Contour elongation

Take-Ups. A take-up is requited on a belt conveyor to ensure the proper belt tension at the drive pulley and along the conveyor, as weU as to ensure the proper troughing contour between idlers. A take-up is also needed to compensate for changes in belt length caused by elastic stretch during start-up, and any elongation characteristics of the belt that occur over a period of time. 

Surfaces beneath affected tubercles often have a striated contour due to increased acidity (see Fig. 3.24). Striated surfaces are caused by preferential attack along microstructural and microcompositional irregularities that have been elongated during steel rolling (see Chap. 7, Acid Corrosion ). 

Fig. 15.7 Conceptual illustration of the behavior of a Newton iteration on a nonlinear, stiff system of algebraic equations. A contour map of a norm of the residual vector F is plotted. The curvature represents nonlinear behavior, and the elongation represents disparate scaling, or stiffness. The desired solution of the problem is represented by the X the current iteration is marked by a dot. The elliptical contours represent residuals of the local linearization at the current iterate.

Figure 15.7 is intended to show conceptually some important mathematical aspects of a scale-disparate, nonlinear problem. The lines are contours of a norm of the residual vector F in a two-dimensional space. The position on the figure (i.e., cartesian coordinates) represents the y vector. As illustrated, the residual norm is characterized by a long, narrow, valley. The solution, which is a global minimum in the residual norm, lies near one end of the valley. In a highly scale-disparate problem, the valleys are greatly elongated and the valley walls are very steep. Nonlinearity is represented by curvature of the valleys. 

In cross section, hemp (Fig. 75, Plate VII) is almost always united in groups with rounded contour the lumen is elongated like a fissure or cavity and sometimes subdivided or radiating, thus differing markedly from the point-like lumen of flax. 

The cross-sections are of ample dimensions and mostly isolated or united in groups of two or three they are elongated with a rounded contour. The full lumen follows sensibly the shape of the external outline and often contains a substance which is coloured yellow by iodine and sulphuric add, while the wall is coloured blue and shows no lignified cuticle, although the various strata of growth of the wall are clearly exhibited. From the lumen sharply defined clefts start, these corresponding with the oblique fissures which are observed in the length of the fibre and which thus occupy the whole thickness of the wall. 

Fig. 2.4 The cross-sectional view of the elongation of the tissue (a) by applied lateral stress to demonstrate the change of shape in natural tissue, and the cross-sectional view of skin and soft tissue is shown in (b) with a barrier dressing that is liquid applied over the tissue. The barrier dressing must conform to the surface contours of the tissue...

Sometimes, a very strong correlation exists between the parameters, and their confidence contour has a strongly elongated shape [10]. This makes convergence during minimization difficult. This is especially the case for the relationships of rate or equilibrium constants, such as eq 20. In these cases a reparametrization is recommended, as eq 20(a), which yields a more spherical shape of the confidence contour and facilitates convergence [10]. 

Computer-generated contour plots of the elongation at break and the toughness, measured by the area under the stress-strain curve, exhibit... 

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