Three-dimensional stack model

Bagster et proposed an ideal three-dimensional stack model for a sphere... 

L. A., Rector, D.R., and Khaleel, M.A. (2003) Three-dimensional electrochemical modeling of planar SOFC stacks. J. Power Sources, 113, 109-114. 

Even though the three-dimensional XY-model accurately predicts the experimentally observed hexatic scattering, the model is unsatisfying for two reasons. First, heat capacity data taken on the 80SI system suggest that the heat capacity exponent, a, is approximately 0.5.22 Second, the original motivation for the stacked hexatic model of well-ordered smectic liquid crystal phases was the intuitive idea that the weakly coupled smectic layers should display some of the novel physics predicted to occur in two dimensions. It is unsatisfying not to have any remnants of that two-dimensional physics survive in the three-dimensional model. 

The optimised interlayer distance of a concentric bilayered CNT by density-functional theory treatment was calculated to be 3.39 A [23] compared with the experimental value of 3.4 A [24]. Modification of the electronic structure (especially metallic state) due to the inner tube has been examined for two kinds of models of concentric bilayered CNT, (5, 5)-(10, 10) and (9, 0)-(18, 0), in the framework of the Huckel-type treatment [25]. The stacked layer patterns considered are illustrated in Fig. 8. It has been predicted that metallic property would not change within this stacking mode due to symmetry reason, which is almost similar to the case in the interlayer interaction of two graphene sheets [26]. Moreover, in the three-dimensional graphite, the interlayer distance of which is 3.35 A [27], there is only a slight overlapping (0.03-0.04 eV) of the HO and the LU bands at the Fermi level of a sheet of graphite plane [28,29],... 

Obviously this model is very simplified, compared with the real crystal which contains many defects, dislocations and entanglements. In particular, it neglects many aspects of the true three-dimensional nature of the lamella which one may have thought to be important the influence of the stacking of folds, which is... 

Pakalapati, S.R., Elizalde-Blancas, F. and Celik, I. (2007) Numerical simulation of solid oxide fuel cell stacks Comparison between a reduced order pseudo three-dimensional model and a multidimensional model, Proceedings of 5th ASME International Fuel Cell Science, Engineering and Technology Conference, New York, USA, June 18-20. 

The most favourable relative configuration of identical chiral molecules is that where all neighbouring molecules are twisted relative to each other. This is achieved by a "double-twist" stacking, illustrated in Fig. 4.32. In three-dimensional euclidean space, this double-twist caimot be realised throughout space some "disclination" singularities must occur [61]. How then can this double twist be most closely approached A simple model, involving nothing more than potatoes, and oven and matches, is useful. The lower-... 

---