## From Quasicrystals to More Complex Systems: Les Houches School, February 23 – March 6, 1998This book is a collection of part of the written versions of the Physics Courses given at the Winter School "Order, Chance and Risk: Aperiodic Phenomena from Solid State to Finance" held at the Les Houches Center for Physics, between February 23 and March 6, 1998. The School gathered lecturers and participants from all over the world. On a thematic level, the content of the school can be viewed both as a continuation (aperiodic phenomena in solid state physics) and an extension (mathematical aspects of fmance and economy) of the previous "Beyond Quasicrystals", also held at Les Houches, March 7-18 1994 and published in the same ·series. One of its important goals was to promote in-depth concrete scientific exchanges between theoretical physicists, experimental physicists and mathematicians on the one hand, and on the other hand practitioners of the economico-fmancial sphere and specialists of financial mathematics. Therefore, besides the mathematical tools and concepts at work in theoretical descriptions, relevant experimental data were also presented together with methods allowing their interpretation. As a result of this choice, the School was stimulated by experimentalists and fmancial market operators who joined the theoretical physicists and mathematicians at the conference. The present volume deals with the theoretical and experimental studies on aperiodic solids with long range order, incommensurate phases, quasicrystals, glasses, and more complex systems (fractal, chaotic), while a second volume to appear in the same series is devoted to the finance and economy facet. |

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### Contents

COURSE | 1 |

Tensorial properties | 16 |

Decagonal symmetry and twinning | 30 |

Copyright | |

36 other sections not shown

### Common terms and phrases

acceptance window algebraic alloys amorphous approximant atomic surfaces automorphism band germs Bloch bound boundary conditions Bragg peaks Brillouin Brillouin zone clusters computation conductivity consider correlation function corresponding Courtens crystal cut and project decagonal defined diffraction pattern diffraction peaks dimension discrete disorder distribution domain dynamical system eigenvalues electronic entropy equation ergodic ergodic theory example Fibonacci Fibonacci strings Figure finite Fourier transform fractal fracton frequency given i-AlCuFe i-phases icosahedral infinite integers invariant lattice length Lett linear Math Mathematics measure metal model sets neutron obtained p-adic parameters Penrose tiling periodic phase space phason strain phonons Phys physical plane point set positive potential properties quasicrystal quasicrystalline quasilattice quasiperiodic quenched disorder R.V. Moody range samples scale scattering Section sequence simulation spectrum structure factor subset symmetry temperature theorem theory topology trajectories transfer matrix transition unit cell values vectors vertices X-ray zero