Contents

• LIST OF ABBREVIATIONS
• GLOSSARY OF SYMBOLS
• INTRODUCTION
  • The Force Field
  • Creating a Coarse-grained Model
  • Working with a Coarse-grained Model
  • Thesis Overview
  
  
• FINDING REARRANGEMENT PATHWAYS
  • Introduction
  • A Double-ended Method: Nudged Elastic Band
  • Optimisation of the Nudged Elastic Band
    • Quenched Velocity Verlet Minimiser
    • L-BFGS Minimiser
  • A Single-ended Method: Eigenvector-following
  • Results
    • Slow-response Quenched Velocity Verlet
    • Choice of the Force Constant
    • Comparison of SQVV and L-BFGS Minimisers for the MB Surface
    • Doubly Nudged Elastic Bands
    • Comparison of the DNEB/L-BFGS and DNEB/SQVV Methods for Permutational Isomerisations of LJ
    • A Revised Connection Algorithm
    • Applications to Isomerisation of LJ and LJ
    • A Dijkstra-based Selector
    • Applications to Tryptophan Zippers
  • Summary
  
  
• PROPERTIES OF REARRANGEMENT PATHWAYS
  • Introduction
  • Localisation
  • Cooperativity
  • Applications to LJ and LJ Clusters and BLJ Liquid
  • Summary
  
  
• ENSEMBLES OF REARRANGEMENT PATHWAYS
  • Introduction
    • Graph Theory Representation of a Finite-state Markov Chain
    • The Kinetic Monte Carlo Method
    • Discrete Path Sampling
    • KMC and DPS Averages
    • Mean Escape Times
  • Chain Graphs
  • Complete Graphs
  • Graph Transformation Method
  • Applications to Sparse Random Graphs
  • Overlapping Sets of Sources and Sinks
  • Applications to Lennard-Jones Clusters
    • Isomerisation of LJ
    • Internal Diffusion in LJ
  • Summary
  
  
• CONCLUSIONS
  • Summary of Contributions
  • Future Research
  • Outlook
  
  
• ROTAMERS IN THE CHARMM19 FORCE FIELD
• ALGORITHMS
• PATHWAY SUMS FOR CHAIN GRAPHS, #MATH944#
• TOTAL ESCAPE PROBABILITY FOR CHAIN GRAPHS, #MATH971#
• FINDING THE SHORTEST AND THE FASTEST PATHS
• Bibliography