Verfügbarkeit: From quasicrystals to more complex systems

From quasicrystals to more complex systems: Les Houches School, February 23 - March 6, 1998

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Bibliographische Detailangaben
Weitere Verfasser:	Axel, Françoise (HerausgeberIn)
Format:	Buch
Sprache:	German
Veröffentlicht:	Berlin [u.a.] Springer [u.a.] 2000
Schriftenreihe:	Centre de Physique <LesHouches>: Centre de Physique des Houches 13
Schlagworte:	Quasicrystals > Congresses Quasikristall Aperiodischer Kristall Konferenzschrift > 1998 > Les Houches
Online-Zugang:	Inhaltsverzeichnis Inhaltsverzeichnis
Beschreibung:	Literaturangaben
Beschreibung:	XX, 374 S. Ill., graph. Darst.
ISBN:	3540674640 2868834825

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Datensatz im Suchindex

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adam_text	CONTENTS COURSE 1 DYNAMICS AND TRANSPORT PROPERTIES OF APERIODIC CRYSTALS BY T. JANSSEN 1. STRUCTURE AND SYMMETRY .................................................................. 1 2. PHONONS........................................................................................ 5 3. DOMAIN WALL MOTION....................................................................... 11 4. ELECTRONS ...................................................................................... 13 5. TENSORIAL PROPERTIES........................................................................ 16 6. SURFACE EFFECTS ............................................................................... 17 7. TRANSPORT PROPERTIES ....................................................................... 19 8. CONCLUDING REMARKS ....................................................................... 20 COURSE 2 DIFFRACTION EXPERIMENTS ON QUASICRYSTALS AND RELATED PHASES BY F. D´ ENOYER 1. INTRODUCTION .................................................................................. 23 2. DECAGONAL QUASICRYSTALS.................................................................. 24 2.1 GENERALITIES ........................................................................... 24 2.2 X-RAY STRUCTURE DETERMINATION OF DECAGONAL QUASICRYSTALS ............. 24 3. DECAGONAL SYMMETRY AND TWINNING................................................... 30 3.1 TENFOLD TWINNING OF AL13FE4 AND AL13 FE4-TYPE STRUCTURE .............. 30 3.2 TWINNING IN THE STRUCTURE OF DECAGONAL PHASES AND FINE STRUCTURE OF DIFFRACTION PEAKS ................................................................. 32 3.3 TWINNING AND MAIN CHARACTERISTIC FEATURES OF DIFFRACTION PATTERNS .. 32 3.4 DESCRIPTION OF MICROSTRUCTURES IN TERMS OF PHASON-STRAIN QUASICRYSTALS ...................................... 35 XIV 4. QUASICRYSTAL TRANSFORMATIONS ........................................................... 41 5. ICOSAHEDRAL SHORT RANGE ORDER IN GLASSES............................................. 42 6. CONCLUSION.................................................................................... 45 COURSE 3 ELECTRONIC PROPERTIES OF QUASICRYSTALS. A COMPARISON WITH APPROXIMANT PHASES AND DISORDERED SYSTEMS GIVEN BY C. BERGER WRITTEN BY C. BERGER AND T. GRENET 1. INTRODUCTION .................................................................................. 49 1.1 QUASIPERIODIC ORDER ................................................................ 50 1.2 QUASICRYSTALS, CRYSTALS AND AMORPHOUS PHASES............................. 52 1.3 SAMPLES OF HIGH STRUCTURAL QUALITY IN TERNARY ALLOYS ..................... 53 1.4 UNEXPECTED PHYSICAL PROPERTIES ................................................ 54 2. CONDUCTIVITY AND DENSITY OF STATES IN QUASICRYSTALS.............................. 54 2.1 LOW ELECTRICAL CONDUCTIVITY VALUES IN I -PHASES ............................ 54 2.2 LOW ELECTRONIC DENSITY OF STATES IN QUASICRYSTALS ......................... 57 3. COMPARISON WITH OTHER METALLIC ALLOYS .............................................. 59 3.1 SCALE OF CONDUCTIVITY IN METALLIC ALLOYS...................................... 59 3.2 EFFECT OF DIFFRACTION ................................................................ 60 3.3 QUANTUM INTERFERENCE EFFECTS IN DISORDERED SYSTEMS .................... 61 3.4 DISORDERED INSULATOR AND ANDERSON LOCALIZATION .......................... 65 4. PERIODICITY AS AN APPROACH TO QUASIPERIODICITY.................................... 65 4.1 APPROXIMANT PHASES ............................................................... 66 4.2 EXPERIMENTAL ELECTRICAL CONDUCTIVITY IN APPROXIMANT PHASES ......... 66 4.3 CALCULATED ELECTRONIC PROPERTIES IN APPROXIMANTS ........................ 68 4.4 LOW DIMENSIONAL PERFECT QUASIPERIODIC MODELS........................... 69 5. QUASICRYSTALS AS ORDERED STRUCTURES OF HIGH SYMMETRY ......................... 72 5.1 PSEUDO BRILLOUIN ZONE ............................................................. 72 5.2 ROLE OF LOCAL ATOMIC CLUSTERS .................................................... 74 6. TOWARDS A METAL-INSULATOR TRANSITION IN QUASICRYSTALS: COMPARISON WITH DISORDERED SYSTEMS ................................................ 