List of Publications

On the Fibonacci tiling and its modern ramifications
by M. Baake, F. Gähler, and J. Mazáč
Israel J. Chem., in press (2024) arXiv DOI

Orbit separation dimension as complexity measure for primitive inflation tilings
by M. Baake, F. Gähler, and P. Gohlke
arXiv

Dynamics and topology of the Hat family of tilings
by M. Baake, F. Gähler, and L. Sadun
arXiv

Fibonacci direct product variation tilings
by M. Baake, F. Gähler, and J. Mazác
J. Math. Phys. 63, 082702 (2022)
arXiv DOI

Cohomology groups for spaces of 12-fold tilings
by N. Bedaride, F. Gähler, and A. Lecuona
IMRN 2022(18), 14181-14254 in print (2022)
arXiv DOI

Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction
by M. Baake, F. Gähler, and N. Manibo
Commun. Math. Phys. 370(2), 591-635 (2019)
arXiv Journal

Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples
by M. Baake and F. Gähler
Topol. Appl. 205, 4-27 (2016)
arXiv DOI

Substitution Rules for Higher-Dimensional Paperfolding Structures
by F. Gähler and J. Nilsson
arXiv

A computer search for planar substitution tilings with n-fold rotational symmetry
by F. Gähler, E. E. Kwan, G. R. Maloney
Discrete Comput. Geom. 53, 445-465 (2015)
arXiv, DOI

Determining pure discrete spectrum for some self-affine tilings
by S. Akiyama, F. Gähler, J.-Y. Lee
Discr. Math. Th. Comp. Sci. (DMTCS) 16:3, 305-316 (2014)
arXiv, Journal

Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces
by E. P. Bugarin, F. Gähler
Acta Phys. Pol. A 126, 438-441 (2014)
arXiv, Journal

Topology of the Random Fibonacci Tiling Space
by F. Gähler, E. Miro
Acta Phys. Pol. A 126, 564-567 (2014)
arXiv, Journal

Comparison of scalable fast methods for long-range interactions
by A. Arnold, F. Fahrenberger, Ch. Holm, O. Lenz, M. Bolten, H. Dachsel, R. Halver, I. Kabadshow, F. Gähler, F. Heber, J. Iseringhausen, M. Hofmann, M. Pippig, D. Potts, G. Sutmann
Phys. Rev. E 88, 063308 (2013),
DOI

Cohomology of One-Dimensional Mixed Substitution Tiling Spaces
by F. Gähler, G. R. Maloney
Topol. Appl. 160, 703 - 719 (2013)
arXiv, DOI

Examples of substitution systems and their factors
by M. Baake, F. Gähler and U. Grimm
Journal of Integer Sequences 16, 13.2.14 (2013)
arXiv, Journal

Substitution rules and topological properties of the Robinson tilings
by F. Gähler
in Aperiodic Crystals, eds. S. Schmid, R.L. Withers and R. Lifshitz, Springer (2013), pp. 67-73
arXiv

Hexagonal inflation tilings and planar monotiles
by M. Baake, F. Gähler and U. Grimm
Symmetry 4, 581-602 (2012),
arXiv, Journal, DOI

Combinatorics and topology of the Robinson tiling
by F. Gähler, A. Julien and J. Savinien
C. R. Acad. Sci. Paris, Ser. I 350, 627-631 (2012)
arXiv, DOI,

Integral cohomology of rational projection method patterns
by F. Gähler, J. Hunton and J. Kellendonk
Alg. & Geom. Top. 13, 1661-1708 (2013)
arXiv, Journal, DOI

Spectral and topological properties of a family of generalised Thue-Morse sequences
by M. Baake, F. Gähler and U. Grimm
J. Math. Phys. 53, 032701 (2012)
arXiv, DOI

Topological invariants of aperiodic tilings
by F. Gähler
RIMS Kôkyûroku 1725, 15-27 (2011)
(slides of invited talk given at RIMS workshop on "Mathematics of Quasi-Periodic Order", Kyoto, June 2010)

Anomalous vibrational dynamics in the Mg₂Zn₁₁ phase
by H. Euchner, M. Mihalkovič, F. Gähler, M.R. Johnson, H .Schober, S. Rols, E. Suard, A. Bosak, S. Ohhashi, A.-P. Tsai, S. Lidin, C. Pay Gomez, J. Custers, S. Paschen, and M. de Boissieu
Phys. Rev. B 83, 144202 (2011).

