Angular-averaged temperatures

Note that P(f) is the angularly averaged function and does not depend on the direction of the end-to-end vector. In a narrow region of temperatures close to the 5-temperature, real chains behave as interpenetrating ones, and the model provides a qualitatively correct piemre of the conformational behavior of flexible chains. 

Radial temperature measurements are best made in the fluid immediately leaving the test bed, thus enabling angular-averaged measurements to be made without disturbing the bed [6]. 

The axial conduction model showed no significant lack of fit when simultaneously fitted to temperature measurements at several bed depths, covering a wide range of mass velocity, particle size and conductivity. Figure 1(b) shows a typical fit to angular-averaged measurements. 

Two components were observed in the LID TOP spectra. The slower component was found to have a cosine angular flux distribution and an average kinetic energy 250 K, approximately the value of T . This component was also characterized by a rotational population distribution described by a rotational temperature T t = 170 20K. These results are comparable to the thermal LID results for Pt(lll), Pd(lll) and Pt(foil) discussed in the previous sections. 

Figure 4. The average change in the squared value of the classical orbital angular momentum ((A/. )) and the standard deviation of the A/. distribution

Correspondence principle. The average number of partial waves required for an adequate treatment of a given system at a given temperature is estimated by the mean angular momentum i of the binary encounter,... 

The ground state behaviour observed for Jahn-Teller impurities in cubic lattices has often been explained a posteriori by fitting experimental data to quantities like the average random strains, the Jahn-Teller energy, E]T, or the % frequency [5]. In particular when EJT/iuov < 1 the observation at low temperatures of a cubic angular pattern is favoured, while if E /Hcoe > 1 a static EPR spectrum is expected [1-3]. 

Fig. 1 Typical angular dependence of KC/Ryy(q) of PNIPAM in water at two different temperatures, where the weight-average molar mass (Mw) and concentration (C) of PNIPAM are 1.3 x 107 g/mol and 6.7 x 10-7 g/mL, respectively. The insert shows the corresponding hydrodynamic radius distributions f(R ) of the PNIPAM chains respectively in the coiled and the globular states [38]...

The sum must be made over all spin pairs in the proton-rich solid. In the absence of large-amplitude molecular motion this Hamiltonian describes a line shape of width of up to 100 kHz. In the presence of molecular motion the angular part of Equation 13.1 becomes time-dependent, and the partial averaging of this term results in reduced linewidths. In polymers the geometry of main-chain motion is limited by the structure of the polymer chain, and is inherently anisotropic. As a general rule, as the measurement temperature is increased the motion tends to become more isotropic in nature as the free volume increases, and the extent of averaging of the dipolar Hamiltonian increases. This... 

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