Communications - December 2009

process they call “simulation-guided optimization,” which alternates between molecular dynamics simulation and linear programming. A trial potential function is chosen, and a number of simulations—with random starting positions for the particles—are run, allowing the particles to interact until they settle into a structure. The result is a list of possible candidate structures for the ground state.

Then linear programming looks for a new potential function that makes all the candidates rank worse than the target configuration, and the whole process is repeated. The researchers call this process a heuristic algorithm because “it is not guaranteed to work.” They tested their potential function 1,200 times with different starting positions of the 20 particles, and all but six converged to the dodecahedron.

Not surprisingly, a process that repetitively applies simulation and linear programming can be computationally very taxing. Indeed, a large part of the mathematicians’ effort went into finding efficient search methods. “The problem is how not to get stuck at some sub-optimal solution,” Cohn says.

Graphs of potential functions against inter-particle distances for

and the kind you might be able to generate, are basically functions with not too many wiggles. We ask the question, ‘Can you get a potential function with essentially no wiggles?’ ”

Cohn/Kumar solutions tend to be smooth, with particle interactions decreasing monotonically with distance. But those for the more conventional approaches—those that employ potential wells—are complex and bumpy, with numerous local maxima and minima. “The problem with potential wells is they are much harder to manufacture in the lab,” Kumar explains. “But the kinds of functions you see in nature, Princeton university professor of chemistry Salvatore torquato, who pioneered an inverse approach to self-assembly.

the inverse approach

Cohn and Kumar’s work builds on earlier research by Salvatore Torquato, a professor of chemistry at Princeton University. Starting with a paper written four years ago, Torquato pioneered what he calls the inverse approach to self-assembly. In the traditional forward approach, known particle interactions are used to predict a likely resulting structure. But the inverse method starts with some desired configuration and derives the optimal inter-particle interactions that would spontaneously organize into that target structure. Torquato has used pure theoretical work as well as numeric computer simulation to find potential functions that can lead to the self-assembly of materials into squares, honeycombs, diamond shapes, and lattices.

“This is a completely different way of thinking about designing these structures, and it’s tailor-made for self-assembly,” he says.

Torquato says the inverse approach

Report from the ACM Nominating Committee

Slate of Nominees for ACM General Election

in accordance with the Constitution and Bylaws of the ACM, the nominating Committee hereby submits the following slate of nominees for ACM’s officers. in addition to the officers of the ACM, two Members at large will be elected. the names of the candidates for each office are presented in random order below:

PRESiDEnt (7/1/10–6/30/12): Alain Chesnais, SceneCaster.com

Joseph A. Konstan,

University of Minnesota

ViCE PRESiDEnt (7/1/10–6/30/12):
Barbara G. ryder,
Virginia Tech

norman P. Jouppi,

Hewlett Packard

SECREtaRY/tREa Su RER
(7/1/10–6/30/12):
Alexander l. Wolf,
Imperial College London
Carlo Ghezzi,
Politecnico di Milano

mEmBERS at LaRGE
(7/1/10–6/30/14):
Vinton G. Cerf,
Google
Fei-yue Wang,
Chinese Academy of Sciences-
Institute of Automation/
University of Arizona
Satoshi Matsuoka,
Tokyo Institute of Technology
Salil Vadhan,
Harvard University

the Constitution and Bylaws provide that candidates for

elected offices of the ACM may also be nominated by petition of one percent of the Members who as of november 1 are eligible to vote for the nominee. Such petitions must be accompanied by a written declaration that the nominee is willing to stand for election. the number of Member signatures required for the offices of President, Vice President, Secretary/treasurer and Members at large, is 687.

the Bylaws provide that such petitions must reach the elections Committee before January 31. original petitions for ACM offices are to be submitted to the ACM elections Committee, c/o Pat ryan, Coo, ACM headquarters, 2 Penn Plaza, Suite 701, new york, ny 10121, uSA, by January 31, 2010. Duplicate copies of the petitions should also be sent to the Chair of the elections Committee, Gerry

Segal, c/o ACM headquarters.

All candidates nominated by petition are reminded of the requirements stated in the Policy and Procedures on nominations and elections that a candidate for high office must meet in order to serve with distinction. Copies of this document are available from rosemary McGuinness, office of Policy and Administration, ACM headquarters. Statements and biographical sketches of all candidates will appear in the May 2010 issue of CACM.