Transition table

A variety of mechanisms have since been suggested to explain the physical basis for the observed transition between flow patterns (Ishii, 1975 Taitel and Dukler, 1976b Taitel et al., 1980 Barnea, 1987 Taitel and Barnea, 1990). Dukler and Taitel (1991b) summarized the various mechanisms to explain such flow pattern transitions (Table 3.1), where the letters in Table 3.1 identify the theoretical curves shown in the accompanied graphs (Fig. 3.7) for different flow directions. A word of caution was given in the reference ... 

The thermodynamics experiments are subdivided into experiments on calorimetry and heat capacity, Table XVI phase transitions, Table XVII properties of gases, liquids, solids, solutions and mixtures, Table XVIII and finally equilibrium and miscellaneous thermodynamic topics , Table XIX. 

A more suitable method to calibrate the temperature behavior of an NMR probe involves the characterization of temperature-dependent melting points and phase transitions. Table 1 is a list of materials that can be applied for the calibration of variable-temperature NMR probes in the temperature range of 279-791 K. 

Whereas the Mossbauer spectra at 77 K of CsM13% (M = V, Mn) can be fitted assuming quadrupole splitting at a single metal site, two sites (a/b =2/1), with coupling constants of opposite sign, must be assumed when M = Cr. In the a and b sites the 12T atoms are in asymmetric and symmetric bridging positions respectively, consistent with axially distorted octahedra. The a to jS phase transition (Table 36) is confirmed from X-ray powder diffraction, but at 165 5 K.278... 

Compounds 1-3 exhibit mechano- and/or thermochromic photoluminescent properties accompanied by cubic-columnar LC phase transitions. Table 1 shows the LC properties of compounds 1-3. Compounds 1 and 3 show cubic phases and columnar phases on rapid cooling and slow cooling, respectively. A columnar phase is not observed for compound 2 on cooling. The differential scanning calorimetry (DSC) measurements of compounds 1-3 show that the cubic phases of compounds 1-3 are metastable phases, while the columnar phases are stable. The X-ray diffraction patterns indicate that compounds 2 and 3 form Pmhn cubic phases and PH a rectangular columnar phases. 

The low-temperature part of the transition is independent of the crosslink density and of the amines, again indicating that the onset of the transition is due to very localised motions, occurring at the scale of an epoxyamine repeat unit. Such a conclusion is supported by the low values of the activation entropies at the onset of the transition (Table 10). 

There is a correlation between reactivity of the pyrrolinones, 3-ethoxyisoindolenone and the oxazolinones and their UV spectra5 2 The pyrrolinones all have distinct n-7r bands as the longest wavelength transitions in their UV spectra (Table 1), they all react by a-cleavage, and they do not cycloadd to olefins. The molecules studied which cycloadd to olefins and do not a-cleave are 3-ethoxyisoindolenone (50) and the methoxyphenyloxazolinones (65 b and 65c). These show no resolved n-rr transitions (Table 4). Of the two molecules, 65a and 65d which undergo both modes of photochemical reactivity, 65d has a slightly resolved n-7r band as a shoulder on the intense tt-tt transition (Table 4). 

Laporte and spin-multiplicity selection rules ( 3.7) and have intensities 103 to 104 times higher than those of crystal field transitions (table 3.6), their absorption edges may extend well into the visible region and overlap crystal field spin-allowed and spin-forbidden peaks. 

Although there is general agreement that the broad band centred at 16,100 cm-1 causing the blue colour of aquamarine represents a Fe2+ —> Fe3+ IVCT transition (table 4.2), uncertainty exists over the assignments of two other bands at 12,200 cm-1 and 10,300 cm-1 (Farrell and Newnham, 1967 Wood and Nassau, 1968 ... 

