Lead core compositional model

Figure 4 Lead isotopic modeling of the composition of the silicate Earth using continuous core formation. The principles behind the modeling are as in Halliday (2000). See text for explanation. The Held for the BSE encompasses all of the estimates in Galer and Goldstein (1996). The values suggested by Kramers and Tolstikhin (1997) and Murphy et al. (2003) also are shown. The mean life (t) is the time required to achieve 63% of the growth of the Earth with exponentially decreasing rates of accretion. The p, values are the 2 U/2°4pb of the BSE. It is assumed that the p of the total Earth is 0.7 (Allegre et ah, 1995a). It can be seen that the lead isotopic composition of the BSE is consistent with protracted accretion over periods of 102-10 yr.

As for the linear properties, numerous approaches have been proposed to predict and explain the nonlinear optical response of nanocomposite materials beyond the hypothesis leading to the simple model presented above ( 3.2.2). Especially, Eq. (27) does not hold as soon as metal concentration is large and, a fortiori, reaches the percolation threshold. Several EMT or topological methods have then been developed to account for such regimes and for different types of material morphology, using different calculation methods [38, 81, 83, 88, 96-116]. Let us mention works devoted to ellipsoidal [99, 100, 109] or cylindrical [97] inclusions, effect of a shape distribution [110, 115], core-shell particles [114, 116], layered composites [103], nonlinear inclusions in a nonlinear host medium [88], linear inclusions in a nonlinear host medium [108], percolated media and fractals [101, 104-106, 108]. Attempts to simulate in a nonlinear EMT the influence of temperature have also been reported [107, 113]. 

A chondritic model for the Earth s mantle is usually based upon the composition of Cl chondrites, adjusted for the loss of volatile elements and for the separation of the siderophile elements into the core. This leads to a mantle composition which is enriched in refractory lithophile elements by about 1.5 times the Cl chondrite value. There are however difficulties with the chondritic model because Cl chondrites and the Earth have different Mg/Si ratios (Fig. 3.9), as was discussed in Chapter 2 (Section 2.4.4). Some authors believe that this difference is original and dates from processes within the solar nebula indicating different evolutionary histories between the two. If this is true then Cl chondrites are not an appropriate starting composition for the composition of the bulk Earth and alternative models have to be considered. 

The two sequential processes that lead to the chemical degradation of a polymer due to oxidation are (1) oxygen diffusion and (2) chemical reaction [15], Researchers [16] have used the so-called unreacted core model to characterize and predict thermo-oxidative degradation in a composite laminate. According to this model, the composite weight loss due to oxidation, q can be expressed as a power law function of time ... 

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