Convolute temperature

CONSOLUTF TEMPERATURE. The upper convolute temperature for two partially miscible liquids is the critical temperature above which the two liquids are miscible in all proportions. In some systems where the mutual solubility decreases with increasing temperature over a certain temperature range, the lower convolute temperature corresponds to the critical temperature below which the two liquids are miscible in all proportions. Some systems such as mclhylclhyl ketone and water have both upper and lower consolute temperatures. 

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

Recent reports 54 seem to indicate that the resolution of the notoriously difficult solid-state spectra of coals may be enhanced by such techniques as double exponential multiplication and convolution difference. Differential relaxation behaviour as discussed in connection with intermolecular effects in carbohydrates and low temperature methods may further improve identification. 

FIGURE 4.2 Linewidth increase with temperature for an S = 1/2 system. The linewidth of a feature in the low-spin heme spectrum from cytochrome a in bovine heart cytochrome oxidase has been fit as a convolution of a constant component from inhomogeneous broadening and a temperature-dependent component from homogeneous broadening (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

In the practice of solid-state bioEPR, a Lorentzian line shape will be observed at relatively high temperatures and its width as a function of temperature can be used to deduce relaxation rates, while a Gaussian line will be observed at relatively low temperatures and its linewidth contains information on the distributed nature of the system. What exactly is high and low temperature, of course, depends on the system for the example of low-spin cytochrome a in Figure 4.2, a Lorentzian line will be observed at T = 80°C, and a Gaussian line will be found at T 20°C, while at T 50°C a mixture (a convolution) of the two distributions will be detected. 

FIGURE 2.6. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying a MHL kinetic law (Xt — 0.7 eV, koo — 4 x 103 cms-1, implying that kg = 0.69 cms-1) and an irreversible follow-up reaction (from bottom to top, k+ = 103, 105, 107, 109s 1). Temperature, 25°C. a Potential-dependent rate constant derived from convolutive manipulation of the cyclic voltammetric data (see the text), b Variation with potential of the apparent transfer coefficient (see the text) obtained from differentiation of the curves in part a. 

An example of the use of the convolution method to detect the change in mechanism is shown in Figure 3.15. A more complete scanning of the passage between the two mechanisms is obtained thanks to the use of convolution and placing data obtained at two temperatures on the same diagram.20... 

ISO 7258 1984 Polytetrafluoroethylene (PTFE) tubing for aerospace applications -Methods for the determination of the density and relative density ISO 7313 1984 Aircraft - High temperature convoluted hose assemblies in polytetrafluoroethylene (PTFE)... 

Biochemical processes such as protein unfolding/refold-ing and supramolecular assembly/disassembly take place on a time scale of seconds to minutes after readjusting the temperature of a system. Most commercially available glass-jacketed cuvettes are not suitable for temperature jumps on this time scale, as a result of the slow kinetics of heat transfer across substances with characteristically high dielectric constants, and their use can convolute the time scale of the temperature change onto the time scale... 

The tip DOS, pKe), and the sample DOS, p.s(e), appear in a symmetric way in determining the tunneling current. In the simplest case, when the temperature is low and the tunneling matrix element is a constant, the tunneling current is a convolution of the tip DOS and the sample DOS over an energy range eV,... 

Fig. 6.5. Computed structures due to the hydrogen dimer, in the quadrupole-induced (0223,2023) components near the So(0) line center at 120 K (the temperature of Jupiter s upper atmosphere). Superimposed with the smooth free — free continuum (dashes) are structures arising from bound — free (below 354 cm-1) and free - bound (above 354 cm-1) transitions of the hydrogen pair (dotted). The convolution of the spectrum with a 4.3 cm-1 slit function (approximating the instrumental profile of the Voyager infrared spectrometer) is also shown (heavy line) [282].

In Ref. [75], it is discussed in more detail why it is advantageous to convolute the response of the temperature grating into the excitation and how to treat systematic errors arising from this approximation and from imperfections of the components in the setup. Especially the switching properties of the Pockels cell require careful analysis, since the switching number increases from 2 in case of pulsed excitation to approximately N in case of pseudostochastic binary sequences. 

Before comparing with experiment, however, the theoretical results at an energy of 40 meV (equivalent to room temperature) were convoluted with the energy resolution function of the detector used for the measurement. This procedure was adopted because deconvolution of the experimental data was found to be numerically unstable. The convoluted theoretical data were then normalized to the experimental data at zero Doppler shift to yield the results shown. The agreement between the convoluted theoretical results and experiment is extraordinarily good, extending as it does over more than three orders of magnitude. These results also reveal... 

Fig. 26 Temperature dependence of partial heat capacity (Cp) of PNIPAM homopolymer, PNIPAM-co-St (4.1 mol %) random copolymer and NIPAM-seg-St (3.9 mol %) segmented copolymer in water the polymer concentration was 1.0 g/L and the heating rate was 0.5 °C/min. The inset shows the de-convolution of stand partial heat capacity (C ) of PNIPAM-seg-St [94]...

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