Cross-sections

The differential cross-section will become an important parameter in describing ion ranges in solids and radiation damage, both of which will be discussed later in this book. The differential cross-section depends strongly on the form of the interatomic potential. 

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Figure 3.14 Lengthwise and cross sectional cut through a mud motor...

We have all used maps to orientate ourselves in an area on land. Likewise, a reservoir map will allow us to find our way through an oil or gas field if, for example we need to plan a well trajectory or If we want to see where the best reservoir sands are located. However, maps will only describe the surface of an area. To get the third dimension we need a section which cuts through the surface. This is the function of a cross section. Figure. 5.44 shows a reservoir map and the corresponding cross section. 

Take an example of estimating gross rock volume, based on seismic data and the results of two wells in a structure (Fig. 7.2). The following cross-section has been generated, and a base case GRV has been calculated. 

Puro, A., Kell, K.-J. Complete determination of stresses in fiber preforms of arbitrary cross section. J. Lightwave Technology. 1992, 10(8) 1010-101f. 

The AUGUR information on defect configuration is used to develop the three-dimensional solid model of damaged pipeline weldment by the use of geometry editor. The editor options provide by easy way creation and changing of the solid model. This model is used for fracture analysis by finite element method with appropriate cross-section stress distribution and external loads. 

In this paper, discontinuities in cylindrical specimens were studied by ultrasonic reflection tomography. The aim was threefold. First, to localize discontinuities from circular C-scan images. Second, to reconstruct quantitative cross-sectional images from circular B-scan profiles (i.e., reflection tomograms). Finally, to obtain three-dimensional information (i.e., discontinuity location, dimension and type) by stacking these reflection tomograms in multiple planes, in the third dimension. 

Elimination of the inaccuracy due to misalignment of cross sectional images ... 

Robb R.A., et. al. The Dynamic Spartial Reconstructor a computed tomography system for high-speed simultaneous scanning of multiple cross section of the heart., J. Med. Syst., V. 4, 1980, p. 253-288. 

We have perfomied some simulations of the eddy current distribution in a test object for a spiral coil and a circular one (see Fig. 4.1). Both coils had 9 turns and the excitation current was 6 mA. Figs. 4.1 show the cross section of the sample at the location of the crack and the amplitude of the eddy current density. One observes a 1.5 higher current density at the sides of the crack for the case of the circular coil. 

Right Fig. 4.2 Cross section of the test object. Comparison between the eddy eurrent density close to a crack in either a massive (bottom) or a stacked sample (top). 

Figure 3 Ferritic probe with a cross section.

Electromagnetic NDT instruments allow to increase the test records reliability. They are most efficient for detection of the rope durability loss as a result of loss of metallic cross-sectional area (LMA) localized faults (LF) like broken wires, localized corrosion etc. 

The INTROS Flaw Detector is able to inspect ropes moving through the magnetic head at speed 0...2 m/s. Limit of sensitivity to wire brake is 1% of the rope meatallic cross-section area, the LMA measure accuracy is not less than 2%. 

Calibration procedure bases on rope specimens and corresponds to the Standard Pratice ASTM 1574. It takes a piece of the rope under test having a nominal metallic cross-section area (LMA=0) to set zero point of the instrument. Rope section with the LMA value known is used to set the second point of LMA calibration charactiristics. It is possible to use the air point calibration when there is no rope in a magnetic head (LMA=100%). 

In empty space a cylindrical sheet of current of any cross section and very longer than it s diameter, material by a long solenoid of length 1 with N single turn traversed by an current I. 

It means that we may determine the cross section of the defect by measuring the variation of the inductance. It is an absolute measurement because the coefficient depends only of... 

During the X-ray apparatus main circuit creation the magnetomotive force for the power winding was selected less than for the high-voltage winding. The yoke cross-section is bigger, than the rod one. 

