The temperature dependence of the magnetic susceptibility is described by the Curie-Weiss law. When T > 0p, [Pg.34]

In these last equations, P, a and r are now the expectation values (solutions) of the quantities defined above, and 0p is the covariance matrix of the parameters. is the number of observables and m the number of parameters. Because the functional dependence of the observables (rotational constants, principal moments of inertia or planar moments) on the structural parameters is strongly non-linear in most cases, an iterative process is essential. Typically, one begins with an assumed structure and expands the moment of inertia functions in terms of the parameters of this structure in a Taylor senes up to the linear term. [Pg.185]

At equilibrium, where the yelocity distribution is Maxwellian, it is straightforward to show that < > = 4 J p/7T, where 0p is the granular temperature. We should note that Eq. (6.109) corresponds to an inelastic Maxwell particle (Maxwell, 1879), and, most importantly, it still contains the exact dependence on tu = (1 + e)/2. We will therefore refer to this kinetic model as the inelastic Maxwell collision model. [Pg.247]

H P depends explicitly on t, a term ih(dPjdt) (whose elements are ih(8Pldt)if) is added on the right. P(u) does not change in time if the operator P is stationary otherwise its elements are (0P/gf)w. [Pg.413]

This linear composition dependence of the free energy of the demixed state Tap(0o) results in the straight lines in Fig. 4.5 that connect the free energies and Fp of the two compositions 0a and 0p- The local curvature of [Pg.147]

Figure 11 The inverse susceptibility temperature dependence is shown for several members of the Bi4Sr4RE2Cu4016+y series. Data were collected in a field of lOkG. The inset shows a comparison of the 0p values for the RE-doped 90K and RE-doped Bismuth n=2 phases. Note the excellent agreement. |

Reliable fluorescence quantum yields and lifetimes in the solid phase are difficult to determine, and accurate data are sparse (see Tables 10 and 11). It is well established that fluorescence and lifetimes of dilute solutions of benzene Increase with decreasing temperature (8,119). In a recent study of similar molecules (156-158), it was shown that the Increase in both 0p and Tp is smooth, and that both these quantities tend towards a limiting value at low temperature. An analysis of the temperature dependence of the two parameters for benzene in a variety of solvents (119) has indicated that the limiting values for both should be reached at a temperature well above 77°K, since the controlling variable is the radiationless Channel III process(es) [Pg.173]

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