Dipole throwing

The Coefficient of Correlation of a Two-composition System in Terms of Probabilities Consider a two-composition texture of concentrations x and x2 shown in the figure below. Following a (mental) process of dipole throwing, we find that fen of them fell with both ends on composition x, k.22 fell with both ends on composition X2, and fen fell with one end on composition x and the other on X2-... 

Hint The probabilities are evaluated by a (mental) process of dipole throwing. Thus the probability that one end of the dipole should fall on region I is L j(L +L2). The probability that this point should fall not closer than a distance... 

The coefficient of correlation, R(r), measures the degree of correlation between the concentrations at two points separated by distance r. It is obtained by randomly throwing a dipole of length r, and is defined as follows ... 

A number of physicochemical properties which have been investigated for a series of simple derivatives of the different tautomeric forms of adenine, prominent among which are dipole moments and ultraviolet absorption spectra, throw additional light on the problem. Table VIII indicates the results of a theoretical evaluation of the dipole moments for the different tautomeric forms (12-19) of adenine as well as the experimental values of the moments in methyl and benzyl derivatives of these forms with the exception of the derivatives of the N(1)H form for which, unfortunately, no experimental data could be obtained because of lack of sufficiently soluble 1-substituted derivatives. 

We have also demonstrated that it was possible to throw light on the orientation fluctuations of polar macromolecules like collagen, by measuring the noise emission conductivity (t versus frequency. The critical time of orientation fluctuations of the collagen permanent dipoles cannot be assimilated to the classical dielectric relaxation time T , but the numerical value of is very near to the reorientation time measured by electrical birefringence. 

They do not, however, throw light on the process by which the vibrational energy of the hot ground-state molecule conveys its excess energy to the solvent. These interactions may be mechanical (impact, or molecular vibration [52]), affecting translational motions, as revealed by effects of solvent viscosity or electromagnetic (dipole-dipole [55,a]) affecting rotational motions, as revealed by effects of solvent polarity. 

The correlation coefficient is calculated by the technique of dipole or needle throwing. Consider a mixture of carbon black in PE with C average carbon black concentration. We fracture one peUet, and we take a photograph of the surface with the aid of a high resolution scanning electron microscope. We take a needle of length r and drop it onto the photograph. Four events can take place (1) both ends could land in carbon black particles with probability Pn (2) both ends could land in the PE matrix with probability P22, (3) the first end lands in carbon black and the second in PE with probability Pu, and (4) the opposite of the previous event with probability P2i- Nadav and Tadmor (1973) calculated the correlation coefficient as... 

The broadening of the surface state level up to 1 eV could reflect the time fluctuations of the water dipoles in the double layer. It could also be caused by the discreteness of the charge, leading to an inhomogeneous potential distribution parallel to the surface. In any case, a lineshape analysis should throw some light onto the microscopic structure of the interfacial region and its potential dependence. 

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