Anisotropy, calculation

Figure 3.3. Equilibrium linear susceptibility (x/Xiso) versus temperature for an infinite spherical sample on a simple cubic lattice. The dotted lines are the results for independent spins, while the solid lines show the results for parallel and random anisotropy calculated with thermodynamic perturbation theory, as well as for Ising spins calculated with an ordinary high-temperature expansions. We notice in this case that the linear susceptibility for systems with random anisotropy is the same as for isotropic spins calculated with an ordinary high-temperature expansion. The dipolar interaction strength is hj = a/2a = 0.004.

Fig. 9 Fluorescence anisotropy calculated for each one of the thirty eigenstates of (dAdT)5.(dAdT)5 with respect the highest eigenstate (30). This is defined as 7, 30 = l/5(3co 20il3o — 1), where 6 30 is the angle formed between the vectors of the transitions < 0 >—>< k > and < 0 >—< 30 >.

Fig. 9 shows the fluorescence anisotropy calculated for a given ground state conformation of (dAdT)r,.(dAdT)r,. We suppose that excitation populates only the highest eigenstate ((30)). If emission arises from any of the lower eigenstates, r is expected to be drastically lower. 

The values in Table 8 refer to the electronic contribution. If, as is sometimes assumed, a correction of approximately 0.29 au is still to be added, then the lower electronic anisotropies calculated by Poulsen et al.46 and Jensen48 would again be in close agreement with the experimental result. 

The magnetocrystalline anisotropy calculated for a variety of combinations of crystal field parameters is shown in Fig. 24. It is noted that the second order crystal field term and the exchange term are the most dominant parameters. 

These surfaces were obtained subject to the two types of limiting behaviour constraints mentioned above (9,10). The limiting large-R behaviour was imposed by using reliable semi-empirical dispersion coefficients and their PgicosO) anisotropies, calculated as functions of the diatom bond length r (9,52), to define the values of the Cg coefficients for all (X,k). As the experimental data could only discern the k=0 and 1 components of the potential (5-7, 9,10), the collapsed diatom limit constraint was imposed by defining the k"2 functions by the requirements that at 5=-l (i.e., at r=0), the sum of (-1) times the A R, and constants for... 

It is quite straightforward, in principle, to extend the second moment anisotropy calculations to cases of lower symmetry. Orthorhombic symmetry, which holds for film drawn at constant width, is of particular interest. This was first treated by Slonim and Urman and more recently by Roe and by Kashiwagi et The latter workers examined the situation in considerable detail and pointed out that the complete description of molecular orientation requires a knowledge of the distribution in the three Euler angles 6, (f) and ij/ say, whereas the second moments are measured through only two parameters 0 and <(> say. We therefore cannot obtain any information about the distribution in ij/, in the absence of simplifying assumptions. 

The success of the model for the loss anisotropy led Owen and Ward to use equivalent assumptions to calculate the modulus anisotropy. The loss anisotropy calculations assume simple shear between the lamellae only, which for parallel lamellae sheet would imply that inter-lamellar shear is not activated when the tensile stress is applied along the initial draw direction i.e. parallel to the lamellar plane normals). A very appreciable fall in tensile modulus was. however, observed in this case, although as e.xpected by comparison with the corresponding loss factor in... 

Aniline, detection and measurement by DNA intercalation, 44-58 Anisotropy, calculation, 48 Anthracene, detection and measurement by DNA intercalation, 44-58 Antibody cloning, 29-31... 

Barrier for spin reversal Given a system with a total spin moment of 5 = 5 and easy-axis anisotropy, calculate the energies of the different Ms components of the ground state wave function. 

The second term on the right side of Eq. (10.81) represents the coherence between excited states 2 and 3. Because such coherences usually decay on a subpicosecond time scale, they are of little significance in conventional measurements of fluorescence amplitudes or anisotropy. We therefore neglected them in Chap. 5. However, coherence can have large effects on the fluorescence at short times [42 4]. Suppose for simplicity that 23 22> and let the angle between the transition dipoles H21 and p i The initial anisotropy calculated from Eq. (10.81) and the orientational averages given in Box 10.5 then is... 

FIGURE 6 Anisotropy calculated from pump-probe signals of ARC trimer. 

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