Anisotropy, definition

PR = perpendicular recording LR = longitudinal recording HFRH = high frequency recording heads RH/HDTV = recording heads for high definition television and Pa = perpendicular perpendicular anisotropy. 

Similar invariance concepts for anisotropic materials were also developed by Tsai and Pagano [2-7]. For anisotropy, the following definitions... 

Definition and Uses of Standards. In the context of this paper, the term "standard" denotes a well-characterized material for which a physical parameter or concentration of chemical constituent has been determined with a known precision and accuracy. These standards can be used to check or determine (a) instrumental parameters such as wavelength accuracy, detection-system spectral responsivity, and stability (b) the instrument response to specific fluorescent species and (c) the accuracy of measurements made by specific Instruments or measurement procedures (assess whether the analytical measurement process is in statistical control and whether it exhibits bias). Once the luminescence instrumentation has been calibrated, it can be used to measure the luminescence characteristics of chemical systems, including corrected excitation and emission spectra, quantum yields, decay times, emission anisotropies, energy transfer, and, with appropriate standards, the concentrations of chemical constituents in complex S2unples. 

Its first invariant A] is equal to zero by definition. The second and third invariants of this tensor arc A — atJaJt and A3 — atjajkakt, respectively. The range of physically allowed values of A2 and A3 is bounded and represented by the so-called Lumley triangle in the (A3, A2) plane (Lumley, 1978). The distanced = (Ay + Af) from the isotropic state, i.e., from the origin (A2 — 0, A3 — 0), is a measure of the degree of anisotropy. See also Escudie and Line (2006) for a more extensive discussion as to how to quantify and visualize how different from isotropic turbulence a stirred vessel is. 

On continuous illumination (i.e. when the incident light intensity is constant), the measured anisotropy is called steady-state anisotropy r. Using the general definition of an averaged quantity, with the total normalized fluorescence intensity as the probability law, we obtain... 

This equation shows that, at time t, each anisotropy term is weighted by a factor that depends on the relative contribution to the total fluorescence intensity at that time. This is surprising at first sight, but simply results from the definition used for the emission anisotropy, which is based on the practical measurement of the overall ly and I components. A noticeable consequence is that the emission anisotropy of a mixture may not decay monotonously, depending of the values of r, and Ti for each species. Thus, r(t) should be viewed as an apparent or a technical anisotropy because it does not reflect the overall orientation relaxation after photoselection, as in the case of a single population of fluorophores. 

Let us recall the definition of the emission anisotropy r (see Chapter 5) in a configuration where the exciting light is vertically polarized and the emitted fluorescence is observed at right angles in a horizontal plane (Figure 6.4) ... 

Definitions of parameters r . Steady-state anisotropy ( , residual equilibrium anisotropy 0C, cone angle ... 

J-splitting, when it exists, imposes the definition of new spin quantities. These quantities also evolve according to relaxation phenomena and may interfere (by relaxation) with the usual magnetization components. This latter interference stems precisely from cross-correlation rates, i.e., relaxation parameters which involve two different mechanisms, for instance the dipolar interaction and the so-called Chemical Shift Anisotropy (27,28) (csa)... 

Note 1 See 3.1.1 for the definition of a uniaxial nematic mesophase, 5.8.1 for the definition of uniaxial mesophase anisotropy, and Definitions 3.3 and 5.8.2 relating to biaxial mesophases. 

With the prineipal phase axes, corresponding to the three directors /, m, and n (see Definition 3.3, Note 1) labelled X, Y, and Z such that >Xxx Xyy the major biaxial mesophase anisotropy,, is defined by... 

The shielded chemical shift is in turn due to the strong magnetic anisotropy of the sp -hybridized carbons. All the above dications are definitively classical, nonbridged cations, as also shown by the chemical shift additivity criterion of Schleyer and coworkers. 

Alternatively, in the so-called Haeberlen notation, the convention is <5zz- isol > l xx- isol > YY- iso / where the capital letters refer to the principal components and the isotropic chemical shift has a definition similar to Equation 1. The anisotropy (A5) and asymmetry ( ) are then defined as ... 

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