75 CONTENTS XV 6.1 SOME EXPERIMENTAL EVIDENCE FOR THE APPROACH TO A METAL-INSULATOR TRANSITION IN QUASICRYSTALS............................. 76 6.2 CROSSING OF THE METAL-INSULATOR TRANSITION IN I -ALPDRE ................. 77 7. CONCLUSION.................................................................................... 79 COURSE 4 EXACT ELECTRON STATES IN 1 D (QUASI-) PERIODIC ARRAYS OF DELTA-POTENTIALS GIVEN BY P. KRAMER WRITTEN BY P. KRAMER AND T. KRAMER 1. INTRODUCTION AND SCOPE.................................................................... 85 2. FINITE PERIODIC STRINGS AT NEGATIVE ENERGY ........................................... 89 2.1 PREVIEW: AN ENERGY GAUGE FOR CRYSTALS ...................................... 89 2.2 BLOCH AND BOUND STATES IN A SINGLE BAND..................................... 90 2.3 THE STRING S N ......................................................................... 95 2.4 RATIONAL BLOCH LABELS .............................................................. 96 2.5 BOUND STATES AND CLUSTERS OF THE STRING S N ................................... 96 2.6 PARTICIPATION NUMBER............................................................... 98 2.7 SUPERCELL INTERPRETATION ........................................................... 99 2.8 LARGE N LIMIT......................................................................... . 99 3. FINITE QUASIPERIODIC STRINGS AT NEGATIVE ENERGY.................................... 100 3.1 PREVIEW: ENERGY GAUGE IN FIBONACCI STRINGS ............................... 100 3.2 SUBSTITUTIONAL SYSTEMS AND THEIR INVARIANTS ................................. 101 3.3 RECURSIVE CALCULATION OF THE TRANSFER MATRIX................................ 102 4. PERIODIC STRINGS AT POSITIVE ENERGY .................................................... 106 4.1 THE S -MATRIX.......................................................................... 107 4.2 THE S -MATRIX FOR THE PERIODIC STRING S N ...................................... 108 5. QUASIPERIODIC STRINGS AT POSITIVE ENERGY ............................................ 110 5.1 THE FIBONACCI-ATLAS ................................................................ 110 6 CONCLUSION.................................................................................... 112 XVI COURSE 5 RANDOM TILING MODELS FOR QUASICRYSTALS BY E. COCKAYNE 1. INTRODUCTION .................................................................................. 115 1.1 BASIC DEFINITIONS..................................................................... 116 1.2 GENERATION OF QUASICRYSTALLINE TILINGS ........................................ 117 1.3 RANDOMIZATION OF TILINGS ......................................................... 120 1.4 A ZOO OF TILING MODELS............................................................. 121 2. MATHEMATICS OF RANDOM TILINGS......................................................... 123 2.1 ENTROPY DENSITY AND PHASON ELASTIC CONSTANTS.............................. 123 2.2 LONG-WAVELENGTH BEHAVIOR AND STABILITY..................................... 126 2.3 DIFFRACTION............................................................................. 127 3. RANDOM TILING RESULTS...................................................................... 128 3.1 MONTE CARLO SIMULATION........................................................... 128 3.2 COMBINATORICS........................................................................ 129 3.3 TRANSFER MATRIX METHOD ........................................................... 130 3.4 BETHE ANSATZ METHOD .............................................................. 132 4. ATOMIC MODELS FOR QUASICRYSTALS ...................................................... 132 4.1 HREM/DIFFRACTION-BASED ......................................................... 133 4.2 MODELS BASED ON REALISTIC INTERATOMIC FORCES .............................. 136 4.3 OTHER MODELS ......................................................................... 138 5. QUASICRYSTAL PHASE TRANSFORMATIONS................................................... 139 5.1 PHASON UNLOCKING ................................................................... 139 5.2 QUASICRYSTAL * (MICRO)CRYSTAL.................................................. 139 6. CONCLUSIONS .................................................................................. 140 COURSE 6 MODEL SETS: A SURVEY BY R.V. MOODY 1. INTRODUCTION .................................................................................. 145 2. MODEL SETS .................................................................................... 147 3. GEOMETRIC SIDE .............................................................................. 149 4. ARITHMETIC SIDE .............................................................................. 150 CONTENTS XVII 4.1 THE ICOSIAN MODEL SETS ............................................................ 150 4.2 P -ADIC MODEL SETS ................................................................... 152 5. ANALYTIC SIDE ................................................................................. 