Flows in Complex Networks: Theory, Algorithms, and Application to Lennard-Jones Cluster Rearrangement

Maria Cameron, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which transitions occur between specific groups of nodes on the network. Sampling tools are built upon the outputs of TPT that allow to generate these reactive trajectories directly, or even transition paths that travel from one group of nodes to the other without making any detour and carry the same probability current as the reactive trajectories. These objects permit to characterize the mechanism of the transitions, for example by quantifying the width of the tubes by which these transitions occur, the location and distribution of their dynamical bottlenecks, etc. These tools are applied to a network modeling the dynamics of the Lennard-Jones cluster with 38 atoms (LJ38) and used to understand the mechanism by which this cluster rearranges itself between its two most likely states at various temperatures.

Original languageEnglish (US)
Pages (from-to)427-454
Number of pages28
JournalJournal of Statistical Physics
Issue number3
StatePublished - Aug 2014


  • Glassy dynamics
  • Markov state models
  • Protein folding
  • Self-assembly
  • Transition path theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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