Quasicrystals and geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 286 S. graph. Darst. |
| ISBN: | 0521372593 |
Internformat
MARC
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| 100 | 1 | |a Senechal, Marjorie |d 1939- |e Verfasser |0 (DE-588)172369932 |4 aut | |
| 245 | 1 | 0 | |a Quasicrystals and geometry |c Marjorie Senechal |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XV, 286 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804124709261934592 |
|---|---|
| adam_text | Contents
Preface page xi
1 Past as prologue 1
1.1 Demise of a paradigm 1
1.2 Ancient views on the structure of crystals 7
1.3 From building blocks to lattices 13
1.4 The ascendance of symmetry 16
1.5 Hilbert s 18th problem 21
1.6 Toward a new definition of crystal 27
1.7 Notes 31
2 Lattices, Vorono i cells,, and quasicrystals 34
2.1 Introduction 34
2.2 Lattices and their duals 37
2.3 Voronoi cells 41
2.4 Symmetry 45
2.4.1 Isometries 46
2.4.2 Symmetry groups 48
2.4.3 The crystallographic restriction 50
2.5 Orbits of Z modules 52
2.6 High dimensional lattices, low dimensionsal crystallography 54
2.6.1 The projection method 54
2.6.2 Uniform distribution 58
2.6.3 Five fold symmetry 59
2.7 Lattices with icosahedral point groups 63
2.7.1 The 1(, quasicrystal 64
2.7.2 The root lattices 65
2.7.3 D6 and £g quasicrystals 68
2.7.4 Is the projection formalism necessary? 71
2.8 Notes 72
viii Contents
3 Introduction to diffraction geometry 74
3.1 Introduction 74
3.2 Diffraction geometry 77
3.2.1 One point diffraction 78
3.2.2 Two point diffraction 78
3.2.3 TV point diffraction 83
3.3 Fourier transforms and the Wiener diagram 86
3.4 Dirac deltas and Dirac combs 91
3.5 The diffraction condition 95
3.6 Searching for deltas 97
3.6.1 Lattice vacancy point sets 99
3.6.2 Poisson combs 99
3.7 Notes 101
4 Order on the line 106
4.1 One dimensional crystals 106
4.2 Fibonacci numbers, strings, and sequences 109
4.3 Projected crystals 114
4.3.1 Projected Fibonacci sequences are crystals 120
4.3.2 Generalizations 123
4.4 Substitution sequences 124
4.5 Circle map sequences 128
4.6 Staircases 131
4.7 Notes 132
5 Tiles and tilings 135
5.1 Tilings and crystals 135
5.2 Some basic concepts of tiling theory 136
5.3 Atlases 140
5.4 Which shapes are tiles? 144
5.5 Orderliness 145
5.6 Some construction techniques 152
5.6.1 Voronoi decompositions 153
5.6.2 Dualization 153
5.6.3 Substitution 156
5.6.4 Multigrids 162
5.6.5 Projection 167
5.7 Notes 169
6 Penrose tilings of the plane 170
6.1 Penrose tiles and matching rules 171
6.2 Up down generation 183
6.3 Pentagrids and their duals 190
6.4 Penrose tilings as projections 195
Contents ix
6.4.1 The canonical projection 195
6.4.2 The vertex atlas 196
6.4.3 The role of the shift vector 197
6.5 Other generalizations of the Penrose tilings 199
6.6 The space V 203
6.7 Notes 204
7 The aperiodic zoo 207
7.1 Matching rules and their classification 207
7.2 The SCD (Schmitt Conway Danzer) tile 209
7.3 Octagonal tilings 213
7.4 Aperiodic triangles 218
7.4.1 Danzer s triangular prototiles: seven fold symmetry 218
7.4.2 The pinwheel tilings: rotations of infinite order! 220
7.5 Icosahedral tilings 220
7.5.1 The three dimensional Penrose tilings 220
7.5.2 The Socolar Steinhardt tilings and Danzer s aperiodic
tetrahedra 222
7.6 Toward a theory of matching rules 223
7.6.1 Matching rules for projected tilings 224
7.6.2 Uncountability is intrinsic 229
7.6.3 Errors are intrinsic „ 231
7.7 Notes 234
8 An atlas of tiling transforms 238
8.1 The atlas 238
8.2 Comments 243
8.2.1 Lattice vacancy tilings 243
8.2.2 The Penrose and Ammann tilings 244
8.2.3 Generalized Penrose tilings 244
8.2.4 A binary tiling 246
8.2.5 A pinwheel tiling 246
8.3 Ordering disorder 247
8.4 Exploring with the computer 247
8.4.1 The tilings 247
8.4.2 fourier .c 251
8.4.3 Line arrangements and zonotopal tilings 254
8.4.4 QuasiTiler 258
Appendix I. A mathematical toolbag 259
Appendix II. De Bruijn s generalized functions 267
References 272
Index 283
|
| any_adam_object | 1 |
| author | Senechal, Marjorie 1939- |
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| bvnumber | BV010292752 |
| classification_rvk | SK 950 UQ 8750 |
| classification_tum | CHE 130f GEO 420f PHY 605f CHE 312f |
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| dewey-full | 548.81 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
| dewey-raw | 548.81 |
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| dewey-sort | 3548.81 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Geowissenschaften Physik Chemie Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T17:49:58Z |
| institution | BVB |
| isbn | 0521372593 |
| language | English |
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| physical | XV, 286 S. graph. Darst. |
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| spelling | Senechal, Marjorie 1939- Verfasser (DE-588)172369932 aut Quasicrystals and geometry Marjorie Senechal 1. publ. Cambridge u.a. Cambridge Univ. Press 1995 XV, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quasikristall (DE-588)4202613-1 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Kristallmathematik (DE-588)4125615-3 gnd rswk-swf Quasikristall (DE-588)4202613-1 s Geometrie (DE-588)4020236-7 s DE-604 Kristallmathematik (DE-588)4125615-3 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006847617&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Senechal, Marjorie 1939- Quasicrystals and geometry Quasikristall (DE-588)4202613-1 gnd Geometrie (DE-588)4020236-7 gnd Kristallmathematik (DE-588)4125615-3 gnd |
| subject_GND | (DE-588)4202613-1 (DE-588)4020236-7 (DE-588)4125615-3 |
| title | Quasicrystals and geometry |
| title_auth | Quasicrystals and geometry |
| title_exact_search | Quasicrystals and geometry |
| title_full | Quasicrystals and geometry Marjorie Senechal |
| title_fullStr | Quasicrystals and geometry Marjorie Senechal |
| title_full_unstemmed | Quasicrystals and geometry Marjorie Senechal |
| title_short | Quasicrystals and geometry |
| title_sort | quasicrystals and geometry |
| topic | Quasikristall (DE-588)4202613-1 gnd Geometrie (DE-588)4020236-7 gnd Kristallmathematik (DE-588)4125615-3 gnd |
| topic_facet | Quasikristall Geometrie Kristallmathematik |
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