Research Group Michael Baake: Preprints & Recent Articles

Mathematical Diffraction Theory

Dynamical Systems

Algebra, Combinatorics and Number Theory

Geometry of Aperiodic Crystals

Mathematical Biology

Further Topics

The papers can be downloaded as pdf or gzipped postscript files.


Mathematical Diffraction Theory

U. Grimm, M. Baake Squiral Diffraction
In: Aperiodic Crystals, ed. S. Schmid et al., Springer, Dordrecht, in press

Venta Terauds, M. Baake Some comments on the inverse problem of pure point diffraction
In: Aperiodic Crystals, ed. S. Schmid et al., Springer, Dordrecht, in press

M. Baake, U. Grimm Mathematical diffraction of aperiodic structures
Chem. Soc. Rev. 41 (2012), 6821-6843

M. Baake, U. Grimm A Comment on the relation between diffraction and entropy
Entropy 14 (2012), 856-864

M. Baake, U. Grimm Kinematic diffraction from a mathematical viewpoint
Z. Kristallogr. 226 (2011), 711-725

M. Baake, U. Grimm Mathematical diffraction theory of deterministic and stochastic structures: An informal summary
Mathematics of Quasi-Periodic Order, ed. S. Akiyama, RIMS Proceedings 1725 (2011), 55-79

M. Baake, H. Kösters Random point sets and their diffraction
Phil. Mag. 91 (2011), 2671-2679

M. Baake, U. Grimm Diffraction of limit periodic point sets
Phil. Mag. 91 (2011), 2661-2670

M. Baake , U. Grimm Surprises in aperiodic diffraction
J. Phys.: Conf. Ser. 226 (2010), 012023

M. Baake, U. Grimm Can Kinematic Diffraction Distinguish Order from Disorder?
Phys. Rev. 79 (2009), 020203 (4 pages) and 80 (2009), 029903 (E)

U. Grimm, M. Baake Homometric Point Sets and Inverse Problems
Z. Krist. 223 (2008), 777-781

M. Baake, U. Grimm The singular continuous diffraction measure of the Thue-Morse chain
J. Phys. A: Math. Theor. 41 (2008), 422001 (6 pages)

M. Baake, M. Birkner, R. V. Moody Diffraction of stochastic point sets: Explicitly computable examples
Commun. Math. Phys. 293 (2010) 611-660

M. Baake, D. Lenz, C. Richard Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
Lett. Math. Phys. 82 (2007), 61-77

T. R. Welberry, B. Sing Deformed Penrose tilings
Phil. Mag. 87 (2007), 2877-2886

B. Sing, T. R. Welberry Deformed model sets and distorted Penrose tilings
Z. Krist. 221 (2006), 621-634

M. Baake, U. Grimm Homometric model sets and window covariograms
Z. Krist. 222 (2007), 54-58

M. Baake, D. Frettlöh, U. Grimm A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
J. Geom. Phys. 57 (2007), 1331-1343

M. Baake, D. Frettlöh, U. Grimm Pinwheel patterns and powder diffraction
Phil. Mag. 87 (2007), 2831-283

D. Frettlöh, B. Sing Computing Modular Coincidences for Substitution Tilings and Point Sets
Discr. Comput. Geom. 37 (2007), 381-407

D. Lenz, C. Richard Pure point diffraction and cut and project schemes for measures: the smooth case
Math. Z. 256 (2007), 347-378

M. Baake (2004) Mathematical Diffraction in Euclidean Spaces
Lecture Notes EPFL Lausanne (pdf, size: 2.6 MB)

M. Baake, R.V. Moody (2004) Weighted Dirac combs with pure point diffraction
J. Reine Angew. Math. (Crelle) 573 61-94. math.MG/0203030 (size: 154 kB)

Baake M, Sing B 2004 Diffraction spectrum of lattice gas models above Tc
Lett. Math. Phys. 68, 165-173; math-ph/0405064

