Map two-dimensional

Hohng, S., Zhou, R., Nahas, M. K., Yu, J., Schulten, K., Lilley, D. M.J., andHa, T. (2007). Fluorescence-force spectroscopy maps two-dimensional reaction landscape of the Holliday junction. Science 318, 279—283. 

Whereas SECM usually uses tips that pass a current in amperometric or voltammetric mode, an important related application uses passive ion-selective sensor tips which can be used for mapping two-dimensional and even three-dimensional ion distributions and concentration profiles over the surface, of species such as protons and zinc ions [53]. 

In this section, I use IR spectroscopy to map two-dimensional water distributions as well as to consider its species in deformed granites. I especially focus on water distributions associated with solution-precipitation process of feldspar, and consider possible transport mechanisms of water. 

Backscattered electron image Surface analysis and elemental mapping Two-dimensional... 

Some discontinuities may be identified by a conventional two-dimensional ultrasonic technique, from which the well-known C-scan image is the most popular. The C-scan technique is relatively easy to implement and the results from several NDE studies have been very encouraging [1]. In the case of cylindrical specimens, a circular C-scan image is convenient to show discontinuity information. The circular C-scan image shows the peak amplitude of a back-scattered pulse received in the circular array. The axial scan direction is shown as a function of transducer position in the circular array. The circular C-scan image serves also as an initial step for choosing circular B-scan profiles. The latter provides a mapping between distance to the discontinuity and transducer position in the circular array. 

These two transducer pairs are activated alternating. For this purpose an ultrasonic instrument is combined with a two channel multiplexer. Figure 8 presents a modified standard instrument USN52 which also implies a modified software. This system performs four measurements per second - alternating the velocity and the thickness are determined. The probe can be scanned over the surface and in every position both, the velocity and the wall thickness are indicated Using the serial interface of the instrument finally a two-dimensional map of velocity or thickness can be generated. 

The Kohonen network or self-organizing map (SOM) was developed by Teuvo Kohonen [11]. It can be used to classify a set of input vectors according to their similarity. The result of such a network is usually a two-dimensional map. Thus, the Kohonen network is a method for projecting objects from a multidimensional space into a two-dimensional space. This projection keeps the topology of the multidimensional space, i.e., points which are close to one another in the multidimensional space are neighbors in the two-dimensional space as well. An advantage of this method is that the results of such a mapping can easily be visualized. 

Equation (3.85) T is a translation vector that maps each position into an equivalent ition in a neighbouring cell, r is a general positional vector and k is the wavevector ich characterises the wavefunction. k has components k, and ky in two dimensions and quivalent to the parameter k in the one-dimensional system. For the two-dimensional lare lattice the Schrodinger equation can be expressed in terms of separate wavefunctions ng the X- and y-directions. This results in various combinations of the atomic Is orbitals, ne of which are shown in Figure 3.13. These combinations have different energies. The /est-energy solution corresponds to (k =0, ky = 0) and is a straightforward linear... 

Both equation 11 and the two-dimensional counterpart of equation 9 can be solved by several standard mathematical techniques, one of the more useful being that of conformal mapping. A numerical solution is often more practical for compHcated configurations. 

A hot gas expander is typieaiiy deseribed by a map of shaft power versus mass flowrate (Figure 7-3). Notiee that there are four parameters ehanging in this partieuiar map w, J, Pj, and Tj. Figure 7-3 is most useful when the family of eurves (whieh are for a eonstant rotational speed) reduees to a single eurve in a two-dimensional spaee. Usually, expander eharaeteristies are a very weak funetion of angular speed. However, in eases where the variations due to rotational speed are important, a third dimension is required. This dimension should be equivalent speed, Ng. 

Figure 12.3 Two-dimensional crystals of the protein bacteriorhodopsin were used to pioneer three-dimensional high-resolution structure determination from electron micrographs. An electron density map to 7 A resolution (a) was obtained and interpreted in terms of seven transmembrane helices (b).

The pulse sequence which is used to record CH COSY Involves the H- C polarisation transfer which is the basis of the DEPT sequence and which Increases the sensitivity by a factor of up to four. Consequently, a CH COSY experiment does not require any more sample than a H broadband decoupled C NMR spectrum. The result is a two-dimensional CH correlation, in which the C shift is mapped on to the abscissa and the H shift is mapped on to the ordinate (or vice versa). The C and //shifts of the //and C nuclei which are bonded to one another are read as coordinates of the cross signal as shown in the CH COSY stacked plot (Fig. 2.14b) and the associated contour plots of the a-plnene (Fig. 2.14a and c). To evaluate them, one need only read off the coordinates of the correlation signals. In Fig. 2.14c, for example, the protons with shifts Sh= 1.16 (proton A) and 2.34 (proton B of an AB system) are bonded to the C atom at c = 31.5. Formula 1 shows all of the C//connectivities (C//bonds) of a-pinene which can be read from Fig. 2.14. 

With a special optical system at the sample chamber, combined with an imagir system at the detector end, it is possible to construct two-dimensional images of the sample displayed in the emission of a selected Raman line. By imaging from their characteristic Raman lines, it is possible to map individual phases in the multiphase sample however, Raman images, unlike SEM and electron microprobe images, have not proved sufficiently useful to justify the substantial cost of imaging optical systems. 

In vertical downward flow as well as in upward and downward inclined flows, the flow patterns that can be observed are essentially similar to those described above, and the definitions used can be applied. Experimental data on flow patterns and the transition boundaries are usually mapped on a two dimensional plot. Two basic types of coordinates are generally used for this mapping - one that uses dimensional coordinates such as superficial velocities, mass superficial velocities, or momentum flux and another that uses dimensionless coordinates in which some kind of dimensionless groups are used as coordinates. The dimensional coordinates maps are inherently limited to the range of data and flow conditions under which the experiments were conducted. In spite of this limitation, it is widely used because of its simplicity and ease of use. Figure 24 provides an example of such a map. 

The 2D chromatograms reveal additional components of the natural mixtures. They also give a map of the essential oil, which is helpful in the identification of the components by the position and the characteristic colours of the derivatives on the plate. A further, considerable improvement in the separation performance can be obtained by using overpressured layer chromatography (OPLC). Harmala et al. (70) used 2D OPLC for the separation of coumarins from the genus Angelica. Figure 10.15 shows the one-dimensional (a) and two-dimensional (b) OPLC separations of 16 coumarins. 

G. J. Opiteck, J. W. Jorgenson, M. A. Moseley III and R. J. Anderegg, Two-dimensional mia ocolumn HPLC coupled to a single-quadrupole mass spectrometer for the elucidation of sequence tags and peptide mapping , 7. Microcolumn Sep. 10 365-375 (1998). 

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