Direct Wolf summation of a polarizable force field for silica
by P. Brommer, P. Beck, A. Chatzopoulos, F. Gähler, J. Roth, and H.-R. Trebin
J. Chem. Phys. 132, 194109 (2010)
PDF (340k), DOI

MLD Relations of Pisot Substitution Tilings
by F. Gähler
Journal of Physics: Conference Series 226, 012020 (2010).
PDF (501k), arXiv, DOI

Integer Cech Cohomology of Icosahedral Projection Tilings
by F. Gähler, J. Hunton, and J. Kellendonk
Z. Kristallogr. 223, 801-804 (2009).
PDF (168k)

Femtosecond Laser Ablation of Aluminum
by S. Sonntag, J. Roth, F. Gähler, and H.-R. Trebin
Applied Surface Science 255(24), 9742 (2009).

Simulating structure and physical properties of complex metallic alloys
by H.-R. Trebin, P. Brommer, M. Engel, F. Gähler, S. Hocker, F. Rösch, and J. Roth,
in Proceedings of the 3rd European School in Materials Science, Ljubljana, May 2007, ed. E. Belin-Ferré, Word Scientific (2009), pp. 291-329.
PDF (880k)

Atomic dynamics of the i-ScZnMg and its 1/1 approximant phase: experiment and simulation
by M. Mihalkovic, S. Francoual, K. Shibata, M. de Boissieu, A.Q.R. Baron, Y. Sidis, T. Ishimasa, T. Lograsso, L.-P. Regnault, F. Gähler, S. Tsutsu, B. Hennion, P. Bastie, T.J. Sato, H. Takakura, R. Currat, and A.P. Tsai
Phil. Mag. 88, 2311-2318 (2008).

Lattice dynamics of the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1/1 approximant
by M. de Boissieu, S. Francoual, M. Mihalkovic, K. Shibata, A.Q.R. Baron, Y. Sidis, T. Ishimasa, D. Wu, T. Lograsso, L.-P. Regnault, F. Gähler, S. Tsutsu, B. Hennion, P. Bastie, T.J. Sato, H. Takakura, R. Currat, and A.P. Tsai
Nature Materials 6, 977-984 (2007).
Article (PDF) (747k), Supplementary information (PDF) (210k)

Potfit: effective potentials from ab-initio data
by P. Brommer and F. Gähler
Modelling Simul. Mater. Sci. Eng. 15, 295-304 (2007).
compressed PostScript (14k), PDF (17k)

Ordering and correlation of cluster orientations in CaCd₆
by P. Brommer, F. Gähler, and M. Mihalkovic
Phil. Mag. 87, 2671-2677 (2007).
compressed PostScript (118k), PDF (132k)

Molecular Dynamics on NEC Vector Systems
by K. Benkert and F. Gähler
in High Performance Computing on Vector Systems 2006, M. Resch et al. (eds.), Springer, Berlin 2007, pp. 145-152.
PDF (165k)

Structural relaxation made simple
by E. Bitzek, P. Koskinen, F. Gähler. M. Moseler, and P. Gumbsch
Phys. Rev. Lett. 97, 170201 (2006).
PDF (614k)

Atomistic simulations on scalar and vector computers
by F. Gähler and K. Benkert
in High Performance Computing on Vector Systems, M. Resch et al. (eds.), Springer, Berlin 2006, pp. 173-186.
compressed PostScript (156k), PDF (148k)

Effective potentials for quasicrystals from ab-initio data
by P. Brommer and F. Gähler
Phil. Mag. 86, 753-758 (2006)
(Proceedings of ICQ9, Ames, Iowa, May 2005).
compressed PostScript (112k), PDF (138k)

Molecular dynamics simulation of aluminium diffusion in decagonal quasicrystals
by S. Hocker, F. Gähler, and P. Brommer
Phil. Mag. 86, 1051-1057 (2006)
(Proceedings of ICQ9, Ames, Iowa, May 2005).
compressed PostScript (276k), PDF (229k)

Aluminium diffusion in decagonal quasicrystals
by S. Hocker and F. Gähler
Phys. Rev. Lett. 93, 075901 (2004).
compressed PostScript (815k), PDF (1311k)

Atomic dynamics and diffusion in decagonal quasicrystals
by F. Gähler and S. Hocker
Ferroelectrics 305, 167-172 (2004).
PDF (1221k)

Atomic Dynamics in Decagonal Al-Ni-Co Quasicrystals
by F. Gähler and S. Hocker
J. Non-Cryst. Solids 334-335, 308-311 (2004).
compressed PostScript (1193k), PDF (1384k)

Phason-elastic energy in a model quasicrystal
by U. Koschella, F. Gähler, J. Roth, and H.-R. Trebin
J. Non-Cryst. Solids 334-335, 276-279 (2004).
compressed PostScript (223k), PDF (163k)

