Transverse component

The interval between the second and third pulse is called the mixing time, during which the spins evolve according to the multiple-spin version of equation B 1.13.2 and equation B 1.13.3 and the NOE builds up. The final pulse converts the longitudinal magnetizations, present at the end of the mixing time, into detectable transverse components. The detection of the FID is followed by a recycle delay, during which the equilibrium... 

The excitation field is the only field seen by the magnetization m the rotating frame. The magnetization processes about it. Starting from equilibrium (Mq=MqM ), transverse components are created and develop according to... 

FIG. 25 (a) Variation of the mean-square gyration radius Rg with the intensity of the field (bias) and with host matrix density Cob- (b) The same for the ratio of its longitudinal and transversal components (c) The ratio between the end-to-... 

The operator a (k) so defined has the property that it takes a vector T) with transversal components into a vector aJ(A) T) whose components are no longer trarisversal. Hence, in order to define the operators ctu(k) and a (k), we need a larger vector space than the one whose elements have only transversal components. Within the scalar product... 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

Several NMR pulse sequences have been developed for measuring the diffusion coefficient. The most successful and currently used experiment is the modified spin-echo experiment (PGSE) proposed by Stejskal in 1967.62 As the echo signal is due to the transversal components of magnetic moments, the echo attenuation normalized for the attenuation due to relaxation can be written as63 ... 

In a ray picture, the wave vector k can be decomposed in a transverse component kx = kT and a propagation vector kz = p. By simultaneously invoking an antiresonance condition for the round-trip phase shift A

cladding material (M> = 2 -k-v + efficient light confinement in the core for a given set of materials is given by ... 

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

These results can be put in a more useful and simpler form if kr is sufficiently large to permit asymptotic forms of the spherical Bessel functions and spherical Hankel functions to be applied. In this case the transverse components of the scattered electric vector are... 

Similar calculations applied to transverse components lead to... 

For a complete suppression of the local magnetic field effects, however, one should also compensate its transversal component perpendicular to the magnet axis. This requires a pair of auxiliary coils, oriented in a correct direction in the magnet s azimuth plane, and capable of generating a transversal field component of the correct magnitude and sign (for more details, see Ref. 70)). 

Note 5 The spontaneous polarization depends on the transverse component, jUt, of the molecular dipole, the number density, p, and the polar or first-rank order parameter,... 

These weaknesses of the SDPC model stimulated Merunka and Rakvin [7, 63] to introduce some modifications to the model. Inspired by the basic ideas of the Fujii model [58,59], they decided to represent the PO4 dipole i in this modified SDPC model, or the MSDPC model, by the vector /Zj = (yu,f, yu, ). This vector has additional transverse components along the a- and fo-axes, beside the longitudinal component along the c-axis. The corresponding impulse is now pi = (pf.p. p ) and the value of the effective mass of the transverse dipole, Mj = Ma = Mb, differs from the value of the effective mass of longi-... 

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