Baake M and Sing B 2004 Kolakoski-(3,1) is a (deformed) model set
Canad. Math. Bull. 47 168-190. math.MG/0206098 (size: 575 kB)

Baake M, Moody R V, Richard C and Sing B 2003 Which distribution of matter diffracts?
Quasicrystals: Structure and Physical Properties ed: H.-R. Trebin, Wiley-VCH, Berlin, pp. 188-207,
math-ph/0301019 (size: 100 kB)

Baake M 2002 Diffraction of weighted lattice subsets
Canad. Math. Bull. 45 483-498 math.MG/0106111 (size: 97 kB)

Baake M 2001 A glimpse at mathematical diffraction theory
Quantum theory and symmetries (Kraków, 2001), 267-272 math-ph/0203006 (size: 40 kB)

Höffe M and Baake M 2000 Surprises in Diffuse Scattering
Z. Krist. 215 (2000) 441-444 (one minor correction), math-ph/0004022 (size: 1.7 MB)

Baake M and Höffe M 1999 Diffraction of random tilings: some rigorous results
J. Stat. Phys. 99 219-261; math-ph/9904005 (size: 370 kB)

Baake M, Moody R V and Pleasants P A B 1999 Diffraction from visible lattice points and k-th power free integers
Discr. Math. 221 3-42, math.MG/9906132 (size: 130 kB)

Höffe M 1999 Diffraction of the Dart-Rhombus Random Tiling
Mat. Science Eng. A 294-296 373-376; math-ph/9911014 (size: 542 kB)

Baake M and Moody R V 1998 Diffractive point sets with entropy
J. Phys. A: Math. Gen. 31 9023-39, math-ph/9809002 (size: 105 kB)

Baake M, Moody R V and Schlottmann M 1998 Limit-(quasi-)periodic point sets as quasicrystals with p-adic internal spaces
J. Phys. A: Math. Gen. 31 5755-65, math-ph/9901008 (size: 89 kB)


Dynamical Systems

M. Baake, F. Gähler, U. Grimm Examples of substitution systems and their factors
J. Int. Seq. 16 (2013), article 13.2.14 (18 pages)

M. Baake, U. Grimm Squirals and beyond: Substitution tilings with singular continuous spectrum
Ergodic Th. & Dynam. Syst. 33(2013), in press

M. Baake, A. van Enter Close-packed dimers on the line: diffraction versus dynamical spectrum
J. Stat. Phys. 143 (2011), 88-101

P. A. B. Pleasants, C. Huck Entropy and diffraction of the k-free points in n-dimensional lattices
submitted in 2011

M. Baake, E. Lau, V. Paskunas A note on the dynamical zeta function of general toral endomorphisms
Monatsh. Math. 161 (2009), 33-42

M. Baake, T. Ward Planar dynamical systems with pure Lebesgue diffraction spectrum
J. Stat. Phys. 140 (2010), 90-102

M. Baake, J. A. G. Roberts, A. Weiss Periodic orbits of linear endomorphisms on the 2-torus and its lattices
Nonlinearity 21 (2008), 2427-2446

B. Sing, V. F. Sirvent Geometry of the common dynamics of flipped Pisot substitutions
Monatsh. Math. 155 (2008), 431-448

K. Matzutt Random Cluster Tessellations
Z. Krist. 223 (2008), 171-177

M. Baake, D. Lenz, R. V. Moody Characterizations of model sets by dynamical systems
Ergodic Th. & Dynam. Syst. 27 (2007), 341-382

Baake M and Lenz D 2004 Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
Ergodic Th. & Dynam. Syst. 24, 1867-1893; math.DS/0302061 (size: 133 kB)

Roberts J A G and Baake M 2003 Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form
Physica A 317 95-112; math.DS/0206096 (size: 102 kB)

Baake M and Roberts J A G 2001 Symmetries and Reversing Symmetries of Toral Automorphisms
Nonlinearity 14 R1-R24, math.DS/0006092 (size: 100 kB)

