Spatial approach

Davies PF et al. A spatial approach to transcriptional profiling mechanotrans-duction and the focal origin of atherosclerosis. TIBTECH 1999 17 347-350. 

Chemical reactions are classified usually as diffusion-controlled, whose rate is limited by a reactant spatial approach to each other, and reaction-controlled (kinetic stage), whose rate is limited by a reaction elementary event. For systems with ideal reactant mixing considered in Section 2.1.1, there is no mechanism of reactant mutual approach. On the other hand, the kinetic equations (2.1.40) distinguish between reaction in physically infinitesimal volumes and the distant reactant motion in a whole reaction volume. In the absence of reaction particle diffusion is described by equation... 

The primary difficulty with the spatial approach is the need to section and analyze column segments. In particular, saturated zeolite materials are difficult to extrude from a column. In our work, therefore, we have used a scooping procedure, in which a stainless steel spoon is used to remove material from one end of the column. This simple approach has yielded smooth contaminant mass profdes, with good reproducibility between replicate columns. A similar procedure was reported by Fuhrmann et al. (1995). 

The evolution of detection systems suitable for multielement determinations has proceeded along two basic lines of development as indicated in Figure 1. One line of development is based upon dispersive systems. Dispersive systems are all multichannel devices which may be further classified as temporal or spatial devices. In the temporal approach, the measurement of intensities in different resolution elements is separated in time. The spatial approach uses detectors which are separated in space. 

Figure 10. A spatial approach for interrelating the local energy demand to the local mechanical parameter a). Oxygen demand distribution as a function of the end distolic volume (b) and the total oxygen demand vs. heart rate (based on Beyar and Sideman s, 1984d).

Fig. 5.32 Results of long-term H2 evolution measurements (a) and HAADF-STEM measurement after reaction (b). The long term measurement (a) on unselected and selected clusters is displayed as a function of time the interpolation of the raw data points dashed lines) serves as a guide to the eye. Deviations from the linear relation (after first 240 min) indicate catalyst deactivation after about 400 min of measurement no further hydrogen evolution is observed. A corresponding micrograph (b) taken of a FUe sample after illumination and H2 production over 25 h shows flocculated NRs as big white spots and groups of cluster ensembles in between. Single clusters have spatially approached but are not coalesced...

The next subsections describe two variants of the principles proposed so far. The first variant is founded on a purely spatial approach while the second makes use of a temporal approach. A preliminary version of the first variant was presented in [12]. 

Recently commercially available X-ray systems for laminography have a spatial resolution limited to hundred microns, which is not enough for modem multilayer electronic devices and assembles. Modem PCBs, flip-chips, BGA-connections etc. can contain contacts and soldering points of 10 to 20 microns. The classical approach for industrial laminography in electronic applications is shown in Fig.2. 

This approach is more close to X-ray stereo imaging and caimot reach enough depth resolution. There are also several systems with linear movement (1-dimensional) through the conical beam [5] as shown in Fig.4. In this case usable depth and spatial resolution can be achieved for specifically oriented parts of the object only. 

To reach enough good spatial resolution a new microlaminography approach has been developed. To avoid most errors from mechanical movements we use minimum movable parts (Fig.5). 

Laminographical approaches can be used for layer-by-layer visualization of the internal microstructure for the flat objects (multilayers, PCBs etc.), that caimot be reconstructed by computerized tomography because of the limited possibilities in rotation. Depth and lateral spatial resolutions are limited by the tube, camera and rotation accuracy. Microfocus X-ray tubes and digital registration techniques with static cameras allow improving resolution. Precision object manipulations and more effective distortion corrections can do further improvement. 

Although the topic of this paper easily extends to other disciplines, only eddy-current inspections will be eonsidered here. Eddy-current inspections do not typically capture spatial information with the signal however, there are large benefits to be found by keeping the spatial component integrated with the eddy-current signal. First, we will explore different approaches to adding spatial data to an eddy-current inspection. 

The atomic force microscope (ATM) provides one approach to the measurement of friction in well defined systems. The ATM allows measurement of friction between a surface and a tip with a radius of the order of 5-10 nm figure C2.9.3 a)). It is the tme realization of a single asperity contact with a flat surface which, in its ultimate fonn, would measure friction between a single atom and a surface. The ATM allows friction measurements on surfaces that are well defined in tenns of both composition and stmcture. It is limited by the fact that the characteristics of the tip itself are often poorly understood. It is very difficult to detennine the radius, stmcture and composition of the tip however, these limitations are being resolved. The AFM has already allowed the spatial resolution of friction forces that exlribit atomic periodicity and chemical specificity [3, K), 13]. 

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