Far-field

The probes are assumed to be of contact type but are otherwise quite arbitrary. To model the probe the traction beneath it is prescribed and the resulting boundary value problem is first solved exactly by way of a double Fourier transform. To get managable expressions a far field approximation is then performed using the stationary phase method. As to not be too restrictive the probe is if necessary divided into elements which are each treated separately. Keeping the elements small enough the far field restriction becomes very week so that it is in fact enough if the separation between the probe and defect is one or two wavelengths. As each element can be controlled separately it is possible to have phased arrays and also point or line focussed probes. 

We first supposed that the field radiated into the piece by the transducer is known, thanks to the Champ-Sons model. Then, the main approximation used consists in making far field assumptions in the beam defect interaction area. In the case of a focused transducer we assume that the incident wavefronts on the defect are plane. This is equivalent to say that the defect is located in or near the transducer focal area and that a defect located outside this zone does not cause a significant echo. In the case of planar contact transducer, the incident wavefronts on the defect are assumed to be spherical The incident field on the defect is therefore approximated by the product of a spatial function gfp,0,z)describing the amplitude distribution in the beam and a time-delayed waveform < ) ft) representing the plane or spherical propagation in the beam. The incident field on the defect can therefore be approximated for ... 

One can calculate the far field solution of this equation in the direction ii for an ideally impulsive plane wave insonation, with incidence n ... 

Side drilled holes are widely used as reference reflectors, especially when angle beam probes are used (e.g. for weld testing). However, the distance law of side drilled holes is different to that of a flat bottomed hole. In the literature [2] a conversion formula is given which allows to convert the diameter of a side drilled hole into the diameter of a flat bottomed hole and vice versa, valid in the far field only, and for diameters greater than 1.5 times the wave length. In practical application this formula can be used down to approximately one nearfield length, without making big mistakes. Fig. 2 shows curves recorded from real flat bottomed holes, and the uncorrected and corrected DGS curves. 

Given that the ultrasonic back-wall echo from the synthesized beam and from the single element output may differ due to the coherent summing, time and frequency response of synthesized beam outputs may be achieved. Therefore, flat wall must be in the far-field or at the focus point as recommended by the standard [1]. 

A wide variety of measurements can now be made on single molecules, including electrical (e.g. scanning tunnelling microscopy), magnetic (e.g. spin resonance), force (e.g. atomic force microscopy), optical (e.g. near-field and far-field fluorescence microscopies) and hybrid teclmiques. This contribution addresses only Arose teclmiques tliat are at least partially optical. Single-particle electrical and force measurements are discussed in tire sections on scanning probe microscopies (B1.19) and surface forces apparatus (B1.20). 

Figure Cl.5.4. Comparison of near-field and far-field fluorescence images, spectra and lifetimes for the same set of isolated single molecules of a carbocyanine dye at a PMMA-air interface. Note the much higher resolution of the near-field image. The spectmm and lifetime of the molecule indicated with the arrow were recorded with near-field excitation and with far-field excitation at two different excitation powers. Reproduced with pennission from Trautman and Macklin [125].

Klar T A and Hell S W 1999 Subdiffraction resolution in far-field fluorescence microscopy Opt. Lett. 24 954-6... 

Under some citcumstances the crack tip stress intensity is different than far-field stresses would indicate because of microstmctural effects behind the crack tip, such as fibers, whiskers, and bridging grains. Often far-field values indicate the crack is propagating at a stress intensity value higher than Kj and this apparent value usually increases as crack length increases. In spite of indications to the contrary, bonds continue to break at the same value of the stress intensity however, the crack tip is being shielded from some of the appHed stress intensity. To minimize confusion about Kj it has been suggested that the farfield value of the stress intensity be called When there are no microstmctural features that effectively reduce the crack tip stress intensity,... 

Printing Office, vol. 2, November 1990, Figs. 2-7 and 2-15, or Kingery and PanniU, Memorandum Report No. 1518, Ballistic Research Laboratories, Aberdeen Proving Ground, U.S., April 1964) can then be used to determine the blast parameters of interest (Fig. 26-9). This method has hmitations in the far field where the peak incident overpressure is less than 4 kN/m" (0.5 psi). In this region, local terrain and weather effects become significant. 

The decrease in with crack depth for fracture of IG-11 graphite presents an interesting dilemma. The utihty of fracture mechanics is that equivalent values of K should represent an equivalent crack tip mechanical state and a singular critical value of K should define the failure criterion. Recall Eq. 2 where K is defined as the first term of the series solution for the crack tip stress field, Oy, normal to the crack plane. It was noted that this solution must be modified at the crack tip and at the far field. The maximum value of a. should be limited to and that the far... 

The decreasing value of K with decreasing flaw size for fracture of IG-11 graphite suggests that the near crack tip failure criterion would be better expressed by combining the near crack tip stress intensification estimated by K with the far field applied stress, Sfraa(Eq. 28). Using simple superposition of the stress perpendicular... 

EXP AC analyzes an interconnected network of building rooms and ventilation systems. A lumped-parameter formulation is used that includes the effects of inertial and choking flow in rapid gas transienl.s. The latest version is specifically suited to calculation of the detailed effects of explosions in the far field using a parametric representation of the explosive event. A material transport capability models the effects of convection, depletion, entrainment, and filtration of... 

In the general case, a buoyant jet has an initial momentum. In the region close to discharge, momentum forces dominate the flow, so it behaves like a nonbuoyant jet. There is an intermediate region where the influence of the initial momentum forces becomes smaller and smaller. In the final region, the buoyancy forces completely dominate the flow and it behaves like a plume. When the jet is supplied at an angle to the vertical direction, it is turned upward by the buoyancy forces and behaves virtually like a vertical buoyant jet in a far field. A negative buoyant jet continuously loses momentum due the opposite direction of buoyancy forces to the supply air momentum and eventually turns downward. 

If the combustion process within a gas explosion is relatively slow, then expansion is slow, and the blast consists of a low-amplitude pressure wave that is characterized by a gradual increase in gas-dynamic-state variables (Figure 3.7a). If, on the other hand, combustion is rapid, the blast is characterized by a sudden increase in the gas-dynamic-state variables a shock (Figure 3.7b). The shape of a blast wave changes during propagation because the propagation mechanism is nonlinear. Initial pressure waves tend to steepen to shock waves in the far field, and wave durations tend to increase. 

Although values for TNT equivalency ranging from 0.3% to 4% have been observed, Brasie and Simpson recommend, for predictive purposes, conservative values for TNT equivalency as follows 2% for near-field, and 5% for far-field effects (based on energy), applied to the full quantity of fuel released. 

One of the complicating factors in the use of a TNT-blast model for vapor cloud explosion blast modeling is the effect of distance on the TNT equivalency observed in actual incidents. Properly speaking, TNT blast characteristics do not correspond with gas explosion blast. That is, far-field gas explosion blast effects must be represented by much heavier TNT charges than intermediate distances. 

If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far field cannot be raled out, and their respective blasts should be superposed. The safe and most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance the determination of a minimum distance between potential blast sources so that their individual blasts may be considered separately, is a factor in present research. 

TNT blast is, however, a poor model for a gas explosion blast. In particular, the shape and positive-phase duration of blast waves induced by gas explosions are poorly represented by TNT blast. Nevertheless, TNT-equivalency methods are satisfactory, so long as far-field damage potential is the major concern. 

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