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Barnett-Jones M, Dickinson PA, Godfrey MJ, et al. Transition state theory and the dynamics of hard disks. Phys Rev E Stat Nonlin Soft Matter Phys. 2013;88(5):052132doi: 10.1103/PhysRevE.88.052132.
Barnett-Jones, M., Dickinson, P. A., Godfrey, M. J., Grundy, T., & Moore, M. A. (2013). Transition state theory and the dynamics of hard disks. Physical review. E, Statistical, nonlinear, and soft matter physics, 88(5), 052132. https://doi.org/10.1103/PhysRevE.88.052132
Barnett-Jones, M, et al. "Transition state theory and the dynamics of hard disks." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 88,5 (2013): 052132. doi: https://doi.org/10.1103/PhysRevE.88.052132
Barnett-Jones M, Dickinson PA, Godfrey MJ, Grundy T, Moore MA. Transition state theory and the dynamics of hard disks. Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052132. doi: 10.1103/PhysRevE.88.052132. Epub 2013 Nov 25. PMID: 24329239.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052132. doi: 10.1103/PhysRevE.88.052132. Epub 2013 Nov 25.

Transition state theory and the dynamics of hard disks.

Physical review. E, Statistical, nonlinear, and soft matter physics

M Barnett-Jones, P A Dickinson, M J Godfrey, T Grundy, M A Moore

Affiliations

  1. School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK.

PMID: 24329239 DOI: 10.1103/PhysRevE.88.052132

Abstract

The dynamics of two- and five-disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z(‡) of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks N is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.

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