By Mikito Toda, Tamiki Komatsuzaki, Tetsuro Konishi, Stephen Berry
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The Next Step: The Magic Transformation and Its Consequences VI. Conclusion Acknowledgments References I. ’’ Simulations are particularly powerful means to carry out such studies. For example, we can follow trajectories for very long times with molecular dynamics and thereby evaluate the global means of the exponential rates of divergence of neighboring trajectories. This is the most common way to evaluate those exponents, the Liapunov exponents. The sum of these is the Kolmogorov entropy, one gross measure of the volume of phase space that the system explores, and hence one Geometric Structures of Phase Space in Multidimensional Chaos: A Special Volume of Advances in Chemical Physics, Part B, Volume 130, edited by M.
J. Wales, J. Chem. Phys. 96, 1376 (1992). ] roughly for Ar3 by Beck et al. in the work just cited, and then they were evaluated more accurately for Lennard-Jones clusters modeling Ar3 and Ar7 by Hinde et al. . Here we ﬁnd a striking difference between these two clusters. We can focus our discussion on the K-entropies as functions of the total energies. Figure 4 shows the variation of the K-entropy for the three-particle Lennard-Jones cluster as a function of energy. 7 e/atom (where e is the energy parameter in the Lennard-Jones potential function), corresponding to the energy at which the system can just cross the saddle.
We do this by 16 r. stephen berry Figure 10. Distributions as shown in Fig. 8 but for a ﬁve-particle Lennard-Jones cluster, going over its lower-energy (‘‘diamond-square-diamond’’) saddle. No signiﬁcant distinction makes the saddle region different from other regions. [Reprinted with permission from R. J. Hinde and R. S. Berry, J. Chem. Phys. 99, 2942 (1993). ] examining the time dependence of the accumulation of action along pathways that take the system through its saddle, ﬁrst for the three-particle system and then for the four-particle system.