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IMA Workshop 11

Numerical Methods for Polymeric Systems

Numerical Methods for Polymeric Systems

May 13-17, 1996

Materials scientists are interested in the structure of polymers
in a wide variety of different states of matter. Some obvious
examples include the arrangement of polymers in crystals and
fibres, glasses, gels and the rubbery state, melts and solutions,
as well as polymers at interfaces and in confined geometries.
Two numerical techniques which are widely used in many of these
areas are Monte Carlo methods and molecular dynamics. Although
several quite different types of Monte Carlo methods have been
used, perhaps the most widely applicable method is Metropolis
sampling, which involves sampling along a realization of a Markov
chain defined on the configuration space of the polymeric system.
The Markov chain must be carefully designed to ensure ergodicity,
so that the required distribution is the unique limit distribution
of the Markov chain.

For dilute polymer solutions (and especially for lattice models
of isolated polymers) Monte Carlo algorithms are becoming well-understood
and one algorithm in particular (the pivot algorithm) is known
to be an extremely effective tool at least for simple systems.
For more strongly interacting systems, such as dense polymer
systems (concentrated solutions or melts) or isolated polymers
with strong attractive forces, the situation is much less advanced.
Although algorithms exist for these cases their behavior is
less well-understood from a theoretical point of view. It would
be useful to bring together people working on Monte Carlo methods
for the simpler systems and for the more complex systems, and
also to involve people who are primarily interested in the analysis
of the algorithms. To make progress in handling the more complicated
systems it seems necessary to invent new algorithms and also
to analyze their behavior.

Monte Carlo methods are at their best when applied to the calculation
of equilibrium properties of a system and, if dynamic information
is required, then perhaps the most useful approach is molecular
dynamics, in which the equations of motion are directly solved
to determine the time dependent properties of the system.

The workshop would bring together workers using Monte Carlo
methods to investigate polymers in different states, and also
investigators from the field of molecular dynamics.

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