Mapping high-speed

Apart from the traditional organic and combinatorial/high-throughput synthesis protocols covered in this book, more recent applications of microwave chemistry include biochemical processes such as high-speed polymerase chain reaction (PCR) [2], rapid enzyme-mediated protein mapping [3], and general enzyme-mediated organic transformations (biocatalysis) [4], Furthermore, microwaves have been used in conjunction with electrochemical [5] and photochemical processes [6], and are also heavily employed in polymer chemistry [7] and material science applications [8], such as in the fabrication and modification of carbon nanotubes or nanowires [9]. 

Recent techniques for detailed mapping and elucidation of processes occurring in pyrotechnic flames have incorporated computer assisted analysis. Ref 66 discusses the implementation of computer automated high speed mapping techniques and optical scanning as applied to spectroscopic analysis of transient combustion and pyrot processes. The considerations involved in the further development of exptl hardware and software have also been discussed... 

Bragg following advice to do so from his father, W. H. Bragg/ The calculations involved were many and tedious, and therefore Henry Lipson, C. Arnold Beevers, A. Lindo Patterson, and George Tunell provided more convenient methods of computing the electron-density functions in the days before high-speed computers were available. Currently, the computation of an electron-density map is simple and fast because of the efficiency of available computers. 

Extensive use of three-dimensional electron-density or difference electron-density maps in crystallography became possible only with the advent of high-speed computers. The magnitude of the problem can be illustrated" for a compound crystallizing in an orthorhombic unit cell with dimensions a = 11.98, 6 = 15.82, c = 11.49 A, Z = 4, for which 4397 (independent) Bragg reflections were measured at a resolution of... 

A. An electron-density map, sampled at a grid separation of 0.3 A in each direction means that, with these unit cell dimensions and four asymmetric units in the unit cell, there will be 76,602/4 = 19,151 grid points (a quarter of the unit cell). The value of p (xyz) must be computed at each of these 19,151 positions. This means that it is necessary to sum 4397 terms (the number of Bragg reflections) at each of 19,151 points (the number of grid points in one quarter of the unit cell) to compute one three-dimensional Fourier map, a total of 84,226,947 calculations. For such a large calculation the use of a high-speed computer is essential... 

Active query methods measure cell impedance, which is then correlated to SoC. The technique often superimposes an active signal (a low amplitude, characteristic high-frequency square or sinusoidal current pulse) onto the battery and then uses a transfer function on the response waveform to determine the ohmic polarization or a direct correlation to SoC. One permutation of this technique uses the voltage response to indigenous current spikes to map impedance in a similar way. This method provides reasonable results, but if hardware is involved it is often complex and expensive even sensors will require a relatively high-speed data acquisition bus to minimize the slew between voltage and current. 

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