Annealed models

Our main focus in this chapter has been on the applications of the replica Ornstein-Zernike equations designed by Given and Stell [17-19] for quenched-annealed systems. This theory has been shown to yield interesting results for adsorption of a hard sphere fluid mimicking colloidal suspension, for a system of multiple permeable membranes and for a hard sphere fluid in a matrix of chain molecules. Much room remains to explore even simple quenched-annealed models either in the framework of theoretical approaches or by computer simulation. 

Finally, paradigms frequently have the look of a sensible refuge in a chaotic sea of competing ideas. Monophyly is portrayed in precisely this way even if several alternative refuges are lurking on the horizon. For example, Carl Woese s alternative, which he calls the genetic annealing model (Woese,... 

Figure 14. Illustration of the extrapolation involved from laboratory scale data (Green et al. 1985) to the geological scale (i.e., months to millions of years). In this case the iso-length contours are fitted using the fanning model of Laslett et al. (1987). Extrapolations of this order magnify the differences between each of the annealing models of Laslett et al. (1987), Carlson (1990) and Crowley (1991). Adapted from Laslett et al. (1987).

Nevertheless, Carlson s essentially semi-empirical method has gained acceptance, and has been used as the basis for further developments such as the multi-kinetic model of Ketcham et al. (1999). This paper is one of three (Carlson et al. 1999, Donelick et al. 1999, Ketcham et al. 1999) that have addressed many of the earlier criticisms of the Carlson (1990) model. This research group has also produced a substantial annealing data-set of mixed-compositional apatites and established a model to deal with crystallographic effects, both of which have been incorporated into their full annealing model. 

Corrigan J (1993) Apatite fission track analysis of Oligocene strata in South Texas, U.S.A. Testing annealing models. Chem Geol 104 227-249... 

But we could as well consider the case in which cu and S (or r) are considered on the same ground. This corresponds to looking at the annealed model (say, in the copolymer case)... 

See Chapters 4 to 9 and relative bibliographic complements. The annealed model is treated for example in [Sinai and Spohn (1996)]. 

Remark 5.3 Notice that the results in Theorem 5.2(2) and Theorem 2.1, applied to the annealed model (i.e. with j3 replaced by ogbA (3)), match, up to a multiplicative constant, for (3 small. 

USING DYNAMIC MECHANICAL ANALYSES TO PROBE THE GLASSY STATE RESPONSE OF A Sub-Tg ANNEALED MODEL EPOXY NETWORK ... 

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