Abstract
Periodic Nodal Surfaces (PNS) of Fourier series are derived and classified as fundamental invariants of structured matter. Relationships to periodic minimal surfaces PMS and to periodic zero potential surfaces (POPS) are given. A basic set of cubic PNS is represented in arithmetic form. The special importance of the invariance of the zeros to the type of the potential is stressed.
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Nesper, R., Schnering, H.G. von: Z. Kristallorg.170, 138 (1985)
Schnering, H.G. von: Jahrb. Heidelberger Akad. Wissensch. 90 (1985)
Neper, R., Schnering, H.G. von: Angew. Chem.98, 111 (1986); Angew. Chem. Int. Ed. Engl.25, 110 (1986)
Schnering, H.G. von, Nesper, R.: Angew. Chem.99, 1097 (1987); Angew. Chem. Int. Ed. Engl.26, 1059 (1987)
Hahn, T. (ed.): Intern. Tables for Crystallography, Vol. 4. Dordrecht: Reidel Publ. Comp. 1983
Faelth, L., Andersson, S.: Z. Kristallogr.160, 313 (1982)
Andersson, S., Hyde, S.T.: Angew. Chem.95, 67 (1983); Angew. Chem. Int. Ed. Engl.22, 69 (1983)
Andersson, S., Hyde, S.T., Schnering, H.G. von: Z. Kristallogr.168, 1 (1984)
Schwarz, H.A.: Gesammelte Mathematische Abhandlungen, Bd. 1 & 2. Berlin: Springer 1890 (Reprinted by New York: Chelsea Publ. Comp. 1972)
Bonnet, O.: C.R. Acad. Sci.37, 539 (1853)
Neovius, E.R.: Bestimmung zweier specieller periodischer Minimalflächen. Helsingfors (1883)
Hoffmann, D.: Math. Intell.9, 8 (1987)
Schoen, A.H.: NASA Technical Note D-5541. Washington, D.C. (1970)
Eliasson, A.-C., Larsson, L., Andersson, S., Hyde, S.T., Nesper, R., Schnering, H.G. von: Starch/Stärke39, 147 (1987)
Charvolin, J., Sadoc, J.S., J. Phys. (Paris)48, 1559 (1987); Hyde, S.T., Andersson, S., Larsson, K., Z. Kristallogr.174, 237 (1986)
Fischer, W., Koch, E.: Z. Kristallogr.179 31 (1987)
Koch, E., Fischer, W.: Z. Kristallogr.183, 129 (1988)
Koch, E., Fischer, W.: Acta Crystallogr. A45, 169 (1989)
Koch, E., Fischer, W.: Acta Crystallogr. A45, 558 (1989)
Schnering, H.G. von, Nesper, R., Oehme, M.: Jahresbericht des Max-Planck-Instituts für Festkörperforschung, Stuttgart 1987
Bertaut, F.: J. Phys. Radium13, 499 (1952)
Bertaut, F.: J. Phys. Chem. Solids39, 97 (1978)
Mackay, A.L.: Angew. Chem.100, 867 (1988); Angew. Chem. Int. Ed. Engl.27, 849 (1988)
Nesper, R., Oehme, M., Schnering, H.G. von: (to be published)
Heine, V., Weaire, D.: Solid State Phys.24, 247 (1970)
Nesper, R.: Angew. Chem. (1991), (in press)
Schnering, H.G. von, Nesper, R.: (to be published)
Schnering, H.G. von, Oehme, M., Rudolf, G.: Acta Chem. Scand. (in press)
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von Schnering, H.G., Nesper, R. Nodal surfaces of Fourier series: Fundamental invariants of structured matter. Z. Physik B - Condensed Matter 83, 407–412 (1991). https://doi.org/10.1007/BF01313411
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DOI: https://doi.org/10.1007/BF01313411