Local thickness

Transmission electron microscopy (topography local thickness substructure—all thickness ranges) STEM/EDX... 

Electron probe microanalysis (composition diffusion profiles local thickness)... 

The Hull cell cathode has a continuous variation of current density along its length, and there are equations which give the primary current density at any point not too near the end. If the local thickness is measured at two points for which P is known, Tcan be calculated. The real current distribution is a function of cathode and anode polarisation as well as of the resistance of the electrolyte. The metal distribution ratio will be... 

Conversely, whenever the stretched lamella of local thickness h exerts a conjoining/disjoining pressure 11(h) which lies above the value of P, then fluid transports out of the... 

II provides a transition between the two asymptotic limits. Viscous stresses now scale by the local thickness of the film, h, and the bubble shape varies from the constant thickness film to the spherical segment. Here the surfactant distribution along the interface may be important. Fortunately, for small capillary numbers, dh/dx < 1 and the lubrication approximation may be used throughout. Region II is quantified below. 

Given that we in principle can never select a sample of local thick disk stars that is guaranteed to not contain any intervening thin disk stars, I would argue that we should keep the selection schemes as simple and as transparent as possible. In this sense the simplest and most robust selection is based on the kinematics of the stars. This is also the least model dependent method. Of course, should positions be available, i.e. height over the galactic plane, these could, and should, be used. 

Local thickness variations in a thin specimen complicate the quantitative analysis of a single element in the absence of precise knowledge of specimen thickness and without the ability to compare the measured x-ray intensities with those of thin standards. To avoid this difficulty, the x-ray intensity for the element of interest can be divided either by the intensity of a region of background between peaks as in the Hall method[8], or by the intensity from another element as in the Cliff-Lorimer method[9]. The former is largely used for biological analysis while the latter has become the standard thin specimen microanalysis method for materials science applications. The Cliff-Lorimer method is expressed in the following equation ... 

In summary, the intensity of the analytical line of any of the elements present in the excited volume to the sample is determined by four groups of data. The first ( Sample ) is only dependent on the sample as a whole (density, local thickness), so being common for all elements in the excited volume. The second ( FactovAf) only depends on atomic data, the third is the fraction of the given element (ca) and the fourth is the detection efficiency at the energy of the detected line. (Mass fractions appear in these formulas, as explained in the Appendix.)... 

X Independent variable In the cross-channel direction X local width of the solid bed y Independent variable In the channel depth direction Y local thickness of the solid bed In the y direction... 

The results of the analytical procedure are shown in Fig. 21 where characteristic distances between the cylinders are plotted as a function of the local thickness of the film. Quite strikingly, we observed a systematic variation of the lateral spacing between the cylinders as the film thickness increases from n to n + 1 layers of cylinders. Moreover, the characteristic spacings in the lower terrace was systematically... 

The same phenomenology must be important locally on Earth, too, where thick evaporite deposits of hydrated salts and local thick beds of methane clathrate in permafrost or seafloor sediments should influence the thermal environment of the crust. The predicted control on the crust s thermal state by hydrate deposits should have consequences for the localization of hydrothermal springs around and within evaporite basins, hydrothermal metamorphism... 

Fig. 14. The upper panel shows a 200 nm x 200 nm STM image of a Cu film grown on Ru(0001) with local thicknesses of 1 and 2 MLs. The regions 1 ML-thick are seen flat. The areas 2 ML-thick are easily recognized by the characteristic strain-relief reconstruction pattern. A fraction of the derivative of the image has been added to increase the contrast in the presence of steps. The lower panel shows differential conductance versus voltage spectra recorded on the 1 and 2 ML patches of the upper panel. The spectra have been shifted vertically for clarity.

Boundary layers appear in flow situations near the walls or other non-deform-able structures that exist in the flow field [3.8]. Their formation and development, stability and local thickness are of great interest to engineers and researchers because all the gradients of property concentration are concentrated here. Consequently, we can write a very simple expression for the flux of the property. 

The presence of the Z-pins affected at least one series of specimens, resulting in a local thickness reduction of up to 0.25 mm. This was taken into account when the data from these specimens were interpreted. 

The density profiles px z) across the wedge are presented on Fig. 14. The subscript indicates that local density px(z) was evaluated across the wedge slabs centered at a distance x from the wedge corner these distances are marked by arrows on Fig. 13. We note that for different distances x, the local thickness h(x) of the wedge slab is different due to this, the range of z values is different for each px(z) profile plotted on Fig. 14. The each part on Fig. 14 displays a set of the density profiles px(z) across three consecutive wedge segments IV, V and VI. 

In conclusion, the local thickness variations imply a relatively shallow depth of burial during the fault activity (below ca. 500 m). Basin modelling and backstripping across the Oseberg area supports this statement (Roberts et al., 1993, 1995). 

Figure 12.5. Histogram of local thicknesses computed for all residues of different protein native structures, when the virtual chain formed by the backbone Cq. atoms is viewed as a discretized thick tube. At a given residue, the local thickness is simply the minimum triplet radius over all triplets containing that residue.

The equation determining the local thickness, h, of a film with fluid surfaces (or, alternatively, determining the pressure distribution at the surfaces of the gap between two solid particles of known shape) is... 

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