By P.J. Hilton, U. Stammbach

ISBN-10: 0387900330

ISBN-13: 9780387900339

Homological algebra has came upon a good number of purposes in lots of fields starting from finite and endless team concept to illustration concept, quantity idea, algebraic topology and sheaf conception. within the re-creation of this extensive creation to the sphere, the authors tackle a few pick out themes and describe their purposes, illustrating the variety and intensity in their advancements. A entire set of workouts is integrated.

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D. Joannopoulos, Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64(4), 1045 (1992) References 25 13. V. A. Catlow, Potential models for ionic oxides. J. Phys. C: Solid State Phys. 18 (6), 1149–1156 (1985) 14. D. Fang, Z. Luo, S. Liu, T. Zeng, L. Liu, J. Xu, W. Xu, Photoluminescence properties and photocatalytic activities of zirconia nanotube arrays fabricated by anodization. Opt. Mater. 35 (7), 1461–1466 (2013) 15.

Cormack, A computer simulation study of the defect structure of calcia-stabilized zirconia. Philos. Mag. A 61(1), 1–22 (1990) Chapter 3 Finite Element Modeling of Nanotubes In order to develop a ﬁnite element model for a given nanotube, it is necessary to set few things. Geometry of the nanotube should be well understood. As discussed in the previous chapters, atomic coordinates in a nanotube structure should be determined. The atomic coordinates is the base of any atomic modeling. Bonding between atoms should be established with respect to the experimental observations.

As discussed in the previous chapters, atomic coordinates in a nanotube structure should be determined. The atomic coordinates is the base of any atomic modeling. Bonding between atoms should be established with respect to the experimental observations. Chemical bonds will be replaced with a proper structural element. After creating the frame-like structure of the nanotube, we can apply boundary conditions and carry out the simulation process. In order to make a clear image of the modeling process, we will try to model a typical nanotube such as SWCNT in the following section.

### A Course in Homological Algebra by P.J. Hilton, U. Stammbach

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