RELAXATION General remarks

General Remarks. The wavefront analysis as presented here, is limited only to the chemical relaxations and excludes any dissipation effects. The space relaxation, manifested as the change of the propagating primary wavefront itself, is met with and corresponds to the initial steady state or an equilibrium state of the system. On the other hand, the time relaxation manifests the changes in the system, caused by the primary wavefront. 

Since 13C relaxation of polymers has already been reviewed (Schaefer, 1974) we can restrict ourselves here to a few general remarks and to more recent papers in this field. Although i3C relaxation in polymers is generally dominated by dipolar relaxation, the NOE factors do not reach the maximum of tj = 2 commonly observed for small molecules. This is due to the fact that polymers usually do not satisfy the extreme narrowing limit only for which this NOE maximum is valid. In this case it is helpful to compare H relaxation data (Cutnell and Glasel, 1977). 

The observed behavior is remarkable Why an electronic transition should affect so much the acoustic damping and more in detail the microscopic relaxation Generally speaking, we could have expected changes in the shape of the acoustic dispersion, due to changes in the electronic screening contribution to the interparticle potential. However, this is not the case, as we showed in Ref. [13] and as it appears from the data here reported. Only the acoustic damping is affected. 

Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than Es, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conformational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition ... 

Remarkably, when our general ME is applied to either AN or PN in Section 4.4, the resulting dynamically controlled relaxation or decoherence rates obey analogous formulae provided the corresponding density matrix (generalized Bloch) equations are written in the appropriate basis. This underscores the universality of our treatment. It allows us to present a PN treatment that does not describe noise phenomenologically, but rather dynamically, starting from the ubiquitous spin-boson Hamiltonian. 

A final remark should be made as to the validity of eq. (2.13). This equation suggests the existence of a set of independent relaxation mechanisms. A general proof for the existence of such mechanisms could be given for visco-elastic solids in terms of the thermodynamics of irreversible processes (52) at small deviation from equilibrium. For liquid systems, however, difficulties arise from the fact that in these systems displacements occur which are not related to the thermodynamic functions. 

Remark 3 The selection of a relaxation among a number of alternatives is based on the trade-off between two competing criteria. The first criterion corresponds to the capability of solving the relaxed problem easily. The second criterion is associated with the type and quality of lower bound that the relaxed problem produces for problem (P). In general, the easier the relaxed problem (RP) is to solve, the greater the gap is between the optimal solution of (P) and the lower bound provided by (RP). 

DOTA-type complexes exist in two diastereomeric forms (m and M) which may have remarkably different water exchange rates as found for [Eu(D0TAM)(H20)]3+ [58,59]. In this 170 and H NMR study performed in acetonitrile-water solvent, it was possible to detect the NMR signals of the coordinated water molecules in both isomers. In a general case, the observation of the bound water signal for Ln(III) poly(amino carboxylates) is not possible due to the fast exchange, and for Gd(III) complexes, to the slow electronic relaxation. 

Another remarkable advantage of the formalism is that the generalization to the non-Hermitian relaxation operator is straightforward. If H is not Hermitian, that is, if H we must go through the entire demonstration of this section we can easily verify the usefulness of introducing the follow-... 

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