Spatial Longitudinal

Secondly, these quotations emphasize the fact that the same river input that fuels longitudinal heterogeneity in reservoirs also forms a strong link between the reservoir and its watershed (e.g., [6]). This link has been conceptualized mostly in the form of load-response empirical models [7, 8], or mass-balance approaches [9]. Curiously, empirical modelers usually consider reservoirs as stirred reactors, ignoring the longitudinal spatial heterogeneity present in most situations and processes. 

Fig. 4. Spatial distribution of (a) relative elemental elongation rate (longitudinal growth rate) and (p) osmotic potential in the apical 10 mm of maize primary roots growing at various vermiculite water contents (see Fig. 3). Growth distributions were obtained by time-lapse photographic analysis of the growth of marked roots points are means from 5 or 6 roots. Osmotic potentials were measured on bulked samples from 30-50 roots points are means s.d. (n = 3-7). Root elongation rates (a, inset) were constant when the measurements were made. Modified from Sharp et al. (1988, 1989).

A simple but illustrative approach for the visualization of flow properties and heterogeneities is to combine the measurement of the velocity distribution with imaging along one spatial direction. In Figure 4.6.2, the longitudinal velocity component vz is plotted versus the transverse position coordinate x. 

A second imaging gradient (Gy) is added in order to obtain a spatial map of the displacements. A notable feature of the stimulated echo protocol is that during the flow encoding time, A, the magnetization is stored along the z axis and is subject to the longitudinal... 

Algeri S., Biagini L., Manfridi A, Pitsikas N. (1991). Age-related ability of rats kept on a life-long hypocaloric diet in a spatial memory test. Longitudinal observations. Neurobiol. Aging 12, 277-82. 

In Fig. 3b, L2 and L4 have substantially different STD values, with L4 showing significantly smaller effect, even though these two protons are equidistant from the P3 proton. This is a simple consequence of the differences in the relaxation rates for these L2 and L4 protons due to differences in their local environments (e.g., in the asymmetric model, the L4-L5 distance is shorter than the L3-L2 distance, and thus L4-L5 protons experience a faster longitudinal relaxation rate than the L4-L5 protons). These observations suggest that caution is needed in quahtative attempts to relate the magnitudes of steady state STDs to spatial proximity of ligand protons to the protein protons. 

Recapitulating, the SBM theory is based on two fundamental assumptions. The first one is that the electron relaxation (which is a motion in the electron spin space) is uncorrelated with molecular reorientation (which is a spatial motion infiuencing the dipole coupling). The second assumption is that the electron spin system is dominated hy the electronic Zeeman interaction. Other interactions lead to relaxation, which can be described in terms of the longitudinal and transverse relaxation times Tie and T g. This point will be elaborated on later. In this sense, one can call the modified Solomon Bloembergen equations a Zeeman-limit theory. The validity of both the above assumptions is questionable in many cases of practical importance. 

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