@inproceedings{8135,
  abstract     = {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.},
  author       = {Edelsbrunner, Herbert and Nikitenko, Anton and Ölsböck, Katharina and Synak, Peter},
  booktitle    = {Topological Data Analysis},
  isbn         = {9783030434076},
  issn         = {21978549},
  pages        = {181--218},
  publisher    = {Springer Nature},
  title        = {{Radius functions on Poisson–Delaunay mosaics and related complexes experimentally}},
  doi          = {10.1007/978-3-030-43408-3_8},
  volume       = {15},
  year         = {2020},
}

@article{8384,
  abstract     = {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.},
  author       = {Ishida, Sadashige and Synak, Peter and Narita, Fumiya and Hachisuka, Toshiya and Wojtan, Christopher J},
  issn         = {15577368},
  journal      = {ACM Transactions on Graphics},
  number       = {4},
  publisher    = {Association for Computing Machinery},
  title        = {{A model for soap film dynamics with evolving thickness}},
  doi          = {10.1145/3386569.3392405},
  volume       = {39},
  year         = {2020},
}