Correlation diagram, time-dependent

The time-dependent matrixelements (( ) 13/at (jtj) can be rewritten in the form of rotational- and radial-matrix elements which couple the amplitudes of the levels in the correlation diagram with the same projection of the angular momentum of the levels in case of the radial matrix elements and with -1-1 or -1 in case of the rotational matrix elements. For details on this procedure see Ref. 2. 

Figure 1.62. (a) Diagrammatic view of the correlation circuit for photoconductivity cross-correlation measurement in (CH) on broadband microstrip lines, (b) Corresponding circuit diagram. The switches are modeled using the approximation of lumped elements with a static capacitance Cg and a resistor having a time-dependent conductance G(/) in parallel. Z is the characteristic impedance of the transmission lines. (Reprinted with permission from ref. 149)... 

The mechanical response of polypropylene foam was studied over a wide range of strain rates and the linear and non-linear viscoelastic behaviour was analysed. The material was tested in creep and dynamic mechanical experiments and a correlation between strain rate effects and viscoelastic properties of the foam was obtained using viscoelasticity theory and separating strain and time effects. A scheme for the prediction of the stress-strain curve at any strain rate was developed in which a strain rate-dependent scaling factor was introduced. An energy absorption diagram was constructed. 14 refs. 

The absorption lines of the low temperature photoreaction products in TS-6 monomer crystals are summarized in the diagram of Fig. 7. The correlation of the A, B, C,. .. photoproduct series to diradical DR intermediates and of the b, c, d,... photoproducts to asymmetric carbene AC intermediates is based on the ESR experiments discussed below. The correlation of the y, 8,6,... series to stable oligomers SO is based on their thermal and optical stability. The correlation of dimer, trimer, tetramer,... molecules follows from the chemical reaction sequences observed in the time resolved optical and ESR measurements as well as from the widths of the one-dimensional potential wells used in the simple electron gas theory , which already has proved successful in its application to dye molecules. Following Exarhos et al. the explicit dependence is given by... 

Correlations of concentrations are measures of the statistical dependence of the concentration of one species on that of one or more of the other species in the system. Such correlations can be determined from measurements of time series of concentrations collected around a stationary state (nonequilibrium or equilibrium). We shall show that from concentration correlations it is possible to construct a skeletal diagram of the reaction system that gives a graphical measure of strong control and regulatory stmcture in reaction networks, gives some information on connectivity, leads to information on the reaction pathway and mechanism, and may simplify the analysis of such networks by identifying possible, nearly separable subsystems [1]. 

Clearly, the final MDS diagram is partially dependent on the parameters of the noise imposed on the system. It is possible that frequency domain approaches to time series analysis [10] may help in a study of the role of frequency transfer functions in the control of chemical networks. We have assumed that all species involved in the mechanism may be identified and measured. For systems with many species this may be difficult. When there are missing species, CMC may still be performed on the measurable subset of species. The effects of the other species are subsumed into the correlations among the known species, and a consistent diagram can be constructed. The MDS diagram, then, may not be an obvious representation of the underlying mechanism. In fact, due... 

Figure 11 shows a representation of e"(o)) = f(e ( o)), called an Argand diagram, for 0.48 M NaClO in a PC-DME mixture (20 weight % PC). Data analysis of the precedingly determined frequency-dependent permittivities of the solvent mixture without NaClO yielded two relaxation regions, one attributable to DME (relaxation time T = 4.7 ps) the other to PC (relaxation time t = 22 ps). The shifts of solvent relaxation times with reference to those of the two pure solvents, t(DME) = 3.6 ps and t(PC) = 39 ps, is correlated to the change in viscosity. Addition of the... 

The kinetic model developed in [83] describes the dependence of the conversion on time and MW for butadiene polymerisation on homogeneous catalysts. Compounds with Co, Al, and H2O are assumed to participate in the formation of AC. Computational and experimental data for the conversion of butadiene are proved to correlate well with each other when polymerisation is carried out with the cobalt octanoate -diethylaluminium chloride - water catalytic system. However, this model considers only one type of active centre and does not provide an explanation for the increase of polybutadiene polymerisation with conversion growth. The polymerisation diagram and mathematical model with two types of AC have been proposed for butadiene polymerisation in the presence of a Li(H-C4H9) - diethylene glycol dimethyl ether catalytic system [84], This approach is suitable for the calculation of changes... 

---