Molecular dynamics simulations were performed for soft- and hard-sphere systems, for number densities ranging from 0.5 to 1.0, and the Kolmogorov-Sinai entropy (KS entropy) and self-diffusion coefficients were calculated. It is found that the KS entropy, when expressed in terms of average collision frequency, is uniquely related to the self-diffusion coefficient by a simple scaling law. The dependence of the KS entropy on average collision frequency and number density was also explored. Numerical results show that the scaling laws proposed by Dzugutov, and by Beijeren, Dorfman, Posch, and Dellago, can be applied to both soft- and hard-sphere systems by changing to more generalized forms.
We obtained new characteristic relations in Type-II and III intermittencies according to the reinjection probability distribution. When the reinjection probability distribution is fixed at the lower bound of reinjection, the critical exponents are -1, as is well known. However when the reinjection probability distribution is uniform, the critical exponent is -1/2, and when it is of form [Formula: see text], -3/4. On the other hand, if the square root of Δ, which represents the lower bound of reinjection, is much smaller than the control parameter ∊, i.e. ∊ ≫ Δ1/2, critical exponent is always -1, independent of the reinjection probability distribution. Those critical exponents are confirmed by numerical simulation study.
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