Baake M 1997 Reversing symmetry groups of cat maps
in: Group 21 vol. II eds Doebner H-D, Scherer W and Schulte C (Singapore: World Scientific) 860-4, math.DS/9911061 (size: 49 kB)

Baake M and Roberts J A G 1997 Reversing symmetry group of GL(2,Z) and PGL(2,Z) matrices with connections to cat maps and trace maps
J. Phys. A: Math. Gen. 30 1549-73 (size: 136 kB)

Baake M and Roberts J A G 1993 Symmetries and reversing symmetries of trace maps
to appear in Proc. of the 3rd Intern. Wigner Symp. Oxford (1993) special issue of Int. J. Mod. Phys. B., math.DS/9901124 (size: 55 kB)
(this issue might never really appear in print ...)


Algebra, Combinatorics and Number Theory

M. J. Loquias, P. Zeiner The coincidence problem for shifted lattices and multilattices
submitted in 2013

P. Zeiner Well-rounded sublattices and coincidence site lattices
In: Aperiodic Crystals, ed. S. Schmid et al., Springer, Dordrecht, in press

M. Baake, R. Scharlau, P. Zeiner Similar sublattices of planar lattices
Canad. J. Math. 63 (2011), 1220-1237

M. J. Loquias, P. Zeiner Colourings of lattices and coincidence site lattices
Phil. Mag. 91 (2011), Issue 19-21, 2680-2689

M. Heuer, P. Zeiner CSLs of the root lattice A4
J. Phys.: Conf. Ser. 226 (2010), doi:10.1088/1742-6596/226/1/012024

P. Zeiner Multiplicativity in the theory of coincidence site lattices
J. Phys.: Conf. Ser. 226 (2010), doi:10.1088/1742-6596/226/1/012025

M. J. Loquias, P. Zeiner Coincidence isometries of a shifted square lattice
J. Phys.: Conf. Ser. 226 (2010), 012026 (10 pages)

E.P. Bugarin, M.L.A.N. de las Peñas, D. Frettlöh Perfect colourings of cyclotomic integers
Geometriae Dedicata 162, Issue 1 (2013), 271-282

J. Nilsson On the Entropy of Random Fibonacci Words
Monatsh. Math. 168, Issue 3-4 (2012), 563-577

M. Baake, N. Neumärker A note on the relation between fixed point and orbit count sequences
J. Integer Seq. 12 (2009), article 09.4.4 (12 pages)

C. Huck Uniqueness in Discrete Tomography of Delone Sets with Long-Range Order
Discrete Comput. Geom. 42 (2009), 740-758

C. Huck A Note on Coincidence Isometries of Modules in Euclidean Space
Z. Krist. 224 (2009), 341-344

C. Huck On the Existence of $U$-Polygons of Class $c\geq 4$ in Planar Point Sets
Discrete Math. 309 (2009), 4977-4981

U. Schwerdtfeger Exact solution of two classes of prudent polygons
European J. Combin. 31 (2010), 765-779

U. Schwerdtfeger Volume Laws for Boxed Plane Partitions and Area Laws for Ferrers Diagrams
Discrete Math. Theor. Comput. Sci. Proc. AI (2008), 531-540

D. Frettlöh Counting perfect colourings of plane regular tilings
Z. Krist. 223 (2008), 773-776

C. Richard, I. Jensen, A. J. Guttmann Area distribution and scaling function for punctured polygons
Electronic J. Comb. 15, no. R53 (2008)

C. Richard, U. Schwerdtfeger, B. Thatte Area limit laws for symmetry classes of staircase polygons
Combin. Probab. Comput. 19 (2010), 441-461

M. Heuer Similar sublattices and coincidence rotations of the root lattice A4 and its dual
Z. Krist. 223 (2008), 817-821

S. Glied, M. Baake Similarity versus Coincidence Rotations of Lattices
Z. Krist. 223, (2008), 770-772

M. Baake, P. Zeiner Coincidences in 4 dimensions
Phil. Mag. 88 (2008), 2025-2032

M. Baake, U. Grimm, M. Heuer, P. Zeiner Coincidence rotations of the root lattice A4
Europ. J. Combin. 29 (2008), 1808-1819

