Commun. Comput. Phys., 12 (2012), pp. 691-702.

Lattice Free Stochastic Dynamics

Alexandros Sopasakis 1*

1 Center for Mathematical Sciences, Lund University, Box 118, 22100 Lund, Sweden.

Received 11 February 2011; Accepted (in revised version) 20 June 2011
Available online 1 March 2012


We introduce a lattice-free hard sphere exclusion stochastic process. The resulting stochastic rates are distance based instead of cell based. The corresponding Markov chain build for this many particle system is updated using an adaptation of the kinetic Monte Carlo method. It becomes quickly apparent that due to the lattice-free environment, and because of that alone, the dynamics behave differently than those in the lattice-based environment. This difference becomes increasingly larger with respect to particle densities/temperatures. The well-known packing problem and its solution (Palasti conjecture) seem to validate the resulting lattice-free dynamics.

AMS subject classifications: 82C20, 82C22, 82C80, 82B20, 82D99, 90B20

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Key words: Lattice-free, microscopic stochastic dynamics, kinetic Monte Carlo.

*Corresponding author.
Email: (A. Sopasakis)

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