---
_id: '8135'
abstract:
- lang: eng
text: Discrete Morse theory has recently lead to new developments in the theory
of random geometric complexes. This article surveys the methods and results obtained
with this new approach, and discusses some of its shortcomings. It uses simulations
to illustrate the results and to form conjectures, getting numerical estimates
for combinatorial, topological, and geometric properties of weighted and unweighted
Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes
contained in the mosaics.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreements No 78818 Alpha and No 638176). It is also partially supported
by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and
Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).
alternative_title:
- Abel Symposia
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
citation:
ama: 'Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay
mosaics and related complexes experimentally. In: Topological Data Analysis.
Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8'
apa: Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius
functions on Poisson–Delaunay mosaics and related complexes experimentally. In
Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8
chicago: Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak.
“Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.”
In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.
ieee: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions
on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological
Data Analysis, 2020, vol. 15, pp. 181–218.
ista: Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on
Poisson–Delaunay mosaics and related complexes experimentally. Topological Data
Analysis. , Abel Symposia, vol. 15, 181–218.
mla: Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics
and Related Complexes Experimentally.” Topological Data Analysis, vol.
15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.
short: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data
Analysis, Springer Nature, 2020, pp. 181–218.
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2021-01-12T08:17:06Z
day: '22'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/978-3-030-43408-3_8
ec_funded: 1
file:
- access_level: open_access
checksum: 7b5e0de10675d787a2ddb2091370b8d8
content_type: application/pdf
creator: dernst
date_created: 2020-10-08T08:56:14Z
date_updated: 2020-10-08T08:56:14Z
file_id: '8628'
file_name: 2020-B-01-PoissonExperimentalSurvey.pdf
file_size: 2207071
relation: main_file
success: 1
file_date_updated: 2020-10-08T08:56:14Z
has_accepted_license: '1'
intvolume: ' 15'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 181-218
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2533E772-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '638176'
name: Efficient Simulation of Natural Phenomena at Extremely Large Scales
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Topological Data Analysis
publication_identifier:
eissn:
- '21978549'
isbn:
- '9783030434076'
issn:
- '21932808'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2020'
...
---
_id: '8384'
abstract:
- lang: eng
text: Previous research on animations of soap bubbles, films, and foams largely
focuses on the motion and geometric shape of the bubble surface. These works neglect
the evolution of the bubble’s thickness, which is normally responsible for visual
phenomena like surface vortices, Newton’s interference patterns, capillary waves,
and deformation-dependent rupturing of films in a foam. In this paper, we model
these natural phenomena by introducing the film thickness as a reduced degree
of freedom in the Navier-Stokes equations and deriving their equations of motion.
We discretize the equations on a nonmanifold triangle mesh surface and couple
it to an existing bubble solver. In doing so, we also introduce an incompressible
fluid solver for 2.5D films and a novel advection algorithm for convecting fields
across non-manifold surface junctions. Our simulations enhance state-of-the-art
bubble solvers with additional effects caused by convection, rippling, draining,
and evaporation of the thin film.
acknowledged_ssus:
- _id: ScienComp
acknowledgement: "We wish to thank the anonymous reviewers and the members of the
Visual Computing Group at IST Austria for their valuable feedback, especially Camille
Schreck for her help in rendering. This research was supported by the Scientific
Service Units (SSU) of IST Austria through resources provided by Scientific Computing.
We would like to thank the authors of [Belcour and Barla 2017] for providing their
implementation, the authors of [Atkins and Elliott 2010] and [Seychelles et al.
2008] for allowing us to use their results, and Rok Grah for helpful discussions.
Finally, we thank Ryoichi Ando for many discussions from the beginning of the project
that resulted in important contents of the paper including our formulation, numerical
scheme, and initial implementation. This project has received funding from the\r\nEuropean
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme under grant agreement No. 638176."
article_number: '31'
article_processing_charge: No
article_type: original
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
- first_name: Fumiya
full_name: Narita, Fumiya
last_name: Narita
- first_name: Toshiya
full_name: Hachisuka, Toshiya
last_name: Hachisuka
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Ishida S, Synak P, Narita F, Hachisuka T, Wojtan C. A model for soap film dynamics
with evolving thickness. ACM Transactions on Graphics. 2020;39(4). doi:10.1145/3386569.3392405
apa: Ishida, S., Synak, P., Narita, F., Hachisuka, T., & Wojtan, C. (2020).
A model for soap film dynamics with evolving thickness. ACM Transactions on
Graphics. Association for Computing Machinery. https://doi.org/10.1145/3386569.3392405
chicago: Ishida, Sadashige, Peter Synak, Fumiya Narita, Toshiya Hachisuka, and Chris
Wojtan. “A Model for Soap Film Dynamics with Evolving Thickness.” ACM Transactions
on Graphics. Association for Computing Machinery, 2020. https://doi.org/10.1145/3386569.3392405.
ieee: S. Ishida, P. Synak, F. Narita, T. Hachisuka, and C. Wojtan, “A model for
soap film dynamics with evolving thickness,” ACM Transactions on Graphics,
vol. 39, no. 4. Association for Computing Machinery, 2020.
ista: Ishida S, Synak P, Narita F, Hachisuka T, Wojtan C. 2020. A model for soap
film dynamics with evolving thickness. ACM Transactions on Graphics. 39(4), 31.
mla: Ishida, Sadashige, et al. “A Model for Soap Film Dynamics with Evolving Thickness.”
ACM Transactions on Graphics, vol. 39, no. 4, 31, Association for Computing
Machinery, 2020, doi:10.1145/3386569.3392405.
short: S. Ishida, P. Synak, F. Narita, T. Hachisuka, C. Wojtan, ACM Transactions
on Graphics 39 (2020).
date_created: 2020-09-13T22:01:18Z
date_published: 2020-07-08T00:00:00Z
date_updated: 2024-02-28T12:57:31Z
day: '08'
ddc:
- '000'
department:
- _id: ChWo
doi: 10.1145/3386569.3392405
ec_funded: 1
external_id:
isi:
- '000583700300004'
file:
- access_level: open_access
checksum: 813831ca91319d794d9748c276b24578
content_type: application/pdf
creator: dernst
date_created: 2020-11-23T09:03:19Z
date_updated: 2020-11-23T09:03:19Z
file_id: '8795'
file_name: 2020_soapfilm_submitted.pdf
file_size: 14935529
relation: main_file
success: 1
file_date_updated: 2020-11-23T09:03:19Z
has_accepted_license: '1'
intvolume: ' 39'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1145/3386569.3392405
month: '07'
oa: 1
oa_version: Submitted Version
project:
- _id: 2533E772-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '638176'
name: Efficient Simulation of Natural Phenomena at Extremely Large Scales
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- '15577368'
issn:
- '07300301'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: A model for soap film dynamics with evolving thickness
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 39
year: '2020'
...