Smith, 1977 Smith et al., 1980,1983) reviewed by Rossman (1984) have centred on origins of the diagnostic basal-plane pleochroism attributed to Fe2+ —> Fe3+ and Fe2+ - Ti4+ IVCT transitions (table 4.2). Extractable from these spectra, however, are absorption bands around 11,900 cm-1 and 8,900 cm-1 attributed to octahedrally coordinated Fe2+ ions. These bands lead to estimated values for A0 and CFSE of about 10,000 cm-1 and 4,400 cm-1, respectively, representing averaged values for Fe2+ ions in the trans-Ml and two cis-M2 octahedra. 

For every chemical element that is considered the allowable valence schemes in the educts and the products are stated, as well as their permissible transitions during chemical reactions. The transition tables may be a standard set, or be defined ad hoc. 

The transition tables for Carbon atoms shown in Figures 7.3 and 7.4 may serve as an illustration. 

Figure 7.3 shows a transition table that has been used for the Streith reaction (ref. 7,18,19) it refers to valence schemes that occur in stable carbon compounds. Figure 7.4 is a transition table that also permits the valence schemes of short-lived transient species in some reaction mechanisms. 

Note that in Figure 7.4 the diagonal entries of the unstable valence schemes indicate that these must disappear during the reaction. Furthermore, an empty row in a transition table means that the respective valence scheme must not exist in the educts, whereas an empty column points to a valence scheme that is forbidden in the products. The transition tables do not only enforce the valence chemical boundary conditions, but they also may be used to specify the allowed direction of a reaction (ref. 14). 

In the case of RG I we have a fixed assignment of the chemical elements to the rows/columns of the BE-matrix B. Thus it is even possible to use different transition tables for a given chemical element in the distinct rows/columns. 

Fig. 7.4 Transition table of a C-atom for a network of reaction mechanisms...

In contrast, we have a different approach with RG II, because there is no predefined assignment of chemical elements to the rows/columns. In addition, for each row/column a set of chemical elements with their respective transition tables can be specified (ref. 11,20). 

The transition table guided RG I (TRG I) of the present version of RAIN operates as follows First the allowable rows/columns of the matrix E are derived from the corresponding rows/columns of B according to the transition tables that apply. Then the differences of the rows/columns of B and E are checked whether or not they yield a matrix that qualifies as a chemically meaningful R-matrix, as specified by the user. 

An alternative to the above TRG I is currently implemented and tested. Here, a set of R-components is derived from B and the applicable transition tables. These R-components are then used to manufacture the R-matrices, and hence the matrices E. 

Since 1979 a TRG II is used as the engine of IGOR (ref. 11). The user of IGOR defines a R-matrix R and selects for each of its rows/columns a set of chemical elements whose valence chemical roles are described by their transition tables. For each row/column of (B,E) the union of the allowed transition tables is formed. From these the valence schemes, their transitions, and the compatible chemical elements are found for the row/columns pairs of B and E. 

Therefore an entirely different approach is preferred. The aforementioned TRG I is used to elaborate trees of reactions, pathways from EM(B) and EM(E) until they merge. Since the reaction pathways have an orientation that is enforced by the transition tables, the latter must be reflected about their main diagonals when the trees are originating from the product side. The chemical constitution of the species generated is represented in canonical form. Thus the identity of any two species is immediately noticed. This does not only eliminate redundancies, but, more importantly, indicates any nodes at which the two trees merge. In this context the distinct resonance structures of a molecule and its tautomeric forms can be treated as equivalent. 

Figure 2 shows the code for the spin-echo pulse sequence. In lines 1-7, NMR object variables are declared. In lines 9-16, these objects are assigned values or specific NMR operations. A lactate spin system is read in from a file using a standard GAMMA text file format. Lines 20-24 are the code for the actual 90°Y-delay-180°Y-delay-acquire pulse sequence. In line 26, the density matrix is parsed into a transition table for the specified observation operator. And the "write results" function in line 27 converts the GAMMA transition table into three arrays of ppm, area and phase values one value for each line found in the transition table. This is a fairly trivial example, and the use of ideal pulses is often not sufficient to account for real-world artefacts in a simulation, but it shows how the object-oriented style of coding results in short amounts of code that is easy to read and comprehend. When compiled with the Visual Studio C++ compiler on a... 

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