Line relaxation

The spin spin relaxation time T2a can be measured by a quadrupolar echo pulse train 90° — x — 90° — (2t — 90°) if the pulse spacing x < C 2/Av is satisfied (i.e., the deuteron spin relaxes as if the quadrupolar splitting Av is absent or if a non-selective excitation is achieved). Due to the large quadrupolar splitting often encountered in LC, the above condition for x cannot be fulfilled experimentally and the two lines relax independently (i.e., r> 21 Av or selective excitation of half of the doublet exists). The quadrupolar echo pulse train then measures50... 

Fig. 3.6 (a) Definition of bottleneck shortest distance and variation of mobile-ion potential with position with (solid line) and without (dotted line) relaxation of host structure, (h) Variation of mobile-ion potential for occupied sites separated by an array of inequivalent, empty sites, (c) Smoothing of the potential of (b) by introduction of mobile ions into second array of sites. 

Figure 7.17 Interface between covulcanized sheets from unfilled SBR and NR (a) Photograph, (b) ID NMR images acquired with single-point imaging and different contrast filters. Smooth line chemical contrast (right scale). Rugged line relaxation...

Numerical method. The choice of the proper numerical solution procedure should be left to specialists. Even when a particular CFD package has been chosen, the user can usually choose different solution strategies for the linearized equations (point or line relaxation techniques versus whole field solution techniques) and associated values of the relaxation parameters. The proper choice of relaxation factors to obtain converged solutions (at all) within reasonable CPU constraints is a matter of experience where cooperation between the engineer and the specialist is required. This is especially true for new classes of fluid flow problems where previous experience is nonexistent. 

Fig. 5. EOM and Cl vertical ionization potentials for BH solid line, relaxed Cl long and short dashes, unrelaxed Cl, using SCF orbitals of BH dashed curve, extensive EOM dotted curve, primitive repartitioned EOM. The EOM results are plotted against the tolerance for retaining shake-up-basis operators in the primary operator space, and the dimension of the primary operator space is given in parentheses for each tolerance. The Cl values are presented at the one configuration level (1C), for single and double excitations Cl (SD), and for single, double, and triple excitations Cl (SDT). EOM calculations are not performed at tolerance of 0.01 au because this tolerance does not result in an appreciable increase in the dimensionality of the f -space. Experimental value is 9.77 eV. Asterisk EOM primary operator space restricted to simple ionization operators.

Pig. 10.1 Comparison of the measured (dots) and the calculated (line) relaxation modulus for the F40 sample. Also shown are the separate contributions of the PAit), P-xit), Psit) and pc t) processes (line A is calculated with all four processes in Eq. (9.19) included, line X is calculated without pA(t)> line B is calculated without PAif) and Px t)> and line C is calculated without PA t)> PxW and psit) thus, the portion between line A and line X is the contribution of the paW process, and so forth). 

Fluorescence Resonance Energy Transfer (FRET), Fig. 1 (a) Jablonski diagram illustrating FRET and related processes, including excitation of the donor, radiative (solid line) and non-radiative (dashed lines) relaxation on the donor and acceptor, vibrational relaxation (short curved arrows), and transitions associated with FRET (dotted lines). Processes that determine the FRET efficiency are indicated in bold, (b) Illustration of spectral overlap between Cy3 (donor) emission and Cy5 (acceptor) absorption, (c) Definition of the angles used to calculate... 

Fiber crimping using a staffer box device may be done before in-line relaxation or before autoclaving. The relaxation process tends to set the crimp. In some autoclave processes, a second crimping step is employed subsequent to relaxation. Fiber may be cut to staple at the machine end for in-line relax processes or batchwise for autoclave processes. Tow can be produced from either process type, although large packages of one ton or more are produced more readily from the in-line relax process. 

These three types of hyperfine interactions with the relevant Mossbauer parameters are most important in solid state research, in addition, one often extracts further helpful information from the temperature and pressure dependence of the Mossbauer parameters, the shape and width of the resonance lines (relaxation phenomena), and the second-order Doppler shift (lattice dynamics). 

FIGURE 6.7. Dynamics of the relaxation of a triple line. At first, the line is pinched by a localized defect and takes on its equilibrium shape, as discussed in section 3.2.2. As the defect is eliminated at time t = 0, the line relaxes and reverts to a horizontal shape. Only a region of size ct is relaxed at time i. 

Figure 5 Inversion-recovery curves for slow exchange between two sites. Lines A and B are the results from one experiment. They show the recovery after a nonselective inversion of both sites, showing that the two sites have slightly different T, values. C and D are obtained from a different experiment. Line C shows the recovery of a site that has been selectively inverted, and line D shows the behaviour of the line that was not perturbed in this experiment. The inverted line relaxes faster, due to a combination of spin-lattice, relaxation and exchange, and the unperturbed line shows the characteristic transient.

Figure 9.16 Sketch showing branch-point motion. The entanglements of the arms with neighboring invisible chains are shown as loops that represent "slip links" that confine each arm. The location of the branch point, on average, is taken to be the centroid of the three locations of the innermost entanglements of each of the three arms. When the arm shown as a bold line relaxes and re-entanglesythe slip links, including the inner-most slip link on this arm, move to a new position. Hence the centroid of the three innermost slip links, and therefore the average location of the branch point, shifts to the position marked with an X" as shown.

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