Simulation of highly stretched chains using long-range Monte Carlo

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Abstract
The behavior of highly stretched chains is not well described by computer simulations using the usual short-range Monte Carlo algorithms. Results from these have been shown to produce unphysical slowing down due to artificial energy barriers imposed by the dynamics. Furthermore, relaxation in the absence of a field from a highly stretched state is shown to be improperly described by the usual Monte Carlo algorithms. We propose a novel model employing long-range moves that should describe the motion in such situations more correctly. We implement this model on a square lattice to study gel electrophoresis. Using a highly efficient numerical code, the time for one long-range move scales as log(N), where N is the number of monomers in the chain. This allows us to conduct simulations of DNA molecules in a regime of molecular weights much greater than previously possible. Our results are in surprisingly good agreement with previous work for short chains using more realistic dynamics, and for longer chains, interesting data is obtained.

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