C. Huck Discrete Tomography of Icosahedral Model Sets
Acta Cryst. A65 (2009), 240-248

D. Frettlöh Self-Dual Tilings with Respect to Star-Duality
Theoret. Comp. Sci. 391 (2008), 39-50

P. Müller, C. Richard Ergodic properties of randomly coloured point sets
Canad. J. Math. 65 (2013), 349-402

M. Baake, M. Heuer, R. V. Moody Similar sublattices of the root lattice A4
J. Algebra 320 (2008), 1391-1408

M. Baake, P. A. B. Pleasants, U. Rehmann Coincidence site modules in 3-space
Discr. Comput. Geom. 38 (2007), 111-138

M. Baake, J. A. G. Roberts The structure of reversing symmetry groups
Bull. Austr. Math. Soc. 73 (2006), 445-459

M. Baake Solution of the coincidence problem in dimensions d \le 4

M. Baake, U. Grimm Multiple planar coincidences with N-fold symmetry
Z. Krist. 221 (2006), 571-581

Baake M and Grimm U 2003 A note on shelling
Discrete Comput. Geom. 30, 573-589; math.MG/0203025 (size: 207 kB)

Allouche J-P, Baake M, Cassaigne J and Damanik D 2003 Palindrome complexity
dedicated to Jean Berstel for his 60th birthday, Theoret. Comput. Sci., 292 9-31 math.CO/0106121 (size: 29 kB)

Baake M 1999 A note on palindromicity
Lett. Math. Phys. 49 217-227, math-ph/9907011 (size: 50 kB)

Baake M and Moody R V 1999 Similarity submodules and root systems in four dimensions
Can. J. Math. 51 1258-1276, math.MG/9904028 (size:120 kB)

Baake M and Moody R V 1998 Similarity submodules and semigroups
in: Quasicrystals and Discrete Geometry ed Patera J
Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp 1-13 (size: 86 kB)

Baake M and Moody R V 1998 Invariant submodules and semigroups of self-similarities for Fibonacci modules
in: Aperiodic '97 ed Verger-Gaugry J-L, Singapore: World Scientific (1998) pp 21-27, math-ph/9809008 (size: 56 kB)

Baake M, Elser V and Grimm U 1997 The entropy of square-free words
Mathl. Comput. Modelling 26 13-26, math-ph/9809010 (size: 71 kB)


Geometry of Aperiodic Order

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

M. Baake, M. Moll Random noble means substitutions
In: Aperiodic Crystals, ed. S. Schmid et al., Springer, Dordrecht, in press

M. Baake, U. Grimm On the notions of symmetry and aperiodicity for Delone sets
Symmetry 4 (2012), 566-580

M. Baake, F. Gähler, U. Grimm Spectral and topological properties of a family of generalised Thue-Morse sequences
J. Math. Phys. 53 (2012), 032701 (24 pages)

D. Frettlöh A fractal fundamental domain with 12-fold symmetry
Symmetry 22, Issue 1-2 (2011), 237-246

F. Gähler MLD Relations of Pisot Substitution Tilings
J. Phys.: Conf. Ser. 226 (2010), 012020

D. Frettlöh About substitution tilings with statistical circular symmetry
Phil. Mag. 88 (2008), 2033-2039

N. Dolbilin, D. Frettlöh Properties of Generalized Böröczki Tilings
European J. Combin. 31 (2010) 1181-1195

D. Frettlöh, R. Lück Ten colours in quasiperiodic and regular hyperbolic tilings
Z. Krist. 223 (2008), 782-784

D. Frettlöh, A.Glazyrin The lonely vertex problem
Beiträge Algebra Geom. 50 (2009), 71-79

C. Huck A note on affinely regular polygons
European J. Combin. 30 (2009), 387-395

D. Frettlöh Substitution Tilings with Statistical Circular Symmetry
European J. Combin. 29 (2008), 1881-1893

C. Huck Uniqueness in Discrete Tomography of Planar Model Sets
Christian Huck, "Discrete Tomography of Delone Sets with Long-Range Order", Ph.D. Thesis, Universität Bielefeld, Logos Verlag, Berlin (2007)