Crack Propagation in Icosahedral Model Quasicrystals
by Ch. Rudhart, F. Rösch, F. Gähler, J. Roth, and H.-R. Trebin
In High Performance Computing in Science and Engineering 2003,
E. Krause, W. Jäger, and M. Resch (eds.), Springer, Heidelberg (2003), pp. 107-116.
compressed PostScript (1070k), PDF (374k)

A Cluster Model of Decagonal Tilings
by M. Reichert and F. Gähler
Phys. Rev. B 68, 214202 (2003).
compressed PostScript (1180k), PDF (1802k)

Finite-Temperature Order-Disorder Phase Transition in a Cluster Model of Decagonal Tilings
by M. Reichert and F. Gähler
Preprint, compressed PostScript (360k), PDF (449k)

Phason elasticity and atomic dynamics of quasicrystals
by F. Gähler, S. Hocker, U. Koschella, J. Roth, and H.R. Trebin
in Quasicrystals - Structure and Physical Properties,
H.-R. Trebin (ed.), VCH Wiley (2003), pp. 338-358.
compressed PostScript (1690k), PDF (1859k)

Computation of Strain Distributions in Quantum Dot Nanostructures by Means of Atomistic Simulations
by F. Gähler, C. Kohler, J. Roth, and H.R. Trebin
In High Performance Computing in Science and Engineering 2002,
E. Krause and W. Jäger (eds.), Springer, Heidelberg (2002), pp. 3-14.
compressed PostScript (4642k)

Generation of Quasiperiodic Order by Maximal Cluster Covering
by F. Gähler, P. Gummelt, and S.I. Ben-Abraham
In Covering of Discrete Quasiperiodic Sets - Theory and Applications to Quasicrystals,
Springer Tracts in Modern Physics Vol. 180, P. Kramer and Z. Papadopolos (eds.), Springer, Berlin (2002), pp. 63-93
compressed PostScript (562k)

Phason elastic constants of a binary tiling quasicrystal
by U. Koschella, F. Gähler, J. Roth, and H.-R. Trebin
J. Alloys Comp. 342, 287-290 (2002)
(Proceedings of 'Quasicrystals 2001', Sendai, September 2001).
compressed PostScript (280k)

Simulation of dislocations in icosahedral quasicrystals with IMD
by G. Schaaf, F. Gähler, C. Kohler, U. Koschella, N. Resta, J. Roth, C. Rudhart, and H.-R. Trebin
In High Performance Computing in Science and Engineering 2001,
E. Krause and W. Jäger (eds.), Springer, Heidelberg (2002), pp. 3-11.
compressed PostScript (474k)

Cluster Models of Decagonal Tilings and Quasicrystals
by F. Gähler and M. Reichert
J. Alloys Comp. 342, 180-185 (2002)
(Proceedings of 'Quasicrystals 2001', Sendai, September 2001).
compressed PostScript (500k)

Recent developements in IMD: Interactions for covalent and metallic systems
by E. Bitzek, F. Gähler, J. Hahn, Ch. Kohler, G. Krdzalic, J. Roth, Ch. Rudhart, G. Schaaf, J. Stadler, and H.-R. Trebin
in High Performance Computing in Science and Engineering 2000,
E. Krause and W. Jäger (eds.), Springer, Heidelberg, pp. 37-47.
compressed PostScript (382k)

Dodecagonal Tilings as Maximal Cluster Coverings
by F. Gähler, R. Lück, S.I. Ben-Abraham, and P. Gummelt
Ferroelectrics 250, 335 (2001).
(Proceedings of Aperiodic'2000, Nijmegen, July 2000).
compressed PostScript (26k)

Dodecagonal Tilings Almost Covered by a Single Cluster
by S.I. Ben-Abraham, P. Gummelt, R. Lück, and F. Gähler
Ferroelectrics 250, 313-316 (2001).
(Proceedings of Aperiodic'2000, Nijmegen, July 2000).

IMD - A Massively Parallel Molecular Dynamics Package for Classical Simulations in Condensed Matter Physics
by J. Roth, J. Stadler, M. Brunelli, D. Bunz, F. Gähler, J. Hahn, M. Hohl, C. Horn, R. Mikulla, G. Schaaf, J. Stelzer, and H.-R. Trebin
in High Performance Computing in Science and Engineering '99,
E. Krause and W. Jäger (eds.), Springer Verlag, Heidelberg, Berlin (2000), pp. 72-81.
compressed PostScript (655k)

A Molecular Dynamics Run with 5 180 116 000 Particles
by J. Roth, F. Gähler, and H.-R. Trebin,
Int. J. Mod. Phys. C11, 317 (2000).

