingredients of a Casimir analog computer. The computer could make it easier to calculate the Casimir force.

Dutch physicist Hendrik Casimir predicted the force in 1948. When two objects are placed very close together – just micrometers apart – quantum electromagnetic field fluctuations will push them together, he said. The force manifests itself only on that tiny scale, so physicists and engineers typically ignored it – but MEMS are so small the force could make their moving parts stick.

In general, calculating the Casimir force mathematically is hugely demanding. Researchers could accomplish it for objects with only the simplest of geometries, such as two parallel plates. But in earlier publications the MIT researchers described a method for calculating the force between complex shapes, such as spheres and cylinders.

Their method relies on calculating the Maxwell Green’s function, which characterizes electromagnetic response to electronic sources around the surface of an object. Because Maxwell’s equations compute such forces in the same way regardless of scale, there’s a mathematical correspondence between calculating the quantum electromagnetics generating the Casimir force in a vacuum and calculating the classical electromagnetic behavior of larger bodies in a conducting fluid, such as saltwater, the researchers say.

That correspondence is the basis for the Casimir analog computer the MIT researchers describe in the PNAS paper. It’s called an analog computer because it measures a quantity related to the Casimir force rather than directly measuring the force. Researchers who wanted to calculate the force between objects of virtually any shape would be able to scale those objects up to centimeters instead of nanometers or micrometers. The objects would be placed in a conducting fluid and bombarded with microwaves. How the bodies respond should represent how the Casimir force would act on similar bodies at the smaller scale, the researchers say.

Instead of calculating the forces exerted by quantum fluctuations, the researchers compute the strength of an electromagnetic field at various points around the larger objects. That puts such calculations within the reach of classical analytical methods available in standard engineering software, the researchers say.

The researchers have shown that this correspondence also can be used to create numerical models that calculate the Casimir force with respect to time. The team has already developed a time-domain numerical solver for high-performance computers that can be used to calculate the force on a variety of complicated shapes.

In a paper published in March, the MIT researchers and physicist Michael Levin of Harvard University’s Society of Fellows described an arrangement of materials that enables Casimir forces to cause repulsion in a vacuum. That could open the door to designing MEMS that actually work to keep from sticking.

For more information on Rodriguez’s research, read the MIT release (at http://web.mit.edu/press/2010/casimir-forces.html) or visit his Web page (http://web.mit.edu/alexrod7/www/research.html). For information on the DOE CSGF, go to http://www.krellinst.org/csgf/.

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