Scalar correlation

Scalar correlation at the diffusive scales can be measured by the scalar-gradient correlation function ... 

These variables are governed by exactly the same model equations (e.g., (4.103)) as the scalar variances (inter-scale transfer at scales larger than the dissipation scale thus conserves scalar correlation), except for the dissipation range (e.g., (4.106)), where... 

In order to illustrate how the multi-variate SR model works, we consider a case with constant Re>. = 90 and Schmidt number pair Sc = (1, 1/8). If we assume that the scalar fields are initially uncorrelated (i.e., pup 0) = 0), then the model can be used to predict the transient behavior of the correlation coefficients (e.g., pap(i)). Plots of the correlation coefficients without (cb = 0) and with backscatter (Cb = 1) are shown in Figs. 4.14 and 4.15, respectively. As expected from (3.183), the scalar-gradient correlation coefficient gap(t) approaches l/yap = 0.629 for large t in both figures. On the other hand, the steady-state value of scalar correlation pap depends on the value of Cb. For the case with no backscatter, the effects of differential diffusion are confined to the small scales (i.e., (), / h and s)d) and, because these scales contain a relatively small amount of the scalar energy, the steady-state value of pap is close to unity. In contrast, for the case with backscatter, de-correlation is transported back to the large scales, resulting in a lower steady-state value for p p. 

The superscript used in the coefficient matrices in (6.192) is a reminder that the statistics must be evaluated at the notional-particle location. For example, e = e(X r), and the scalar standard-deviation matrix and scalar correlation matrix p are computed from the location-conditioned scalar second moments X )(X, t). 

D spectra are in principle possible for heteronuclei coupled by either dipolar or scalar interactions. However, the magnetic moments of heteronuclei are sizably smaller than that of the proton, and since cross relaxation depends on the square of the magnetic moment it appears that this is a serious limitation for the observation of NOESY or ROESY cross peaks. However, as already discussed, in scalar-coupled systems the relevant coherences build up with sin(nJ/jt). Since Jjj in directly bound 13C- H and l5N- H moieties is of the order of 102 Hz, as opposed to about 10 Hz between proton pairs, it is conceivable that scalar correlation experiments are successful. Heterocorrelated spectra have the advantage of allowing one to detect signals of protons attached to carbons or nitrogens when they are within a crowded envelope. 

FIGURE 6 Comparison of strong and weak long-range scalar correlations in an HMBC spectrum. A strong intensity correlation is observed between carbon 2 and protons 4 and 6, since the parameters are optimized for three-bond separations on an aromatic ring. Only a weak intensity correlation is observed between carbon 2 and protons I and 3, since this corresponds to a two-bond separation. 

Figure 8 Residue-specific resonance assignment using TOCSY spectra. Portion of the amide region of a 2D1H—1H TOCSY spectrum (r — 80 ms) of the 37-residue spider toxin K-atracotoxin-Hv1c.44 Intraresidue scalar correlations from the backbone amide proton to each of the side chain protons (so-called amide skewers ) are shown for residues Ala6, Cys10, and Val29. The side chain protons corresponding to each correlation are indicated on the spectrum.

New isotropic mixing sequences suitable for scalar correlation experiments in solids have been designed using symmetry principles similar to those employed in the construction of the C7 dipolar recoupling sequence. Compared with existing methods, the new isotropic mixing sequences are... 

Model Translational correlation time, t, Scalar correlation time Ref. 

In addition to vector correlations and the wealth of information they provide, an essential question to ask is If state Xi> of fragment 1 is formed, what is the probability to form state 2) of fragment 2 These scalar correlations can be obtained from the quantum state specific translational energy distribution of one of the fragments. How this works becomes clear if one considers the energy balance equation of the photoreaction ... 

Donaldson, C. (1975). On the modeling of the scalar correlations necessary to construct a second-order closure description of turbulent reacting flows, in Turbulent Mixing in Nonreactive and Reactive Flows, S. N. B. Murthy, ed.. Plenum Press, New York, pp. 131-162. 

---