Correlation angles

Example Problem Consider the case of 240-MeV 32S interacting with 181Ta, which fissions. What would be the laboratory correlation angle between the fragments if the full linear momentum of the projectile was transferred to the fissioning system ... 

For a given arrangement A, the two Fock angles cox.rjx) are the hyperradial correlation angle lux — tim rx/Bx) and the bending angle r]x — cos (lix.rx). The expression of the hamiltonian Ti in Fock Body-Frame coordinates is... 

We are interested in < E (0[,(t)i)E3(62,, where <> means the average over the ensemble of surfaces, the subindexes 1 and 2 refer to two different points of observation and the subindexes A and B belong to two different conditions of illumination, which for example arise from two different wavelengths, two different incident angles, etc.. If A = B and 1 = 2, the above expression gives the angular distribution of the mean scattered intensity, otherwise it turns to be the intensity correlation coefficient y from < E Eb >, assuming that we deal with fully developed speckle. 

The lubricating properties of tears are an important feature in normal blinking. Kalachandra and Shah measured the coefficient of friction of ophthalmic solutions (artificial tears) on polymer surfaces and found no correlation with viscosity, surface tension or contact angle [58]. The coefficient of friction appears to depend on the structure of the polymer surfaces and decreases with increasing load and sliding speed. 

The correlation fiinction G(/) quantifies the density fluctuations in a fluid. Characteristically, density fluctuations scatter light (or any radiation, like neutrons, with which they can couple). Then, if a radiation of wavelength X is incident on the fluid, the intensity of radiation scattered through an angle 0 is proportional to the structure factor... 

The dimensionality of a data set is the number of variables that are used to describe eac object. For example, a conformation of a cyclohexane ring might be described in terms c the six torsion angles in the ring. However, it is often found that there are significai correlations between these variables. Under such circumstances, a cluster analysis is ofte facilitated by reducing the dimensionality of a data set to eliminate these correlation Principal components analysis (PCA) is a commonly used method for reducing the dimensior ality of a data set. 

The preparation of 5-azothiazoles uses the nucleophilic character of C-5 carbon in reaction with the appropriate diazonium salt (402, 586). These 5-azothia2oles form 1 1 complexes with Ag (587). 2-Amino-4-methyl-5-arylazothiazoles give reduction waves involving two-electron transfer the Ej/ values correlate to the angle between the thiazole and phenyl rings (588). 

The 2eta potential and contact angle as well as flotation recovery correlate well in some flotation systems as shown in Figure 9 (20). 

Fig. 9. Correlation of contact angle, flotation recovery, surface coverage by collector, and 2eta potential. Solid, quart2, collector reagent, 4 x 10 Af dodecylammonium acetate. = recovery, % A = zeta potential, mV Q — contact angle, degrees and = surface coverage, % of one monolayer. Ref.

---