Equilibrium epoch

Figure 18 Schematic of epochs for a chemical reaction in solution. E represents the equilibrium epochs, G-D represents the generative-dissipative epochs, I represents the intrinsic or gas-phase epochs, and R represents the recrossing epoch. Adapted from ref. 215.

We wish to make two points about epochs before going on to a discussion of specific systems. First, the picture that we have presented is one where the reactive trajectories arise out of equilibrium, climb the reaction barrier, and then go on to a product equilibrium state. This picture clearly does not hold for nonequilibrium processes such as the photodissociation systems we have discussed. However, the return of these systems to equilibrium often shows the same intrinsic, dissipative, and equilibrium epochs as in equilibrium reaction systems. Thus, one may be able to identify epochs in photodissociation dynamics as well, as has been already discussed in conjunction with the simulation of ICN photodissociation in rare gas solution. ... 

Figure 2.5. A Monte Carlo calculation showing the merging history of a DM halo with final mass comparable to the Coma cluster (101bMq) from Cavaliere, Menci Tozzi (1999). The solid heavy line shows the mass as a function of redshift of the primary cluster. The lighter solid lines show the growth of subclusters that eventually merge into the main cluster. The merger epochs are indicated by the vertical dotted lines. The figure shows that there are episodes of near equilibrium punctuated my major merging events.

Figure 16.8. Relic density of gravitationally-produced WIMPZILLAs as a function of their mass Mx Hi is the Hubble parameter at the end of inflation, 1 i, is the reheating temperature, and Mpi 3 x 1019 GeV is the Planck mass. The dashed and solid lines correspond to inflationary models that smoothly end into a radiation or matter dominated epoch, respectively. The dotted line is a thermal distribution at the temperature indicated. Outside the thermalization region WIMPZILLAs cannot reach thermal equilibrium. (Figure from Chung, Kolb Riotto (1998).)...

The Frumkin epoch in electrochemistry [i-iii] commemorates the interplay of electrochemical kinetics and equilibrium interfacial phenomena. The most famous findings are the - Frumkin adsorption isotherm (1925) Frumkin s slow discharge theory (1933, see also - Frumkin correction), the rotating ring disk electrode (1959), and various aspects of surface thermodynamics related to the notion of the point of zero charge. His contributions to the theory of polarographic maxima, kinetics of multi-step electrode reactions, and corrosion science are also well-known. An important feature of the Frumkin school was the development of numerous original experimental techniques for certain problems. The Frumkin school also pioneered the experimental style of ultra-pure conditions in electrochemical experiments [i]. A list of publications of Frumkin until 1965 is available in [iv], and later publications are listed in [ii]. 

The depletion in FeO may be understood in at least two ways. First, the crystalline grains may be equilibrium condensates from a hot solar nebular composition gas with iron sequestered to metals or sulfides (see e.g. Chapter 4). In this case the condensed grains either had to condense slowly to form crystal domains, or had been reheated and thermally annealed at a later epoch. The second, alternative explanation is that ferromagnesian amorphous silicate grains were thermally annealed in a reducing environment, e.g. in the presence of carbon. Heating such precursors leads to the formation of metallic spheroids embedded between the forsterite crystals, as the initial FeO component is reduced (see e.g. Fig. 8.3 and Connolly et al. 1994 Jones Danielson 1997 Leroux et al. 2003 Davoisne et al. 2006). Because carbon is ubiquitously present in primitive Solar System materials, this pathway offers a natural explanation to the observed FeO-poor silicate crystals. It is yet to be determined whether low-temperature crystallization processes, discussed in Section 8.1.1, would also lead to FeO depletion. 

If we know that a certain reaction step with a clearly smaller reaction rate takes place, then we can correct the scheme in this way for this particular p, , of course. However, in this case it is compulsory that the individual terms in the transition matrix are again properly standardized. Each element of the transition matrix for a certain epoch out of the equilibrium is then divided by the corresponding elements for the equilibrium, so that the weighting factors for the equilibrium tend to approach again to 1. 

At the Other end of the spectrum are the punctuated equilibrium evolutionists, those who point to fossil evidence that demonstrates epochs in Earth s history when new species appeared explosively fast ( evolution by jerks ). These proponents argue that differences between older and newer species are so vast that they are clearly distinguishable. 

We divide the discussion into four topics. In Section 9.1 we are concerned with the one-dimensional thermal equilibrium configuration of an atmosphere in the absence of internal motion. In Section 9.2 we expand the temperature field to three dimensions and investigate the dynamical properties of atmospheres. In Section 9.3 we address the question of how determinations of chemical composition imply the evolution of planets and the Solar System as a whole. Finally, in Section 9.4 we review measurements of the excess heat emitted by the planets, and discuss the importance of these measurements for determining the status of planetary evolution in the present epoch. 

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