Anisotropy distribution

Fig. 8. Photofragment center-of-mass translational energy distribution P(Et) and anisotropy distribution 0 Et) for the photolysis of C2H2. The arrows mark the energetic thresholds for the corresponding electronic states of the fragment C2H. The out-of-phase correlation between the mild oscillations of 0 and the structures in P(Et) is indicated by vertical dashed lines.

Fig. 11. Photofragment translational energy distribution (upper panel) and anisotropy distribution (lower panel) for the photolysis of H2S. The arrow in the upper panel marks the energetic onset for the generation of SH(A2S+, 1/) + H.

Fig. 14 are the simulated distributions including the different parent rotational levels. An interesting observation from these distributions is that the shape of the multiplet peak corresponding to each 011 (/I) rotational level for the perpendicular polarization is not necessarily the same as that for the parallel polarization see for example the peak labelled v = 0, N = 22. From the simulations, relative populations are determined for the OH (A) product in the low translational energy region from H2O in different rotational levels for both polarizations. The anisotropy parameters for the OH product from different parent rotational levels are determined. Experimental results indicate that the ft parameters for the 011 (/I) product from the three parent H2O levels Ooo, loi, I11, are quite different from each other. Most notably, for the 011 (/I, v 0, N = 22) product the ft parameter from the foi H2O level is positive while the ft parameters from the Ooo and In levels are negative, indicating that the parent molecule rotation has a remarkable effect on the product anisotropy distributions of the OH(A) product. The state-to-state cross-sections have also been determined, which also are different for dissociation from different rotational levels of H2O. 

Hence, it was thought that anisotropy distribution for the dots might still be broad presumably by the non-uniformity or fluctuation of machining process by the FIB technique. 

FigureBl.5.16 Rotational relaxation of Coumarin 314 molecules at the air/water interface. The change in the SFI signal is recorded as a fimction of the time delay between the pump and probe pulses. Anisotropy in the orientational distribution is created by linearly polarized pump radiation in two orthogonal directions in the surface. (After [90].)...

The anisotropy of the product rotational state distribution, or the polarization of the rotational angular momentum, is most conveniently parametrized tluough multipole moments of the distribution [45]. Odd multipoles, such as the dipole, describe the orientation of the angidar momentum /, i.e. which way the tips of the / vectors preferentially point. Even multipoles, such as the quadnipole, describe the aligmnent of /, i.e. the spatial distribution of the / vectors, regarded as a collection of double-headed arrows. Orr-Ewing and Zare [47] have discussed in detail the measurement of orientation and aligmnent in products of chemical reactions and what can be learned about the reaction dynamics from these measurements. 

This method has been devised as an effective numerical teclmique of computational fluid dynamics. The basic variables are the time-dependent probability distributions f x, f) of a velocity class a on a lattice site x. This probability distribution is then updated in discrete time steps using a detenninistic local rule. A carefiil choice of the lattice and the set of velocity vectors minimizes the effects of lattice anisotropy. This scheme has recently been applied to study the fomiation of lamellar phases in amphiphilic systems [92, 93]. 

Figure 3 Characteristic solid state NMR line shapes, dominated by the chemical shift anisotropy. The spatial distribution of the chemical shift is assumed to be spherically symmetric (a), axially symmetric (b), and completely asymmetric (c). The top trace shows theoretical line shapes, while the bottom trace shows rear spectra influenced by broadening effects due to dipole-dipole couplings.

Heterogeneity, nonuniformity and anisotropy are based on the probability density distribution of permeability of random macroscopic elemental volumes selected from the medium, where the permeability is expressed by the one-dimensional form of Darcy s law. 

Real differences between the tensile and the compressive yield stresses of a material may cause the stress distribution within the test specimen to become very asymmetric at high strain levels. This cause the neutral axis to move from the center of the specimen toward the surface which is in compression. This effect, along with specimen anisotropy due to processing, may cause the shape of the stress-strain curve obtained in flexure to dif-... 

---