6 research outputs found
On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups
We are interested in the maximum possible number of facets that Dirichlet
stereohedra for three-dimensional crystallographic groups can have. The problem
for non-cubic groups was studied in previous papers by D. Bochis and the second
author (Discrete Comput. Geom. 25:3 (2001), 419-444, and Beitr. Algebra Geom.,
47:1 (2006), 89-120). This paper deals with ''full'' cubic groups, while
''quarter'' cubic groups are left for a subsequent paper. Here, ''full'' and
''quarter'' refers to the recent classification of three-dimensional
crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston
(math.MG/9911185, Beitr. Algebra Geom. 42.2 (2001), 475-507).
Our main result in this paper is that Dirichlet stereohedra for any of the 27
full groups cannot have more than 25 facets. We also find stereohedra with 17
facets for one of these groups.Comment: 28 pages, 12 figures. Changes from v1: apart of some editing (mostly
at the end of the introduction) and addition of references, an appendix has
been added, which analyzes the case where the base point does not have
trivial stabilize
Foundation, analysis, and numerical investigation of a variational network-based model for rubber
Since the pioneering work by Treloar, many models based on polymer chain statistics have been proposed to describe rubber elasticity. Recently, Alicandro, Cicalese, and the first author rigorously derived a continuum theory of rubber elasticity from a discrete model by variational convergence. The aim of this paper is twofold. First, we further physically motivate this model and complete the analysis by numerical simulations. Second, in order to compare this model to the literature, we present in a common language two other representative types of models, specify their underlying assumptions, check their mathematical properties, and compare them to Treloar's experiments. © 2012 Springer-Verlag Berlin Heidelberg.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity
info:eu-repo/semantics/publishe