Numerical Methods for Polymeric Systems

1. Front Matter

   Pages i-xi

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2. Convergence Rates for Monte Carlo Experiments

   • Alistair Sinclair

   Pages 1-17

3. Umbrella Sampling and Simulated Tempering

   • Neal Madras

   Pages 19-32

4. Monte Carlo Study of Polymer Systems by Multiple Markov Chain Method

   • Enzo Orlandini

   Pages 33-57

5. Measuring Forces in Lattice Polymer Simulations

   • Ronald Dickman

   Pages 59-74

6. A Knot Recognition Algorithm

   • Marc L. Mansfield

   Pages 75-82

7. Geometrical Entanglement in Lattice Models of Ring Polymers: Torsion and Writhe

   • Maria Carla Tesi

   Pages 83-97

8. Oriented Self-Avoiding Walks with Orientation-Dependent Interactions

   • S. Flesia

   Pages 99-119

9. A Monte Carlo Algorithm for Studying the Collapse Transition in Lattice Animals

   • C. E. Soteros, M. M. Paulhus

   Pages 121-139

10. Monte Carlo Simulation of the Θ-Point in Lattice Trees

    • E. J. Janse Van Rensburg, N. Madras

    Pages 141-157

11. Molecular Dynamics Simulations of Polymer Systems

    • Burkhard Dünweg, Gary S. Grest, Kurt Kremer

    Pages 159-195

12. Dynamics of Polymers Near the Theta Point

    • Jeffrey Kovac

    Pages 197-201

13. Self Diffusion Coefficients and Atomic Mean-Squared Displacements in Entangled Hard Chain Fluids

    • Steven W. Smith, Carol K. Hall, Benny D. Freeman, Julie A. McCormick

    Pages 203-215

14. Back Matter

    Pages 217-223

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Polymers occur in many different states and their physical properties are strongly correlated with their conformations. The theoretical investigation of the conformational properties of polymers is a difficult task and numerical methods play an important role in this field. This book contains contributions from a workshop on numerical methods for polymeric systems, held at the IMA in May 1996, which brought together chemists, physicists, mathematicians, computer scientists and statisticians with a common interest in numerical methods. The two major approaches used in the field are molecular dynamics and Monte Carlo methods, and the book includes reviews of both approaches as well as applications to particular polymeric systems. The molecular dynamics approach solves the Newtonian equations of motion of the polymer, giving direct information about the polymer dynamics as well as about static properties. The Monte Carlo approaches discussed in this book all involve sampling along a Markov chain defined on the configuration space of the system. An important feature of the book is the treatment of Monte Carlo methods, including umbrella sampling and multiple Markov chain methods, which are useful for strongly interacting systems such as polymers at low temperatures and in compact phases. The book is of interest to workers in polymer statistical mechanics and also to a wider audience interested in numerical methods and their application in polymeric systems.

• Markov
• Polymer
• Simulation
• algorithm
• mechanics
• molecular dynamics
• numerical methods

• Department of Chemistry, University of Toronto, Toronto, Canada

  Stuart G. Whittington

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