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International Union of Crystallography
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MaThCryst forthcoming activities
Seventh MaThCryst School in Latin America, February 2024, Lima; (Peru)
Twelth basic training course on symmetry and group theory, July 2024, Tsukuba (Japan)
MaThCryst recent activities
Eleventh basic and second advanced training course on symmetry and group theory, July 2023, Tsukuba (Japan)
Summer School, June 2023, Nancy (France)
Tenth training course on symmetry and group theory, August 2022, Tsukuba (Japan)
2022 Spring Festival Crystallographic School and Workshop on Crystal-field Applications February 2022, Berijing (China)
Crystallography Online: Workshop on the use and applications of the structural and magnetic tools of the Bilbao Crystallographic Server January 2022, Leioa (Spain)
Mathematics and Computer Science for Materials Innovation, September 2021, online
Ninth training course on symmetry and group theory, September 2021, Tsukuba (Japan)
2021 SIAM Conference on Mathematical Aspects of Materials Science, May 2021, Bilbao (Spain)
AMS Sectional Meeting, November 2019, Gainesville, FL (USA)
ECM32 Satellite, August 2019, Wien (Austria)
Eighth training course on symmetry and group theory, July 2019, Tsukuba (Japan)
Second Shanghai International Crystallographic School, July 2019, Shanghai (China)
Summer School, June 2019, Nancy (France)
Sixth MaThCryst School in Latin America, November 2018, Bogotà (Colombia)
More...
ECM26 XXVI European Crystallographic Meeting
MaThCryst Satellite Conference
Darmstadt, Germany, 27 - 29 August 2010
The XXVI European Crystallographic Meeting was held from 29 August to 2 September 2010 in Darmstadt, Germany.
The IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst) organised a Satellite Conference devoted to the analysis of crystal structure topology and mathematical interpretation of crystal structures.
Program
Lectures were completed with exercises distributed to the participants.
- Foundations of aperiodic structures made comprehensible (in cooperation with
the IUCr Commission on Aperiodic Crystals).
- Aperiodic crystals in the higher-dimensional description. Incommensurately modulated structures (IMS), composite structures (CS) and quasiperiodic structures (QS) - similarities and dissimilarities
- 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
- Some periodic crystal structures get simpler in higher-dimensions.
- Introduction to Quaternions and Geometric Algebra and their applications in crystallography.
- Three dimensional Euclidean space
- Clifford's geometric algebra of R3
- Subalgebra of quaternions
- Reflection in terms of plane normal vector
- Combination of reflections as geometric products
- Representations of point groups
- 3+1 dimensional space time
- Time reversal as reflection at space hyperplane
- Magnetic point groups
- Explicit computations of symmetry transformations
- Homomorphism between unit quaternions and rotations
- Neighbouring grains of cubic polycrystals in coincidence misorientation
- Preferred grain boundaries and twinning of cubic crystals
- Triple junctions and quadruple nodes in cubic polycrystals
- Textures of arbitrary polycrystals described as distributions of unit quaternions
- Mathematics of minimal surfaces
- mean curvature
- variational definition of mean curvature
- some famous examples: helicoid, catenoid, Scherk, ...
- triply periodic examples: P, D, G, ...
- mathematical properties: maximum principle, stability
- mathematical tools to construct minimal surfaces: Plateau problem, Weierstrass data, perturbation methods
- significance of minimal versus constant mean curvature, Willmore/Helfrich etc.
- assumed periodicity versus self organizing structures
- minimal and cmc surfaces for given space groups: 1-parameter families, bifurcations, distinct families
- classification problem for minimal surfaces w.r.t. a given space group
- genus of nets via quotient graphs
- minimal genus nets with good embeddings
- catenated net-dual net pairs
- minimal surfaces as bicontinuous cellular patterns whose labyrinths are defined by these net pairs
- tricontinuous partitions and branched minima surfaces
- off-surface properties of minimal surfaces, including domain sizes and the problem of determining a skeletal (medial) representation from a given minimal surface
- non-cubic minimal surfaces (in particular rhombohedral and tetragonal geometry) as transition surfaces between the cubic TPMS
Speakers
- Prof. Hans Grimmer, PSI Villigen (Switzerland)
- Prof. Eckhard Hitzer, Fukui, (Japan)
- Prof. Walter Steurer, ETH Zürich (Switzerland)
- Prof. Karsten Grosse-Brauckmann, Darmstadt (Germany)
- Prof. Gerd Schroeder-Turk, Erlangen (Germany)
- Prof. Stephen Hyde, Canberra (Australia)
Exposition
A series of models illustrating the minimal surfaces was on display during the whole satellite conference.
Poster presentations
Participants presented posters, which remained on display during the three days of the satellite.
Schedule
- 9:00-10:30 Morning session I
- 10:30-11:00 Coffee break
- 11:00-12:30 Morning session II
- 12:30-14:00 Lunch break
- 14:00-15:30 Afternoon session I
- 15:30-16:00 Coffee break
- 16:00-18:00 Afternoon session II
Abstracts and didactic material
- Program and abstracts for the posters and for the contributed oral talks
- Quaternions and their application in crystallography (H. Grimmer)
- Skeletons in the Labyrint (G. Schröder-Turk)
- Exercises on 3-D periodic minimal surfaces and nets (S. Hyde)
- Aperiodic structures,.notions of .order and disorder (S. I. Ben-Abraham)
Participants
Name | Institution | |
---|---|---|
Stephen Hyde | Australian National University | |
Joke Hadermann | University of Antwerp, Belgium | |
Claudio Aguilar | Universiy Austral of Chile | |
Massimo Nespolo | Nancy Université France | |
Paolo Celani | Stoe&Cie GmbH, Germany | |
Rachel Eloirdi | Institute for Transuranium Elements, Germany | |
Christian Groçe | Georg August Universitât Gôttingen, Germany | |
Karsten Grosse-Brauckmann | Techniche Universitât Darmstadt, Germany | |
Tim Gruene | Georg-August-Universitât, Germany | |
Wilfrid E. Klee | Baden-Baden, Germany | |
Holger Kohlmann | Saarland University, Germany | |
Sandrina Meis | Ruhr-University Bochum, Germany | |
Gerd Schroeder-Turk | Universitât Erlangen-Nuernberg, Germany | |
Navdeep Sidhu | University of Goettingen, Germany | |
Leonore Wiehl | Goethe-Universitât Frankfurt, Germany | |
Hans Wondratschek | Karlsruher Institut fûr Technologie, Germany | |
Shelomo Ben-Abraham | Ben-Gurion University of the Negev, Israel | |
Eckhard Hitzer | University of Fukui, Japan | |
Takeo Matsumoto | Kanazawa University, Japan | |
Ryoko Tomiyasu | High Energy Accelerator Research Organization, Japan | |
Wilfried Wunderlich | Tokai University, Japan | |
Bernd Souvignier | Radboud University, The Netherlands | |
Leonid Pereyaslavets | Institut of Protein Research, RAS, Russia | |
Mois Ilia Aroyo | University of the Basque Country, Spain | |
Hans Grimmer | Paul Scherrer Institut, Switzerland | |
Walter Steurer | ETH Zûrich, Switzerland | |
Jonathan Coome | Durham University, UK |
Venue
The Satellite was held in the same venue as the ECM26 congress: the Darmstadtium congress centre.
Contact
Inquiries .
The Organizers of the ECM26 MaThCryst Satellite Conference observed the basic policy of non-discrimination and affirmed 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 existed which would have prevented the participation of bona fide scientists.