Mantle Plane

The (df )2 of each observation is its squared distance to the first two-component plane ( the Mantle Plane ). 

More than 93.5 percent of the variance is explained by the first two components, which tells us that two degrees of freedom describe most of the natural isotopic variation with the five chronometers. This observation has led to the concept of the Mantle Plane of Zindler et al. (1982), since a plane is defined by only two independent variables, and has been extensively discussed by Allegre et al. (1987). 

Let us decide that the cutoff value is fc = 2, so the matrix Vk is made of the first two columns of V. As expected, the remaining part of the data, i.e., the components three to five, which has been formally ascribed to noise, is very small. This is apparent in the last column of Table 4.12, where the (d )2 values have been listed. What Zindler et al. (1982) called the distance of a datum to the Mantle Plane is the square-root of (d, )2. Interestingly, many of the deviating points are those for which a HIMU component (Zindler and Hart, 1986) has been recognized (St Helena, Rio Grande, Australs). In order to account for this additional component, it is left to the reader to show that a third component would work adequately, o... 

Figure 4.13 Principal component analysis of the mean isotopic data for oceanic islands (courtesy of Vincent Salters). In the top left corner, the plane of the first two components (the Mantle Plane of Zindler et al, 1982) explains 93 percent of the variance. Component 1 is dominated by lead isotopes, component 2 by Sr and Nd isotopes. Other components are plotted for reference. In the top right corner, the Mantle Plane is viewed sideways along the direction of the second component, so the distance of each point to the plane can be easily seen. In the bottom left corner, it is viewed along the axis of the first component. The bottom right corner shows how little variance is left with components 3 and 4.

The greater stability of the core than of the mantle requires that fission occur along a plane between layers of the core. The number of layers is odd (five) accordingly the fission is not symmetric, as for the lighter fissionable nuclei (with four layers in the core), but is asymmetric. 

The way of compactification Here we chose the simplest compactifica-tion x5 = x5 -h 2tt llc. This is a cylindrical compactification. However more complicated cases are also possible, albeit not arbitrary ones. A branch of GR lists all the cases now we mention only the 2-dimensional example that from a plane by cut and sew you can produce of course a compact cylinder, but the mantle of a cone as well. 

Figure J.7H llliisttjlitui ut lhe X-ray Mantling wave field formed h) lhe inlcrtercnce between lhe iircuieni and reflected plane wave above a mirror. t(irfa M e leal fur dciaiU). A/ter ftedryk at (IWOj Ctipynght IWO by ilw A A AS...

If we plot Wilson s (1982) numerical model of 10 M star on a plane of homology invariants we see that the structure of the core stays very close to that of polytrope of index N=3 except for the very outer mantle. 

Figure 7.2 The relation between the particle growth in the disk mid-plane traced by the millimeter opacity index and that of the inner disk surface traced by the 9.7 pm silicate emission feature. The star symbols represent individual disks. Data points are from van Boekel etal. (2003), Natta etal. (2004),Furlanc/ al. (2006), Rodmann et al. (2006), and Lommen el al. (2007). Typical errors are 10-30% in both /3 and silicate band strength. Note also that differences in how the silicate band strengths were derived may introduce slight systematic offsets for the different data sets. The circle symbols represent dust opacity models calculated for the interstellar medium at a range of densities. From top to bottom the circles are Ry = 3.1 and Ry = 5.5 from Weingartner Draine (2001), a Spitzer-constrained dust opacity for dense clouds from Pontoppidan et al. (in preparation) and the particle growth simulation for protostellar envelopes [thin ice mantles, Ossenkopf Henning (1994)].

Peacock S. M. (2001) Are the lower planes of double seismic zones caused by serpentine dehydration in subducting oceanic mantle Geology 29, 299-302. 

If the electrode surface is strictly a plane with a well-defined boundary, such as an atomically smooth metal disk mounted in a glass mantle, the area A in the Cottrell equation is easily understood. On the other hand, real electrode surfaces are not smooth planes, and the concept of area becomes much less clear. Figure 5.2.2 helps to define two different measures of area for a given electrode. First there is the microscopic area, which is computed by integrating the exposed surface over all of its undulations, crevices, and asperities, even down to the atomic level. An easier quantity to evaluate operationally, is the geometric area (sometimes called the projected area). Mathemati-... 

Mantle in z = 0 plane (extends beyond diffusion layer boundary)... 

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