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New algorithm speeds simulations of complex fluids
James
E. Kloeppel, Physical Sciences Editor
217-244-1073; kloeppel@illinois.edu
1/23/04
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CHAMPAIGN,
Ill. — Computer simulations play an essential role in the study
of complex fluids – liquids that contain particles of different
sizes. Such liquids have numerous applications, which depend on a fundamental
understanding of their behavior. But the two main techniques for the
atomistic simulation of liquids – the molecular dynamics technique
and the Monte Carlo method – have limitations that greatly reduce
their effectiveness.
As reported in the Jan. 23 issue of the journal Physical Review Letters,
researchers at the University of Illinois at Urbana-Champaign have developed
a geometric cluster algorithm that makes possible the fast and accurate
simulation of complex fluids.
“The main advantage of the molecular dynamics method – its
ability to provide information about dynamical processes – is
also its main limitation,” said Erik Luijten, a professor of materials
science and engineering at Illinois. “Many complex fluids
contain particles of widely different sizes, which move at vastly different
time scales. A simulation that faithfully captures the motions of the
faster as well as the slower particles would be impractically slow.”
By contrast, the Monte Carlo method can circumvent the disparity in
time scales, since it is designed to extract equilibrium properties
without necessarily reproducing the actual physical motion of the atoms
or molecules. However, attempts to create appropriate “artificial
motion” have been limited to ad hoc solutions for specific situations.
Thus, a Monte Carlo method capable of efficiently simulating systems
containing particles of different sizes has remained a widely pursued
goal.
Luijten and graduate student Jiwen Liu have resolved this issue in a
very general way by creating artificial movements of entire clusters
of particles. The identification of appropriate clusters is a crucial
component of the simulation.
In 1987, researchers at Carnegie Mellon University resolved a similar
problem for magnetic materials by simultaneously flipping entire groups
(or clusters) of magnetic spins. This finding, which relied on an intricate
mathematical mapping dating back to the early 1970s, greatly accelerated
calculations for model magnets. Many researchers realized that a similar
approach would have an even bigger impact if it could be applied to
fluids.
“Thus, a cluster algorithm for the simulation of fluids became
a ‘Holy Grail’ for scientists studying fluids by means of
computer simulations,” Luijten said. “However, magnetic
materials possess a symmetry that is absent in fluids, making it apparently
impossible to use the ideas that were so
successful in magnets.”
Exploiting an idea developed for mixtures of spheres, Luijten and Liu
were able to reconcile the asymmetric nature of fluids with the mathematical
foundations underlying the identification of clusters.
Their simulation method utilizes a geometric cluster algorithm that
identifies “natural” groups of particles on the basis of
the elementary forces that act between the particles. This approach
greatly accelerates the simulation of complex fluids. Indeed, the greater
the disparity in size between particles, the more advantageous their
method becomes.
“This algorithm provides us with a new tool to study fluids that
were not previously accessible by simulations,” Luijten said.
“It has the potential to advance our understanding of a great
variety of liquid systems.”
The U.S. Department of Energy and the National Science Foundation funded
the work.
