- EAN13
- 9782759819522
- Éditeur
- EDP sciences
- Date de publication
- 30/06/2016
- Collection
- Savoirs Actuels
- Langue
- français
- Fiches UNIMARC
- S'identifier
Livre numérique
-
Aide EAN13 : 9782759819522
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Papier - EDP sciences 69,00
Group action analysis developed and applied mainly by Louis Michel to the
study of N-dimensional
periodic lattices is the central subject of the book. Di_ erent basic
mathematical tools
currently used for the description of lattice geometry are introduced and
illustrated through
applications to crystal structures in two- and three-dimensional space, to
abstract multi-dimensional
lattices and to lattices associated with integrable dynamical systems.
Starting from general Delone
sets the authors turn to di_ erent symmetry and topological classi_ cations
including explicit construction
of orbifolds for two- and three-dimensional point and space groups.
Voronoï and Delone cells together with positive quadratic forms and lattice
description by root
systems are introduced to demonstrate alternative approaches to lattice
geometry study. Zonotopes
and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly
visualized using
graph theory approach. Along with crystallographic applications, qualitative
features of lattices of
quantum states appearing for quantum problems associated with classical
Hamiltonian integrable
dynamical systems are shortly discussed.
The presentation of the material is presented through a number of concrete
examples with an extensive
use of graphical visualization. The book is aimed at graduated and post-
graduate students and
young researchers in theoretical physics, dynamical systems, applied
mathematics, solid state physics,
crystallography, molecular physics, theoretical chemistry, ...
study of N-dimensional
periodic lattices is the central subject of the book. Di_ erent basic
mathematical tools
currently used for the description of lattice geometry are introduced and
illustrated through
applications to crystal structures in two- and three-dimensional space, to
abstract multi-dimensional
lattices and to lattices associated with integrable dynamical systems.
Starting from general Delone
sets the authors turn to di_ erent symmetry and topological classi_ cations
including explicit construction
of orbifolds for two- and three-dimensional point and space groups.
Voronoï and Delone cells together with positive quadratic forms and lattice
description by root
systems are introduced to demonstrate alternative approaches to lattice
geometry study. Zonotopes
and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly
visualized using
graph theory approach. Along with crystallographic applications, qualitative
features of lattices of
quantum states appearing for quantum problems associated with classical
Hamiltonian integrable
dynamical systems are shortly discussed.
The presentation of the material is presented through a number of concrete
examples with an extensive
use of graphical visualization. The book is aimed at graduated and post-
graduate students and
young researchers in theoretical physics, dynamical systems, applied
mathematics, solid state physics,
crystallography, molecular physics, theoretical chemistry, ...
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