Qualitative discussion concluding remarks

MS2 to 11 i(q. Q) have lower energies than that from GS to U (q. Q) However, the transition MSI — (g, Q) populates MS2, whereas the transition MS2— Ui(q. Q). in its turn, transfers the system to MSI. In such a way, the consideration carried out shows that in the framework of the adiabatic potential scheme presented in Fig. 8 it is possible to go from GS into MS 1 and MS2, from MSI into MS2 and vice versa. The indicated ways of population of the metastable states on the basis of the obtained adiabatic potential scheme are in qualitative agreement with experimental data [8]. However, at this stage, the estimation of the wavelengths of the corresponding transitions seems to be premature. 

1 Departamento de Ciencias de la Tierra y Fisica de la Materia Condensada, Universidad de Cantabria, Avda. Los Castros s/n. 39005 Santander, Spain 2Departamento de Fisica Moderna, Universidad de Cantabria, 

Other Jahn-Teller systems explored through DFT 455 

The vibrational Eg mode is described by the Qe ( 3z2 — r2) and Q,. ( x2 — v2) coordinates. Under a Qe 0 distortion a MX6 complex becomes tetragonally elongated (Fig. 1) with four short equatorial ligands at a distance Req = R0 — a and 

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]. 

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The chapter is organized as follows Section 4.2 describes flexodomains in the planar geometry. Particular emphasis is placed on the most recent theoretical results, where for the first time arbitrary ratios of the elastic constants ifi, if2 are considered as well as driving by an AC electric field. Section 4.3 deals with the effects of flexoelectricity on dissipative EC patterns. The focus is on qualitatively new phenomena that are not covered by the standard model of EC. In Section 4.4 we analyse the competition between flexodomains and EC patterns at low AC driving frequencies. The chapter ends with a discussion and some concluding remarks in Section 4.5. 

In order to illustrate this issue, the paper considers an industrial controlled system on which a comparison study is performed. First the system failure is represented by a model that complies with the BDMP formalism. Second, the minimal cut sequences are extracted from this model. Section 2 describes the case study and gives the definition of the BDMP formalism. Section 3 applies the MBSA stated above while considering only the process failures. Then a control architecture is described, and added to the model in section 4. For integrating these new failures in the model, three models are proposed and discussed. In the same section, the set of minimal cut sequences is updated, and compared with the previous one. This comparison shows that the control failures have a significant influence on the qualitative analysis of the system. Finally, the last section draws up concluding remarks and outlooks. 

Now let us see how this result is to be understood in terms of the DLVO theory. At first glance, it seems remarkable that any consistency at all can be found in tests as arbitrary as the CCC determination. It is not difficult, however, to show that these results are quite close to the values predicted in terms of the DLVO model for interacting blocks with flat faces. From an inspection of Figure 13.8, we concluded that the system at k = 108 m l would be stable with respect to coagulation, whereas the one at k = 3 108 m l would coagulate. Furthermore, we examined the energy barrier to draw these conclusions. Next we must ask how the qualitative criteria we used in discussing the curves can be translated into an analytical expression. 

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