From the Plateau problem to periodic minimal surfaces in lipids, surfactants and diblock copolymers

We present the novel method for generation of periodic surfaces based on the simple Landau-Ginzburg model of microemulsion. We test the method on four minimal surfaces (P,D,G, and I-WP), find two new surfaces of cubic symmetry, show how to obtain periodic surfaces of high genus and n-tuply-continuous phases. We point that the Landau model used here should be generic for all systems characterized by internal interfaces, including the diblock copolymer systems.Comment: 15 pages, Plain TeX , figures available on request or at http://saka.ichf.edu.pl/WTGRH/surfaces.htm

Atomic Nuclei with Tetrahedral and Octahedral Symmetries

We present possible manifestations of octahedral and tetrahedral symmetries in nuclei. These symmetries are associated with the OhD and TdD double point groups. Both of them have very characteristic finger-prints in terms of the nucleonic level properties - unique in the Fermionic universe. The tetrahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra; it does not preserve the parity. The octahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra as well but it does preserve the parity. Microscopic predictions have been obtained using mean-field theory based on the relativistic equations and confirmed by using 'traditional' Schroedinger equation formalism. Calculations are performed in multidimensional deformation spaces using newly designed algorithms. We discuss some experimental fingerprints of the hypothetical new symmetries and possibilities of their verification through experiments.Comment: 24 pages, LaTeX, Invited lecture on the XXXVII School of Nuclear Physics, Zakopane 2002, Polan

Quantum rotors and their symmetries

A connection between nuclear symmetries other than those of an ellipsoidal nucleus and the properties of the implied rotational spectra are discussed. The discussion is focussed on a few examples of exotic shapes predicted recently by microscopic calculations. Some possible interpretation difficulties related to experiment are shortly mentioned.Comment: Invited talk at "High Spin Physics 2001", see http://www.fuw.edu.pl/~hs2001/ , to be published in Acta Physica Polonica