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Fractal properties of model trajectories with exponential velocity autocorrelation functions

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  • Powles, J.G.
  • Fowler, R.F.

Abstract

The length, L(ϵ), at scale, ϵ, has been determined for four different models for atomic motion in a fluid, three distinct types of random walk with constant speed and the Langevin model. This has been done for trajectories in one, two, three and sometimes four dimensions. All these motions have exactly exponential velocity autocorrelation functions. However, the functional form of L(ϵ) is different for the different models, contrary to a recent assertion (S. Toxvaed, Phys. Lett. A 114 (1986) 159). A theory for L(ϵ) is lacking, except for the limits of ϵ small and ϵ very large. Our results can be used as ‘experimental results’ for the testing of such theories which are quite different from the conventional analysis of molecular motion in fluids. A comparison is made of these model results for L(ϵ) with those for simulated trajectories in realistic models of liquids and for the actual trajectories of suspended particles in solution.

Suggested Citation

  • Powles, J.G. & Fowler, R.F., 1987. "Fractal properties of model trajectories with exponential velocity autocorrelation functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(2), pages 318-334.
    • Handle: RePEc:eee:phsmap:v:141:y:1987:i:2:p:318-334
    DOI: 10.1016/0378-4371(87)90169-5
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