Transverse correlation effect

The preceding discussion is based on the assumption that the incident laser is a plane wave. If the laser is a focused Gaussian beam, with a beam size o comparable to or smaller than the film thickness, transverse correlation effects will arise. Molecules situated outside the laser beam will exert torques on molecules inside the beam conversely, molecules inside the beam could also exert torques on those on the outside. The result is that the transverse dependence of the reorientation profile is not the same function as the transverse profile of the incident laser beam (e g., Gaussian). Put in another way, one may recognize that Equation (8.53) is basically a diffusion equation, where the elastic term plays the role of the diffusive mechanism. As a result of this diffusive effect, as in marty other physical processes, the spatial profile of the response is not the same as the excitation profile. 

The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

The exploitation of cross-correlation effects in high magnetic fields has introduced a new form of NMR spectroscopy called transverse relaxation-optimised spectroscopy or TROSY. The cross-correlation of the optimised dipole-dipole (DD) and chemical shift anisotropy (CSA) relaxation mechanisms leads to differential transverse relaxation rates for the two components of the l5N- H doublet in undecoupled spectra of l5N-labelled proteins. For one component, DD and CSA relaxation constructively add to produce very efficient relaxation, leading to a broad line, whereas for the other component, the two relaxation mechanisms constructively interfere, leading to a narrow line when the two mechanisms are nearly equal. There is no optimum field where DD and CSA relaxation are equal for all amide bonds, because DD relaxation between the amide protons and other nearby protons differs for each residue.72 Clearly, the overall effectiveness of TROSY is optimized when the non-exchangeable protons in the macromolecule... 

We present a detailed theoretical calculation, with experimental verification, of the nonlocal molecular reorientation of the nematic-liquid-crystal director axis induced by a cw Gaussian laser beam. The natures of the torque balance equations and the solutions are significantly different for normally and nonnormally incident laser beams. The nonlocal effects resulting from molecular correlation effects are particularly important for laser spot sizes that are different (smaller or larger) from the sample thickness. Experimental measurements for the transverse dependence of the molecules and the dependence of the Freedericksz threshold as a function of the laser beam sizes are in excellent agreement with theoretical results. We also comment on the effect of these nonlocal effects on transverse optical bistability. 

The static longitudinal and transverse polarizabilities of polyyne chains have been calculated at the CCSD(T)/cc-pVTZ level of theory in order to address their scaling with chain length (L) . For n = 1-9, the transverse component of the polarizability evolves linearly with L whereas the longitudinal component scales as This exponent is smaller than for the free electron in a box, which has been attributed to electron-electron repulsions in contrast to electron correlation effects. 

The free-induction decay of transverse magnetization has been analyzed in terms of polymer dynamics [23-26]. A solid echo technique was employed for the same purpose [27, 28]. The so-called dipolar correlation effect on the stimulated echo turned out to be a particularly simple and robust tool in this context too [15, 29, 30]. Finally, double-quantum NMR spectroscopy was suggested [31, 32] as a means of probing features of chain dynamics. 

The dipolar correlation effect is based on stimulated-echo signals [2] and therefore contains elements both of transverse and longitudinal relaxation. Flip-flop spin diffusion as well as material transport may contribute to the exchange mechanism identified this way. An interesting result of the dipolar correlation effect study is the temperature dependence of the fraction of the more mobile segments which was shown to obey the empirical law (see Fig. 39) [168]... 

Boundary layer similarity solution treatments have been used extensively to develop analytical models for CVD processes (2fl.). These have been useful In correlating experimental observations (e.g. fi.). However, because of the oversimplified fiow description they cannot be used to extrapolate to new process conditions or for reactor design. Moreover, they cannot predict transverse variations In film thickness which may occur even In the absence of secondary fiows because of the presence of side walls. Two-dimensional fully parabolized transport equations have been used to predict velocity, concentration and temperature profiles along the length of horizontal reactors for SI CVD (17,30- 32). Although these models are detailed, they can neither capture the effect of buoyancy driven secondary fiows or transverse thickness variations caused by the side walls. Thus, large scale simulation of 3D models are needed to obtain a realistic picture of horizontal reactor performance. 

When the free stream—be it forced or due to buoyancy effects—is transverse to the mass evolution from the regressing fuel surface, no stagnant film forms, in which case the correlation given by Eq. (6.153) is not explicitly correct. 

From this, we may deduce that the relativistic correction to the correlation energy is dominated by the contribution from the s electron pair, and that the total relativistic effect involving the exchange of a single transverse Breit photon is obtained to sufficient accuracy for our present purposes at second-order in many-body perturbation theory. 

An estimate of the effect of separation of the points upon the correlation coefficient is given in Fig. 3 (C7). Batchelor (B6) has been able to predict many of the basic characteristics of the correlation coefficient shown in Fig. 3 for both the transverse, and longitudinal fluctuating velocities. Much has been written about the characteristics of double, triple, and in a few cases higher correlations (K4, L5). It is beyond the scope of this discussion to consider these more refined measures of the statistical characteristics of turbulence. It suffices to indicate that at present a reasonable beginning has been made in the evaluation of the microscopic characteristics of turbulence but that much more experimental work must be carried out in order to supply the quantitative information required to make the extensive theoretical effort capable of quantitative application. 

New techniques for data analysis and improvements in instrumentation have now made it possible to carry out stmctural and conformational studies of biopolymers including proteins, polysaccharides, and nucleic acids. NMR, which may be done on noncrystalline materials in solution, provides a technique complementary to X-ray diffraction, which requires crystals for analysis. One-dimensional NMR, as described to this point, can offer structural data for smaller molecules. But proteins and other biopolymers with large numbers of protons will yield a very crowded spectrum with many overlapping lines. In multidimensional NMR (2-D, 3-D, 4-D), peaks are spread out through two or more axes to improve resolution. The techniques of correlation spectroscopy (COSY), nuclear Overhausser effect spectroscopy (NOESY), and transverse relaxation-optimized spectroscopy (TROSY) depend on the observation that nonequivalent protons interact with each other. By using multiple-pulse techniques, it is possible to perturb one nucleus and observe the effect on the spin states of other nuclei. The availability of powerful computers and Fourier transform (FT) calculations makes it possible to elucidate structures of proteins up to 40,000 daltons in molecular mass and there is future promise for studies on proteins over 100,000... 

---