Molecular Dynamics Simulations with IMD
by J. Roth, J. Stadler, M. Brunelli, F. Gähler, J. Hahn, M. Hohl, C. Horn, R. Mikulla, G. Schaaf, and H.-R. Trebin, in Computer Simulation Studies in Condensed Matter Physics XII, D. P. Landau, S. P. Lewis and H. B. Schüttler (eds.), Springer Verlag, Heidelberg, Berlin (2000), p. 169.
compressed PostScript (70k)

Cluster coverings as an ordering principle for quasicrystals
by F. Gähler
Mat. Sci. Eng. A 294-296, 199-204 (2000)
(Proceedings of the 7th International Conference on Quasicrystals, Stuttgart 1999).
compressed PostScript (41k), PDF (444k)

Cohomology groups for projection tilings of codimension 2
by F. Gähler and J. Kellendonk
Mat. Sci. Eng. A 294-296, 438-440 (2000)
(Proceedings of the 7th International Conference on Quasicrystals, Stuttgart 1999).
compressed PostScript (29k), PDF (54k)

Cluster Coverings: A Powerful Ordering Principle for Quasicrystals
by F. Gähler
pp. 118-127 in Quasicrystals - Current Topics, E. Belin-Ferré, C. Berger, M. Quiquandon, and A. Sadoc (eds.), World Scientific, Singapore 2000.
compressed PostScript (32k)

Covering Cluster Description of Octagonal MnSiAl Quasicrystals
by S. I. Ben-Abraham and F. Gähler
Phys. Rev. B 60, 860-864 (1999)
compressed PostScript (38k), PDF (230k)

Atomic self-diffusion in dodecagonal quasicrystals
by J. Roth and F. Gähler
Eur. Phys. J. B 6, 425-445 (1998)

Computing With Crystallographic Groups
by F. Gähler
pp. 101-105 in Aperiodic'97, M. de Boissieu, J.-L. Verger-Gaugry and R. Currat (eds.), World Scientific, Singapore 1999 (Proceedings of the International Conference on Aperiodic Crystals, Alpe d'Huez 1997).
compressed PostScript (98k), PDF (77k)

The Symmetry Structure of the Elser-Sloane Quasicsrystal
by M. Baake and F. Gähler
pp. 63-67 in Aperiodic'97, M. de Boissieu, J.-L. Verger-Gaugry and R. Currat (eds.), World Scientific, Singapore 1999 (Proceedings of the International Conference on Aperiodic Crystals, Alpe d'Huez 1997).
compressed PostScript (118k), PDF (94k)

Cluster Interactions for Quasiperiodic Tilings
by F. Gähler
pp. 95-98 in Proceedings of the 6th International Conference on Quasicrystals, eds. S. Takeuchi and T. Fujiwara, World Scientific, Singapore 1998.
compressed PostScript (70k), PDF (55k)

Self-Affine Quasiperiodic Tilings
by F. Gähler
pp. 972-976 in GROUP 21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, Volume 2, eds. H.-D. Doebner, W. Scherer and C. Schulte, World Scientific, Singapore 1997.
compressed PostScript (36k)

Computing Maximal Subgroups and Wyckoff Positions of Space Groups
by B. Eick, F. Gähler and W. Nickel
Acta Cryst. A 53 , 467-474 (1997)
compressed PostScript (54k)

Atomic Self-Diffusion in Quasicrystals: A Molecular Dynamics Study
by J. Roth and F. Gähler
pp. 815-820 in Diffusion in Materials: DIMAT-96, Part 1, eds. H. Mehrer et al., Scitex Publications, Uetikon 1997.
compressed PostScript (145k)

Atomare Selbstdiffusion in Quasikristallen
by J. Roth and F. Gähler
in Simulationstechniken in der Materialwissenschaft , eds. P. Klimanek, W. Pantelon,
Freiberger Forschungshefte B279, p. 259 (1996), Technische Universität Bergakademie Freiberg.
compressed PostScript (75k)

The Diffraction Pattern of Selfsimilar Tilings
by F. Gähler and R. Klitzing
pp. 141-174 in The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody, Kluwer 1997
(NATO Advanced Study Institute Series C, Vol. 489).
PDF (1375k)

Thermodynamics of Random Tiling Quasicrystals
by F. Gähler
pp. 236-239 in Quasicrystals, Ch. Janot and R. Mosseri (eds.), World Scientific 1995
(Proceedings of the 5th International Conference on Quasicrystals, Avignon, 1995).
compressed PostScript (106k), PDF (87k)

Atomic Self-Diffusion in Quasicrystals
by F. Gähler and J. Roth
pp. 183-187 in Aperiodic'94, G. Chapuis and W. Paciorek (eds.), World Scientific 1995
(Proceedings of the International Conference on Aperiodic Crystals, Les Diablerets, 1994).
compressed PostScript (130k), PDF (171k)

Specific Heat and Self-Diffusion in Quasicrystals
by D. Joseph and F. Gähler
pp. 188-192 in Aperiodic'94, G. Chapuis and W. Paciorek (eds.), World Scientific 1995
(Proceedings of the International Conference on Aperiodic Crystals, Les Diablerets, 1994).

