Parallelisation of Generalised Atmospheric Rosenbluth Methods and their Applications

交互式自回避行走，聚合物折叠的规范晶格模型，及其变体，作为一个基准模型，用于测试设计来模拟聚合物折叠的算法的性能。该项目中计划的模拟的一个主要挑战是开发能够有效地对相当复杂的聚合物构型进行采样的合适算法。在[1]中给出了对晶格聚合物的可用算法的极好回顾，特别关注基于生长的算法的最新发展。用于在受限环境中模拟聚合物的一种最先进的算法是PERM，修剪和丰富的Rosenbluth方法[2]及其对均匀采样的扩展。与multicanonical sampling [3]的结合导致了multicanonical PERM [4]，而认识到PERM执行均匀采样的固有能力使我开发了flatPERM [5]，这是PERM的平坦直方图版本。该算法[6，7]的进一步扩展允许包含传统的蒙特-卡罗移动。一个主要的挑战是通过开发合适的并行版本来提高这类算法的效率，以利用使用多核和GPU的现代计算机架构。直到最近，这一领域才取得了一些有希望的进展[8]，但仍有许多工作要做，特别是在进一步改善数据管理方面。J. Janse货车Rensburg自回避行走的Monte Carlo方法J. Phys.A，42（2009）323001。[2]P.格拉斯伯格。修剪富集Rosenbluth方法：链长高达1000 000的聚合物的模拟。E 56（1997）3682. [3]B。贝格和T.诺伊豪斯一阶相变的多规范算法。第249章. [4]M. Bachmann和W.扬克多规范链增长算法Phys.Rev.Lett.91（2003）208105。[5]T. Prellberg和J. Krawczyk。修剪和丰富Rosenbluth方法的平面直方图版本。物理修订信函92（2004）120602。[6]A. Rechnitzer和E. J. Janse货车Rensburg广义大气Rosenbluth方法（GARM）。物理学杂志。A 41（2008）442002。[7]E. J. Janse货车Rensburg和A.雷奇尼策自我回避行走的广义大气采样。J.Phys.A42（2009）335001。[8]S.坎贝尔和E. J. Janse货车Rensburg平行烫发J. Phys. A 53（2020）265005.

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 managementReferences[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 chainlength 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 enrichedRosenbluth method. Phys. Rev. Lett. 92 (2004) 120602.[6] A. Rechnitzer and E. J. Janse van Rensburg. Generalized atmospheric Rosenbluthmethods (GARM). J. Phys. A 41 (2008) 442002.[7] E. J. Janse van Rensburg and A. Rechnitzer. Generalized atmospheric sampling ofself-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.