---
res:
bibo_abstract:
- 'We describe arrangements of three-dimensional spheres from a geometrical and
topological point of view. Real data (fitting this setup) often consist of soft
spheres which show certain degree of deformation while strongly packing against
each other. In this context, we answer the following questions: If we model a
soft packing of spheres by hard spheres that are allowed to overlap, can we measure
the volume in the overlapped areas? Can we be more specific about the overlap
volume, i.e. quantify how much volume is there covered exactly twice, three times,
or k times? What would be a good optimization criteria that rule the arrangement
of soft spheres while making a good use of the available space? Fixing a particular
criterion, what would be the optimal sphere configuration? The first result of
this thesis are short formulas for the computation of volumes covered by at least
k of the balls. The formulas exploit information contained in the order-k Voronoi
diagrams and its closely related Level-k complex. The used complexes lead to a
natural generalization into poset diagrams, a theoretical formalism that contains
the order-k and degree-k diagrams as special cases. In parallel, we define different
criteria to determine what could be considered an optimal arrangement from a geometrical
point of view. Fixing a criterion, we find optimal soft packing configurations
in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools
from computational topology on real physical data, to show the potentials of higher-order
diagrams in the description of melting crystals. The results of the experiments
leaves us with an open window to apply the theories developed in this thesis in
real applications.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Mabel
foaf_name: Iglesias Ham, Mabel
foaf_surname: Iglesias Ham
foaf_workInfoHomepage: http://www.librecat.org/personId=41B58C0C-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.15479/AT:ISTA:th_1026
dct_date: 2018^xs_gYear
dct_language: eng
dct_publisher: IST Austria@
dct_title: Multiple covers with balls@
...