ECM26 XXVI European Crystallographic Meeting
MaThCryst Satellite Conference
Darmstadt, Germany, 27 – 29 August 2010
The XXVI European Crystallographic Meeting will be held from 29 August to 2 September 2010 in Darmstadt, Germany.
The IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst) organises a Satellite Conference devoted to the analysis of crystal structure topology and mathematical interpretation of crystal structures.
Lectures will be completed with exercises distributed to the participants.
* Foundations of aperiodic structures made comprehensible (in cooperation with the IUCr Commission on Aperiodic Crystals).
1. Aperiodic crystals in the higher-dimensional description. Incommensurately modulated structures (IMS), composite structures (CS) and quasiperiodic structures (QS) – similarities and dissimilarities
2. Crystallography of Quasicrystals. Fibonacci sequence, Penrose tiling, octagonal tiling, random tilings – matching rules, symmetry, scaling. nD -embedding, symmetry, structure factor. Description of real quasicrystal structures
3. Some periodic crystal structures get simpler in higher-dimensions.
* Introduction to Quaternions and Geometric Algebra and their applications in crystallography.
1. Three dimensional Euclidean space
2. Clifford’s geometric algebra of R3
3. Subalgebra of quaternions
4. Reflection in terms of plane normal vector
5. Combination of reflections as geometric products
6. Representations of point groups
7. 3+1 dimensional space time
8. Time reversal as reflection at space hyperplane
9. Magnetic point groups
10. Explicit computations of symmetry transformations
11. Connection between unit quaternions and rotations. Computing the pair of unit quaternions corresponding to the (ordered) product of two rotations.
12. Coincidence site lattices (CSLs) generated by rotations of cubic lattices. Properties of the CSL that can immediately be read off the quaternions representing the rotation.
13. Twinning of cubic crystals.
14. Describing textures of polycrystals as unit quaternion distributions. Examples.
* Mathematics of minimal surfaces
1. mean curvature
2. variational definition of mean curvature
3. some famous examples: helicoid, catenoid, Scherk, …
4. triply periodic examples: P, D, G, …
5. mathematical properties: maximum principle, stability
6. mathematical tools to construct minimal surfaces: Plateau problem, Weierstrass data, perturbation methods
7. significance of minimal versus constant mean curvature, Willmore/Helfrich etc.
8. assumed periodicity versus self organizing structures
9. minimal and cmc surfaces for given space groups: 1-parameter families, bifurcations, distinct families
10. classification problem for minimal surfaces w.r.t. a given space group
* Prof. Hans Grimmer, PSI Villigen (Switzerland)
* Eckhard Hitzer, Fukui, (Japan)
* Prof. Walter Steurer, ETH Zürich (Switzerland)
* Prof. Karsten Grosse-Brauckmann (Germany)
A series of models illustrating the minimal surfaces will remain on display during the whole satellite conference.
Contributed oral presentations
The afternoon of August 29 will be devoted to oral talks (approximately 30 minutes) selected from the submitted abstract.
Participants are welcome to present posters, which will remain on display during the three days of the satellite.
Abstracts for the posters and for the contributed oral talks have to fit one page A4 size and should follow the templates available as OpenOffice writer, Rich-Text Format and Microsoft Word files. Abstract prepared with a Microsoft editor should be saved as Word2003 (.doc) and not Word2007 (.docx) format.
Abstracts should be submitted by email ; they will be collected in a PDF file and made available for download from this website after the school.
Limited financial support will be available for students and young scientists. Applications should be submitted via the ECM26 website.
Inquiries about the scientific program of the school should be sent to Mathcryst.Commission@crm2.uhp-nancy.fr .
The Organizers of the ECM26 MaThCryst Satellite Conference will observe the basic policy of non-discrimination and affirms the right and freedom of scientists to associate in international scientific activity without regard to such factors as citizenship, religion, creed, political stance, ethnic origin, race, colour, language, age or sex, in accordance with the Statutes of the International Council for Science. At this conference no barriers will exist which would prevent the participation of bona fide scientists.
Source: homepage http://www.crystallography.fr/mathcryst/darmstadt2010.php