Quasiperiodic Ground States Without Matching Rules
by F. Gähler and H.-C. Jeong
J. Phys. A28, 1807-1815 (1995).
compressed PostScript (208k), PDF (236k)

Comment on "Cluster Approach to Quasicrystals"
by F. Gähler
Phys. Rev. Lett. 74, 334 (1995).
compressed PostScript (13k)

Binary Tiling Quasicrystals and Matching Rules
by F. Gähler, M. Baake and M. Schlottmann
Phys. Rev. B50, 12458-12467 (1994).

Phonons in Models for Icosahedral Quasicrystals: Low Frequency Behaviour and Inelastic Scattering Properties
by J. Los, T. Janssen and F. Gähler
J. Phys. I (France) 3, 1431-1461 (1993).

The Phonon Spectrum of the Octagonal Tiling
by J. Los, T. Janssen and F. Gähler
Int. J. Mod. Phys. B7, 1505-1525 (1993).

The Dualisation Method Revisited: Dualisation of Product Laguerre Complexes as a Unifying Framework
by F. Gähler and P. Stampfli
Int. J. Mod. Phys. B7, 1333-1349 (1993).

Scaling Properties of Vibrational Spectra and Eigenstates for Tilings Models of Icosahedral Quasicrystals
by J. Los, T. Janssen and F. Gähler
J. Phys. I (France) 3, 107-134 (1993).

Matching Rules for Quasicrystals: The Composition-Decomposition Method
by F. Gähler
J. Non-Cryst. Solids 153 & 154, 160-164 (1993)
(Proceedings of the 4th International Conference on Quasicrystals, St. Louis 1992).
compressed PostScript (87k), PDF (84k)

Lattice Dynamics of 3-Dimensional Tilings Modelling Icosahedral Quasicrystals
by J. Los, T. Janssen and F. Gähler
J. Non-Cryst. Solids 153 & 154, 581-585 (1993)
(Proceedings of the 4th International Conference on Quasicrystals, St. Louis 1992).

Comparison of HREM Images and Contrast Simulations for Dodecagonal Ni-Cr Quasicrystals
by C. Beeli, F. Gähler, H.-U. Nissen and P. Stadelmann
J. Phys. France 51, 661-674 (1990).

Classification of Space Groups for Quasicrystals with (2+1)-Reducible Point Group
by F. Gähler
pp. 69-78 in Quasicrystals and Incommensurate Structures in Condensed Matter,
M. J. Yacaman, D. Romeu, V. Castano and A. Gomez (eds.), World Scientific 1990.
compressed PostScript (46k)

Crystallography of Dodecagonal Quasicrystals
by F. Gähler
pp. 272-284 in Quasicrystalline Materials, Ch. Janot and J.M. Dubois (eds.), World Scientific 1988.
compressed PostScript (130k), PDF (178k)

Quasiperiodic Structures: The Generalized Grid-Projection Method
by V. E. Korepin, F. Gähler and J. Rhyner
Acta Cryst. A44, 667-672 (1988).

Some Mathematical Problems Arising in the Study of Quasicrystals
by F. Gähler
J. Physique Colloque 47, C3-115-123 (1986).

Equivalence of the Generalised Grid and Projection Methods for the Construction of Quasiperiodic Tilings
by F. Gähler and J. Rhyner
J. Phys. A: Math. Gen. 19, 267-277 (1986).

Comment on "Structure of Rapidly Quenched Al-Mn"
by F. Gähler and J. Rhyner
Phys. Rev. Lett. 55, 2369 (1985).

Wave Fields in Weyl Spaces and Conditions for the Existence of a Preferred Pseudo-Riemannian Structure
by J. Audretsch, F. Gähler and N. Straumann
Comm. Math. Phys. 95, 41-51 (1984).

PhD Thesis

Quasicrystal Structures from the Crystallographic Viewpoint
by F. Gähler
Diss. ETH No. 8414, ETH Zürich, 1988.
compressed PostScript (333k)