M. Baake, C. Huck Discrete Tomography of Penrose Model Sets
Phil. Mag. 87 (2007), 2839-2846

B. Sing Iterated Function Systems in Mixed Euclidean and p-adic Spaces
Complexus Mundi - Emergent Patterns in Nature (2006), 267-276

M. Baake, P. Gritzmann, C. Huck, B. Langfeld, K. Lord Discrete Tomography of Planar Model Sets
Acta Cryst. A 62 (2006), 419-433

D. Frettlöh Duality of Model Sets Generated by Substitutions
Rev. Roum. Math. Pures Appl. 50 (2005), 619-639

P. Zeiner Multiple CSLs for the body centered cubic lattice
J. Phys: Conf. Ser. 30 (2006), 163-167

P. Zeiner Coincidences of hypercubic lattices in 4 dimensions
Z. Krist. 221 (2006), 105-114

Baake M and Grimm U 2004 Bravais colourings of planar modules with N-fold symmetry
Z. Krist. 219, 72-80. math.CO/0301021 (size: 71 kB)

Baake M and Grimm U 2003 Combinatorial problems of (quasi-)crystallography
In: Quasicrystals, ed. Trebin H.R., Wiley VCH, Weinheim 2003, pp. 160-171

Baake M, Grimm U and Moody R V 2002 What is aperiodic order?
Preprint, math.HO/0203252 (size: 617 kB)

Baake M and Moody R V 2000 Self-Similar Measures for Quasicrystals
in: Directions in Mathematical Quasicrystals eds Baake M and Moody R V
CRM Monograph Series, AMS, Providence, RI (2000), math.MG/0008063 (size: 290 kB)

Schlottmann M 2000 Generalized Model Sets and Dynamical Systems
in: Directions in Mathematical Quasicrystals eds Baake M and Moody R V
CRM Monograph Series, AMS, Providence, RI (2000) in press (size: 100 kB)

Richard C 1999 An alternative view on quasicrystalline random tilings
J. Phys. A: Math. Gen. 32 8823-8829, cond-mat/9907262 (size: 60 kB)

Baake M 1998 A Guide to Mathematical Quasicrystals
in: Quasicrystals eds Suck J-B, Schreiber M and Häußler P (Berlin: Springer) in press, math-ph/9901014 (size: 418 kB)

Baake M and Gähler F 1998 Symmetry structure of the Elser-Sloane quasicrystal
in: Aperiodic '97 ed Verger-Gaugry J-L, Singapore: World Scientific (1998) pp 63-67, cond-mat/9809100 (size: 47 kB)

Baake M and Moody R V 1998 Multi-component model sets and invariant densities
in: Aperiodic '97 ed Verger-Gaugry J-L, Singapore: World Scientific (1998) pp 9-20, math-ph/9809005 (size: 617 kB)

Baake M and Moody R V 1998 Self-similarities and invariant densities for model sets
in: Algebraic Methods and Theoretical Physics ed Aubin Y St (New York: Springer) in press, math-ph/9809006 (size: 135 kB)

Richard C, Höffe M, Hermisson J and Baake M 1998 Random tilings: concepts and examples
J. Phys. A: Math. Gen. 31 6385-408, cond-mat/9712267 (size: 2.1 MB)

Schlottmann M 1998 Cut-and-Project Sets in Locally Compact Abelian Groups
in: Quasicrystals and Discrete Geometry ed Patera J
Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp 247-264 (size: 105 kB)

Baake M 1997 Combinatorial aspects of colour symmetries
J. Phys. A: Math. Gen. 30 2687-98, mp_arc/02-323 (size: 85 kB)

