Multimode model

In this work we have attempted to model the available experimental data for CaO Cu2+ using a variety of parameter sets taken from the literature. We conclude that only O Brien s multimode model [7], for which hw 216 cm 1 and jX/hoy 8, can satisfactorily account for all the data. These systems are particularly attractive to both the theoretician and experimentalist fascinated by Jahn-Teller funny business in that the states pertaining to j = 1/2 and 3/2 span just a few wave numbers. We have demonstrated how a number of modem physical techniques can be employed to elucidate further the low-lying vibronic structure. In particular it should be possible to obtain a direct measure of the tunnelling splitting from a high-held, high-frequency EPR experiment. 

Inkson et al. (61) and McLeish (62) in a recent review have proposed also a multimode pom-pom model in an attempt to account for the multiple levels of branching believed to be present in LDPE molecules. Because the precise structure and degree of branching of LDPE molecules are unknown, with no experimental techniques to determine them, the potential exists for these multimode models to characterize the LDPE macro-molecular structure through fitting with experimental rheological data. 

This is a straightforward generalization of Eq. 34 in the multimode model, being an average of hojjCO h lihojj/2)/2, with weight //, whose sum equals 7. by Eq. 39. 

The Hamiltonian for the reactant-state potential in the multimode model is given by Eq. 37. In the semiclassical regime, both the coordinate r/, and its conjugate... 

A second approach uses the unimodal model-independent method, which begins with the assumption that the size distribution consists of a finite number of fixed size classes. The detector response expected for this distribution is simulated, and then the weight fractions in each size class are optimized through a minimization of the sum of squared deviations from the measured and simulated detector responses. The third system uses the multimodal model-independent method. For this, diffraction patterns for known size distributions are simulated, random noise is superimposed on the patterns, and then the expected element responses for the detector configuration are calculated. The patterns are inverted by the same minimization algorithm, and these inverted patterns are compared with known distributions to check for qualitative correctness. 

Figure 3. The multimode model. The Effective S is plotted against the scaling factor A (where Q2 = Agi for all modes) for changing values of J. The energy gap is fixed at 3000 cm and the total S value for the exciton state is 1.0.

An exact derivation and implementation of the constitutive equations needed for this multimode model is not given here the interested reader is refeued to References 13 and 67. What is important to note is that the method just desctihed allows the determination of the relaxation spectrum from a simple set of uniaxial tensile or compression experiments at different strain rates and does not require lengthy relaxation experiments. The nonlinearity in stress is the same as used in the flow stress itself... 

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