155 6. DYNAMICAL SYSTEMS SIDE .................................................................. 157 7. DIFFRACTION .................................................................................... 160 7.1 COMMENTS ............................................................................. 163 COURSE 7 ACCEPTANCE WINDOWS COMPATIBLE WITH A QUASICRYSTAL FRAGMENT GIVEN BY J. PATERA WRITTEN BY Z. MAS´ AKOV´ A, J. PATERA AND E. PELANTOV´ A 1. INTRODUCTION .................................................................................. 167 2. NOTATION AND AUXILIARY FACTS............................................................. 171 3. LOCAL INVARIANCE AND THE FORWARD GROWTH ........................................... 174 4. THE MAXIMAL ACCEPTANCE WINDOW ..................................................... 178 5. EXAMPLE: ANALYSIS OF TWO-DIMENSIONAL QUASICRYSTAL DATA..................... 180 6. COMMENTS AND REMARKS .................................................................. 189 COURSE 8 COUNTING SYSTEMS WITH IRRATIONAL BASIS FOR QUASICRYSTALS GIVEN BY J.P. GAZEAU WRITTEN BY J.P. GAZEAU AND R. KREJCAR 1. INTRODUCTION .................................................................................. 195 2. THE SET OF * -INTEGERS ....................................................................... 197 3. TAU-INTEGER LABELLING OF THE FIBONACCI CHAIN....................................... 199 4. TAU-INTEGER LABELLING OF DIFFRACTION PATTERN......................................... 202 5. TAU-INTEGER LABELLING OF TWO-DIMENSIONAL STRUCTURES ............................ 205 6. ARITHMETICS AND ALGEBRA OF THE * -INTEGERS .......................................... 211 XVIII COURSE 9 ACOUSTIC-LIKE EXCITATIONS IN STRONGLY DISORDERED MEDIA GIVEN BY E. COURTENS WRITTEN BY E. COURTENS AND R. VACHER 1. INTRODUCTION .................................................................................. 219 2. THE CASE OF MASS-FRACTAL MEDIA ........................................................ 221 2.1 THE STRUCTURE OF MASS FRACTALS ................................................... 222 2.2 THE CONCEPT OF MUTUALLY SELF-SIMILAR SERIES OF MSSS ................... 226 2.3 THE DYNAMICS OF MASS FRACTALS.................................................. 227 3. THE CASE OF GLASSES......................................................................... 234 3.1 WHAT IS ALREADY ESTABLISHED ...................................................... 236 3.2 SPECTROSCOPY OF ACOUSTIC EXCITATIONS IN THE TERAHERTZ REGIME * THREE REMARKS ...................................... 240 3.3 SOME STUDIES NEAR THE END OF ACOUSTIC BRANCHES IN GLASSES ............ 243 4. CONCLUSIONS .................................................................................. 249 COURSE 10 INTERMITTENT DYNAMICS AND AGEING IN GLASSY SYSTEMS BY J.-PH. BOUCHAUD 1. INTRODUCTION .................................................................................. 261 2. A SIMPLE MODEL: TRAPS AND INTERMITTENT DYNAMICS .............................. 263 3. RELATION WITH MODE-COUPLING DESCRIPTIONS ......................................... 265 4. SELF-INDUCED QUENCHED DISORDER AND OPEN QUESTIONS............................ 267 COURSE 11 A SHORT INTRODUCTION TO ERGODIC THEORY AND ITS APPLICATIONS BY F.M. DEKKING 1. DYNAMICAL SYSTEMS ........................................................................ 273 1.1 EXAMPLES .............................................................................. 273 1.2 RECURRENCE ............................................................................ 277 1.3 ERGODIC THEOREM..................................................................... 278 CONTENTS XIX 1.4 UNIQUE ERGODICITY ................................................................... 280 1.5 EXPECTED RECURRENCE TIME ........................................................ 281 2. SPECTRAL PROPERTIES OF DYNAMICAL SYSTEMS .......................................... 282 2.1 THE SPECTRUM OF A DYNAMICAL SYSTEM ......................................... 282 2.2 MIXING.................................................................................. 283 3. ENTROPY OF DYNAMICAL SYSTEMS ......................................................... 284 3.1 ISOMORPHISM.......................................................................... 286 3.2 ENTROPY AND HAUSDORFF DIMENSION............................................. 287 4. EPILOGUE ....................................................................................... 288 COURSE 12 FRACTALITY AND THE KINETICS OF CHAOS BY G.M. ZASLAVSKY 1. INTRODUCTION .................................................................................. 291 2. MAPPING THE DYNAMICS.................................................................... 295 3. TOPOLOGICAL ZOO (SINGULAR ZONES) ...................................................... 297 4. SELF-SIMILAR HIERARCHY OF ISLANDS....................................................... 300 5. QUASI-TRAPS ................................................................................... 