By Mikito Toda, Tamiki Komatsuzaki, Tetsuro Konishi, Stephen Berry
Read Online or Download Advances in Chemical Physics Vol. 130 - Part B: Geometrical Structures of Phase Space In Multi-dimensional Chaos: Applications To Chemical Reaction Dynamics In Complex Systems PDF
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Additional resources for Advances in Chemical Physics Vol. 130 - Part B: Geometrical Structures of Phase Space In Multi-dimensional Chaos: Applications To Chemical Reaction Dynamics In Complex Systems
Berry, J. Chem. Phys. 99, 2942 (1993). ] 20 r. stephen berry Figure 15. 71 K. The trajectories from top to bottom in each ﬁgure correspond to 256, 512, 1024, 2048, 4096, and 8192 steps. Only at the energy of part c does two-phase equilibrium occur. [Reprinted with permission from C. Amitrano and R. S. Berry, Phys. Rev. E 47, 3158 (1993). ] speciﬁc challenge, recognized by the people whose work has just been described, was ﬁnding a way to transform the representation to a form that would separate the reaction coordinate from all the others in a way that would make it possible to recognize and study the kind of regularity that the threebody and four-body systems show.
The forest of faint curves in the background are actions of some of the other modes. Only the reaction coordinate shows any regularity at this high energy; all the other degrees of freedom are very chaotic. And, it is quite apparent, the reaction coordinate’s degree of freedom is indeed very regular in the saddle region. This is completely in accord with the expectation based on Hernandez and Miller’s recognition that the reaction coordinate must separate from the others somewhere in the vicinity of the saddle point, simply because the frequency of that mode must be imaginary .
Berry, J. Chem. Phys. ] dimension’’ D2, are those given in Table I; for sufﬁciently long trajectories, this quantity equals the fractal or Hausdorff dimension D0. The point to be made here is the obvious one that this dimensionality increases with the energy of the system, but that this is not a simple monotonic increase. There is a symptom here of something we will explore more and more extensively. The inference we draw from these results is becoming clear when we compare these numbers with the patterns of the power spectra in Fig.