Parallelisation of Generalised Atmospheric Rosenbluth Methods and their Applications

Interacting Self-avoiding Walks, the canonical lattice model of polymer collapse, and its
variants, serves as a benchmark model for testing the performance of algorithms designed to
simulate polymer folding.
A major challenge for the simulations planned in this project is the development of
suitable algorithms that are capable of efficiently sampling rather complicated polymer con-
figurations. An excellent review of available algorithms for lattice polymers, with a particular
focus on recent developments in growth-based algorithms is given in [1].
One state-of-the art algorithm for simulating polymers in a confined environment is the
PERM, the pruned and enriched Rosenbluth method [2], and its extensions to uniform
sampling. A combination with multicanonical sampling [3] led to multicanonical PERM [4],
whereas recognising the inherent ability of PERM to perform uniform sampling led me to
develop flatPERM [5], a flat histogram version of PERM. Further extensions of this algorithm
[6, 7] allow for the inclusion of conventional Monte-Carlo moves.
A major challenge is to enhance efficiency of this class of algorithms by developing suitable
parallelised versions to take advantage of modern computer architecture using multiple cores
and GPUs. Only very recently there has been some promising progress in this area [8], but
much work remains to be done, especially in further improving data management



References
[1] E. J. Janse van Rensburg. Monte Carlo Methods for the Self-Avoiding Walk. J. Phys.
A, 42 (2009) 323001.
[2] P. Grassberger. Pruned-enriched Rosenbluth method: simulation of polymers of chain
length up to 1000 000. Phys. Rev. E 56 (1997) 3682.
[3] B. Berg and T. Neuhaus. Multicanonical algorithms for rst order phase transitions.
Phys. Lett. B 267 (1991) 249.
[4] M. Bachmann and W. Janke. Multicanonical chain-growth algorithm. Phys. Rev. Lett.
91 (2003) 208105.
[5] T. Prellberg and J. Krawczyk. Flat histogram version of the pruned and enriched
Rosenbluth method. Phys. Rev. Lett. 92 (2004) 120602.
[6] A. Rechnitzer and E. J. Janse van Rensburg. Generalized atmospheric Rosenbluth
methods (GARM). J. Phys. A 41 (2008) 442002.
[7] E. J. Janse van Rensburg and A. Rechnitzer. Generalized atmospheric sampling of
self-avoiding walks. J. Phys. A 42 (2009) 335001.
[8] S. Campbell and E. J. Janse van Rensburg. Parallel Perm. J. Phys. A 53 (2020) 265005.