What is a Crystal ?
CRISTAUX
MATHEMATIQUES
PAVAGE
FONCTIONS
Abstract : An historical survey of our knowledge of crystal structure and of the mathematical problem of paving space with one or a few types of stones show that a crystal has not necessarily a translation lattice. The recently discovered crystals of alloys Al with 14% Mn have an ecosahedral symetry (incompatible qith translation lattice). Their electron micrographs show a structure similar to a Penrose tiling. It seems that long range order characterizing crystals can be obtained from projection of a thin slab of genuine crystal in higher dimension so that crystal physical properties can be described by quasi-periodic functions (as generalizing periodic ones) or may be almost periodic functions.
MICHEL
P/85/68
IHES
12/1985
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_85_68.pdf
1985
Fairly symmetric hyperbolic manifolds
VARIETES
ESPACES HYPERBOLIQUES
SYMETRIE
TESSELLATIONS
KUIPER
M/89/48
IHES
07/1989
A4
20 f.
EN
TEXTE
PREPUBLICATION
M_89_48.pdf
1989
Review of "Concrete mathematics" (a book by Knuth and al.)
MATHEMATIQUES DISCRETES
INFORMATIQUE
PROBLEMES MATHEMATIQUES
SOMMES
FONCTIONS INTEGRALES
THEORIE DES NOMBRES
COEFFICIENTS BINOMIAUX
FONCTIONS GENERATRICES
NOMBRES SPECIAUX
PROBABILITE
DEVELOPPEMENTS ASYMPTOTIQUES
CARTIER
M/91/12
IHES
02/1991
A4
9 f.
EN
TEXTE
PREPUBLICATION
M_91_12.pdf
1991