HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
IMA Workshop 11
Numerical Methods for Polymeric Systems
May 13-17, 1996

Organizer: Stuart Whittington

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.


Back to Mathematical Methods in Materials Science Page
Go