Baake M, Hermisson J and Pleasants P A B 1997 The torus parametrization of quasiperiodic LI-classes
J. Phys. A: Math. Gen. 30 3029-56, mp_arc/02-168 (size: 211 kB)

Hermisson J, Richard C and Baake M 1997 A guide to the symmetry structure of quasiperiodic tiling classes
J. Phys. I France 7 1003-18, mp_arc/02-180 (size: 117 kB)


Mathematical Biology

M. Baake, U. Schlägel The Peano-Baker series
Proceedings of the Steklov Institute of Mathematics 275 (2011), 155-159

U. von Wangenheim, E. Baake, M. Baake Single-crossover recombination in discrete time
J. Math. Biol. 60 (2010), 727-760

Redner O 2004 Discrete Approximation of non-compact operators describing continuum-of-alleles models
Proc. Edinb. Math. Soc. 47 449-472, math.SP/0301024 (size: 238 kB)

Redner O and Baake M 2004 Unequal crossover dynamics in discrete and continuous time
J. Math. Biol. 49 201-226, math.DS/0402351 (size: 134 kB)

Hermisson J, Redner O, Wagner H and Baake E 2002 Mutation-selection balance: ancestry, load, and maximum principle
Theor. Pop. Biol. 62 9-46, cond-mat/0202432 (size: 271 kB)

Baake M and Baake E 2003 An exactly solved model for mutation, recombination and selection
Canad. J. Math. 55 3-41 (size: 161 kB)

Hermisson J, Wagner H and Baake M 2000 Four-state quantum chain as a model of sequence evolution
J. Stat. Phys. 102 315-43, cond-mat/0008123 (size: 142 kB)

Baake E, Baake M and Wagner H 1998 Quantum mechanics versus classical probability in biological evolution
Phys. Rev. E 57 1191-2 (size: 46 kB)

Wagner H, Baake E and Gerisch T 1998 Ising quantum chain and sequence evolution
J. Stat. Phys. 92 1017-52 (size: 356 kB)

Baake E, Baake M and Wagner H 1997 The Ising quantum chain is equivalent to a model of biological evolution
Phys. Rev. Lett. 78 559-62 (size: 64 kB) and (Erratum) Phys. Rev. Lett. 79 1782 (size: 22 kB)


Further Topics

M. Baake, N. Neumärker, J. A. G. Roberts Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
Discr. Cont. Dynam. Syst. A 33 (2013), 527-553

C. Huck, M. Spieß Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets
J. Reine Angew. Math. (Crelle) (submitted in 2011), in press

Hermisson J 2000 Aperiodic and correlated disorder in XY-chains: exact results
J. Phys. A: Math. Gen. 33 57-69, cond-mat/9808238 (size: 105 kB)

Redner O and Baake M 2000 Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models
J. Phys. A: Math. Gen. 33 3097-109, cond-mat/9910136 (size: 108 kB)

Hermisson J 1999 Renormalization of two-dimensional Ising systems with irrelevant, marginal and relevant aperiodic (dis)order
Mat. Science Eng. A 294-296 642-645 (size: 67 kB)

Hermisson J and Grimm U 1998 Surface properties of Aperiodic Ising quantum chains
Phys. Rev. B 57 673-6, cond-mat/9711096 (size: 60 kB)

Hermisson J, Grimm U and Baake M 1997 Aperiodic Ising quantum chains
J. Phys. A: Math. Gen. 30 7315-35, cond-mat/9706106 (size: 138 kB)

Chayes L, Machta J and Redner O 1998 Graphical Representations for Ising Systems in External Fields (size: 61 kB)
J. Stat. Phys. 93 17-32, cond-mat/9806312 (size: 62 kB)

Redner O, Machta J and Chayes L 1998 Graphical representations and cluster algorithms for critical points with fields and figures 1 and 2
Phys. Rev. E 58 2749-2752, cond-mat/9802063 (sizes: 38 kB, 4 kB, 4 kB)