Landscape picture

In Section VII we conclude our results and discuss several issues arising from our proposals. We revisit our original motivation—that is, to find a simple model, in the sense of dynamical systems, that captures several common aspects of slow dynamics in liquid water, or more generally supercooled liquids or glasses. Our attempt is to make clear the relation and compatibility between the potential energy landscape picture and phase space theories in the Hamiltonian dynamics. Importance of heterogeneity of the system is discussed in several respects. Unclarified and unsolved points that still remain but should be considered as crucial issues in slow dynamics in molecular systems are listed. 

IS is not owned only by liquid water, but it is common to many other molecular systems. In particular, the ragged landscape picture is useful and now even popular to understand cluster dynamics. Extensive works by Berry clarified how the structural transition or isomerization process of Ar cluster takes place reflecting the raggedness of potential functions [46]. 

We examine the relation of the mode coupling theory of glassforming liquid dynamics to the Gibbs-Goldstein landscape picture of relaxation, and identify, using both scaling relationships and thermodynamic calculations, where the crossover between the two domains occurs. 

In the zeolite system, faujasite has the lowest value of the order parameter, and in the quartz system, it has the highest [18]. In the energy landscape picture, the surface tension and difference between the minimum of free energy corresponding to two structures play an important role in determining nucleation barrier between two metastable phases or one metastable phase and one stable solid (SS) phase. However, it is very hard to obtain surface tension between two metastable solid (MS) phases. 

Regard the energy landscape pictured in Fig. 3.3 and suppose that the protein is initially trapped in the basin of attraction surrounding state A. According to Kramers theory (Van Kampen 1992 Risken 1996), the protein state will eventually escape from this basin due to thermal perturbations, and the escape rate... 

The landscape picture can be extended to systems at higher temperature, where entropic effects may become important, by introducing the concept of a/ree energy landscape. The definition of a meaningful free energy requires that a number of possibly collective coordinates q r) = qi r),q2 r),q-i r),... sufficient... 

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