One more significant aspect of modem microscopy is the quantitative interpretation of the images in terms of the microstmcture of the object. Although most microscopes include or can be combined with powerful image processing systems, the interpretation of the contrast is still the main problem. On the other hand, reliable micromorpbological information could be easily obtained from a set of thin flat cross sections which reveal only density information, from which case accurate two- and three-dimensional numerical parameters of the internal microstmcture could be calculated. 

Considering existing microscopical techniques, one can find that non-destmctive information from the internal stmcture of an object in natural conditions can be obtained by transmission X-ray microscopy. Combination of X-ray transmission technique with tomographical reconstmction allows getting three-dimensional information about the internal microstmcture [1-3]. In this case any internal area can be reconstmcted as a set of flat cross sections which can be used to analyze the two- and three-dimensional morphological parameters [4]. For X-ray methods the contrast in the images is a mixed combination of density and compositional information. In some cases the compositional information can be separated from the density information [5]. Recently there has been a... 

A first example of application of microtomography is taken from life sciences. Here X-ray microscopy and microtomography allows to reconstruct the internal three-dimensional microstructure without any preparation and sometimes even of living objects. Fig. la shows an X-ray transmission microscopical image of bone (femoral head). Several reconstructed cross-sections are shown in Fig.lb. Fig.lc shows the three-dimensional reconstruction of this bone. 

Another important application area is the non-destructive defectoscopy of electronic components. Fig.2a shows an X-ray shadow image of a SMC LED. The 3-dimensional displacement of internal parts can only be visualized non-destructively in the tomographic reconstmction. Reconstructed cross sections through this LED are shown in Fig.2b. In the same way most electronic components in plastic and thin metal cases can be visualized. Even small electronic assemblies like hybrid ICs, magnetic heads, microphones, ABS-sensors can be tested by microtomograpical methods. 

One more application area is composite materials where one wants to investigate the 3D structure and/or reaction to external influences. Fig.3a shows a shadow image of a block of composite material. It consists of an epoxy matrix with glass fibers. The reconstructed cross-sections, shown in Fig.3b, clearly show the fiber displacement inside the matrix. The sample can be loaded in situ to investigate the reaction of matrix and fibers to external strain. Also absorption and transmission by liquids can be visualized directly in three-dimensions. This method has been applied to the study of oil absorption in plastic granules and water collection inside artificial plant grounds. 

Another application areas of microtomography are biology and agriculture. Fig.4a shows an X-ray transmission image through the tulip bulb in wet conditions. Damaged area can be found in the surface of this bulb. Fig.4b shows the reconstructed cross section with information about depth of damaged volume. 

Fig.l.Microtomography of bone shadow image (a), reconstructed cross-sections (b) and full 3-D reconstruction (c)... 

In case of some samples besides the cross sectional CT-slice also a projectional image is of interest. In these cases the test mode Digital Radiography (DR) is applied. In the DR-mode the object is not turned, but scanned horizontally and vertically. Again the very high dynamic of the detector and the mechanical accuracy of the complete system are of large benefit to the image quality. 

Now integrate the equation (5) taking into account the formulae for pi and pN. As a result we arrive to the specific volume flow rate in a film, referred to the unit of length for cross section ... 

Use now this equation to describe liquid film flow in conical capillary. Let us pass to spherical coordinate system with the origin coinciding with conical channel s top (fig. 3). It means that instead of longitudinal coordinate z we shall use radial one r. Using (6) we can derive the total flow rate Q, multiplying specific flow rate by the length of cross section ... 

Sizing of 3-D Surface Cracks with Complex Cross-Sections and Different Orientations Using Leakage Field. 

In this paper, computations are performed for sizing of surface cracks with different orientations with respect to the applied field, complex cross-sections, and unknown shapes by using the algoritlim from It is shown that the algoritlim allows to perform sizing of cracks with complex cross-sections independent of the shape of the crack for orientation angles not exceeding 45°. 

THE ALGORITHM FOR SIZING OF CRACKS WITH COMPLEX CROSS-SECTIONS... 

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