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Periodic nodal surfaces and exponential scale
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Veröffentlicht/Copyright:
30. Juni 2011
Abstract
Both, Periodic Nodal Surfaces (PNS) and exponential scale surfaces (ES), are suitable tools to investigate and describe the organisation of crystal structures. Therefore the mathematical relationship between ES and PNS is investigated. It is shown that the function cos (x) within the range 0 ≤ x ≤ 2π can be developed into a series in terms of orthogonal functions Φn(x) = Σk = 1ncnk exp (cos ((k–1)x)). An orthonormal set of functions Φn(x) has been evaluated using Gram-Schmidt orthonormalization. Series representation of cos (x) and sin (x) in terms of exp (sin ((k–1)x)) is impossible.
Published Online: 2011-06-30
Published in Print: 2011-08
© by Oldenbourg Wissenschaftsverlag, Dresden, Germany
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Artikel in diesem Heft
- Structural relationships of BaGe5 to clathrate I and II
- Structural ordering principles in quasi one-dimensional Wigner crystals of the series Na1+xCuO2 (0 ≤ x ≤ 1)
- Syntheses, crystal structures, magnetic properties and vibrational spectra of nitridoborate-halide compounds Sr2[BN2]Br and Eu2[BN2]X (X = Br, I) with isolated [BN2]3– units
- Temperature-dependent neutron diffraction on TiI3
- High-pressure synthesis of rare-earth metal disulfidesand diselenides LnX2 (Ln = Sm, Gd, Tb, Dy, Ho, Er and Tm; X = S, Se)
- Synthesis, crystal structure and spectroscopic properties of Y3O2Cl[SeO3]2 : Eu3+
- Crystal structure, chemical bonding and magnetic properties of the new antimonides Ce2Ir3Sb4, La2Ir3Sb4, and Ce2Rh3Sb4
- New rod packings, polyhedra, and virus structures
- Topological modeling of reconstructive phase transitions through periodic hyperbolic surfaces: the β-quartz to keatite type transition
- On the continuous transformations between genus-3 minimal surfaces approximants
- Periodic nodal surfaces and exponential scale
- Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry
