内容简介:

The discovery of quasicrystals in 1984 by D. Shechtman [1] (see also [2] where the term quasicrystal was coined) destroyed the fundamental concepts of crystallography which relied on a traditional definition of a crystal as a periodic arrangement of identical unit cells. In his experiments with a rapidly cooled Al-Mn alloy, Shechtman obtained a sharp diffraction pattern with a rotational symmetry incompatible with periodicity. His findings forced the International Union of Crystallography to redefine the notion of a crystal as any solid having discrete diffraction diagram [3].
Quasicrystals are a new class of materials which thank to their unique properties such as electrical, optical, hardness and nonstick features are finding new and promising applications e.g. in nonstick coatings, thermal barriers. infrared sensor etc. Two decades after the first publication [1] on quasicrystals, a soft quasicrystal was found in nature [4] and a number of materials including liquid crystals, polymers, nanoparticles and colloids enriched the family of soft quasicrystals [4], enhancing the potential applications of these quasi-periodic structures.
In my talk I will present a brief history of the discovery of quasicrystals and I will discuss some of the fascinating mechanical and mathematical properties of quasicrystals. In particular I will focus on elastic constitutive relations in which besides the phonon space there is also a contribution from the phason space. I will present the form of the energy density function in some of these quasi-periodic structures. Recent findings of natural quasicrystals will also be mentioned.
References
[1] D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[2] D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).
[3] International Union of Crystallography, Acta Crystallogr. A 48, 922 (1992).
[4] T. Dotera, Israel J. Chem. 51, 1197 (2011).

报告人简介:

W?odzimierz Domański, is currently a Professor of the Institute of Mathematics and Cryptology, a faculty of Cybernetics at the Military University of Technology. He was a Fulbright Postdoctoral Fellow Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, USA. His research interests include propagation and interaction of nonlinear waves in solids and asymptotic methods.

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