6,516 research outputs found
Recursive tilings and space-filling curves with little fragmentation
This paper defines the Arrwwid number of a recursive tiling (or space-filling
curve) as the smallest number w such that any ball Q can be covered by w tiles
(or curve sections) with total volume O(vol(Q)). Recursive tilings and
space-filling curves with low Arrwwid numbers can be applied to optimise disk,
memory or server access patterns when processing sets of points in
d-dimensional space. This paper presents recursive tilings and space-filling
curves with optimal Arrwwid numbers. For d >= 3, we see that regular cube
tilings and space-filling curves cannot have optimal Arrwwid number, and we see
how to construct alternatives with better Arrwwid numbers.Comment: Manuscript accompanying abstract in EuroCG 2010, including full
proofs, 20 figures, references, discussion et
Compaction of Quasi One-Dimensional Elastoplastic Materials
Insight in the crumpling or compaction of one-dimensional objects is of great
importance for understanding biopolymer packaging and designing innovative
technological devices. By compacting various types of wires in rigid
confinements and characterizing the morphology of the resulting crumpled
structures, here we report how friction, plasticity, and torsion enhance
disorder, leading to a transition from coiled to folded morphologies. In the
latter case, where folding dominates the crumpling process, we find that
reducing the relative wire thickness counter-intuitively causes the maximum
packing density to decrease. The segment-size distribution gradually becomes
more asymmetric during compaction, reflecting an increase of spatial
correlations. We introduce a self-avoiding random walk model and verify that
the cumulative injected wire length follows a universal dependence on segment
size, allowing for the prediction of the efficiency of compaction as a function
of material properties, container size, and injection force.Comment: 7 pages, 6 figure
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