Amoeba Monte Carlo algorithms for random trees with controlled branching activity: efficient trial move generation and universal dynamics

Abstract

The reptation Monte Carlo algorithm is a simple, physically motivated and efficient method for equilibrating semi-dilute solutions of linear polymers. Here we propose two simple generalizations for the analogue {\it Amoeba} algorithm for randomly branching chains, which allow to efficiently deal with random trees with controlled branching activity. We analyse the rich relaxation dynamics of Amoeba algorithms and demonstrate the existence of an unexpected scaling regime for the tree relaxation. In particular, our results suggests that the equilibration time for Amoeba algorithms scales in general like $N^2⟨n_{\mathrm{lin}}{⟩}^{\Delta }$, where $N$ denotes the number of tree nodes, $⟨n_{\mathrm{lin}}⟩$ the mean number of linear segments the trees are composed of and $\Delta \simeq 0.4$.

17 pages, 5 figures; Physical Review E, in press

References in corpus (16)

• From a melt of rings to chromosome territories: The role of topological constraints in genome folding
• Ring polymers in the melt state: the physics of crumpling
• Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: Towards the physics of crumpling
• Simulations of lattice animals and trees
• On the Tree-Like Structure of Rings in Dense Solutions
• DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling
• The collapse transition of randomly branched polymers -renormalized field theory
• Contact statistics highlight distinct organizing principles of proteins and RNA
• Computer simulations of melts of randomly branching polymers
• Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure
• Conformational statistics of randomly-branching double-folded ring polymers
• Beyond Flory theory: Distribution functions for interacting lattice trees
• Computer simulations of randomly branching polymers: Annealed vs. quenched branching structures
• From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers
• Scaling properties of RNA as a randomly branching polymer
• Phase behaviour of semiflexible lattice polymers in poor-solvent solution: mean-field theory and Monte Carlo simulations

Cited by in corpus (5)

• Entropy of self-avoiding branching polymers: mean field theory and Monte Carlo simulations
• The configurational entropy of random trees
• Configurational entropy of randomly double-folding ring polymers
• Ring polymers in two-dimensional melts double-fold around randomly branching "primitive shapes"
• Coherent modeling of double-folded ring polymers and their underlying random tree structure