301 6. BOUNDARY LAYER AS A QUASI-TRAP ......................................................... 303 7. FRACTAL AND MULTIFRACTAL SPACE-TIME OF KINETICS ................................... 304 8. DIMENSION SPECTRUM OF THE MULTIFRACTAL SPACE-TIME............................. 307 9. FRACTIONAL KINETICS.......................................................................... 309 10. CONCLUSIONS .................................................................................. 312 COURSE 13 LONG-TAILED DISTRIBUTIONS IN PHYSICS GIVEN BY M.F. SHLESINGER WRITTEN BY M.F. SHLESINGER, J. KLAFTER AND G. ZUMOFEN 1. INTRODUCTION .................................................................................. 315 2. FRACTAL TIME................................................................................... 319 3. SLOW RELAXATIONS ............................................................................ 321 4. FRACTAL SPACE PROCESSES ................................................................... 321 5. NONLINEAR DYNAMICS ....................................................................... 324 XX COURSE 14 DISTRIBUTION OF GALAXIES: SCALING VS. FRACTALITY BY R. BALIAN 1. INTRODUCTION .................................................................................. 329 2. ALGEBRA OF POINT DISTRIBUTIONS .......................................................... 330 2.1 DENSITIES AND CORRELATIONS ........................................................ 330 2.2 COUNTS IN CELLS ....................................................................... 332 3. SCALE INVARIANCE ............................................................................. 333 3.1 SCALING OF CORRELATIONS ............................................................ 333 3.2 THE VOID PROBABILITY ............................................................... 333 3.3 SCALING OF COUNTS IN CELLS ......................................................... 334 4. FRACTALITY ...................................................................................... 336 4.1 CORRELATION DIMENSION............................................................. 336 4.2 HAUSDORFF DIMENSION FOR OCCUPIED CELLS ..................................... 337 4.3 RENYI INDEX ........................................................................... 338 4.4 MULTIFRACTAL DIMENSION ............................................................ 340 5. CONCLUSION.................................................................................... 343
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spelling	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998 ed. F. Axel ... Berlin [u.a.] Springer [u.a.] 2000 XX, 374 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Centre de Physique <LesHouches>: Centre de Physique des Houches 13 Literaturangaben Quasicrystals Congresses Quasikristall (DE-588)4202613-1 gnd rswk-swf Aperiodischer Kristall (DE-588)4492275-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1998 Les Houches gnd-content Aperiodischer Kristall (DE-588)4492275-9 s DE-604 Quasikristall (DE-588)4202613-1 s Axel, Françoise edt Centre de Physique (Les Houches) Sonstige (DE-588)2057705-9 oth Centre de Physique <LesHouches>: Centre de Physique des Houches 13 (DE-604)BV011876452 13 http://digitale-objekte.hbz-nrw.de/storage/2006/07/07/file_64/1465770.pdf Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009047334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998 Centre de Physique <LesHouches>: Centre de Physique des Houches Quasicrystals Congresses Quasikristall (DE-588)4202613-1 gnd Aperiodischer Kristall (DE-588)4492275-9 gnd
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title	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998
title_auth	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998
title_exact_search	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998
title_full	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998 ed. F. Axel ...
title_fullStr	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998 ed. F. Axel ...
title_full_unstemmed	From quasicrystals to more complex systems Les Houches School, February 23 - March 6, 1998 ed. F. Axel ...
title_short	From quasicrystals to more complex systems
title_sort	from quasicrystals to more complex systems les houches school february 23 march 6 1998
title_sub	Les Houches School, February 23 - March 6, 1998
topic	Quasicrystals Congresses Quasikristall (DE-588)4202613-1 gnd Aperiodischer Kristall (DE-588)4492275-9 gnd
topic_facet	Quasicrystals Congresses Quasikristall Aperiodischer Kristall Konferenzschrift 1998 Les Houches
url	http://digitale-objekte.hbz-nrw.de/storage/2006/07/07/file_64/1465770.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009047334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV011876452
work_keys_str_mv	AT axelfrancoise fromquasicrystalstomorecomplexsystemsleshouchesschoolfebruary23march61998 AT centredephysiqueleshouches fromquasicrystalstomorecomplexsystemsleshouchesschoolfebruary23march61998

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