Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe

Weygaert, Rien van de

doi:10.1109/isvd.2007.48

Cited by 14 publications

(13 citation statements)

References 13 publications

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“…While other cosmic structure analysis tools do not include a facility to select weblike features according to tailor-made aspects and characteristics, this is precisely the mission of the Felix procedure. We directed Felix towards a case study of the the filamentary infrastructure and architecture of cosmic voids and demonstrated that it successfully extracts the network of tenuous filaments pervading their interior [72], [73], [74], [75] .…”

Section: Resultsmentioning

confidence: 99%

“…They use Voronoi tessellations as a template for distribution of matter and related galaxy population [76], [77], [74], and its subsequent evolution.…”

Section: Voronoi Evolution Modelsmentioning

confidence: 99%

“…The models we use here are considerably more sophisticated, and represent a rather realistic depiction of the cosmic web in void-dominated cosmologies, see e.g. [72], [73], [74], [75]. Voronoi tessellation.…”

Section: Voronoi Evolution Modelsmentioning

confidence: 99%

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Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Shivashankar

Pranav

Natarajan

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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Abstract-The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, walls and voids are relatively well separated, when compared to filaments, which span a relatively larger range. The large scale filamentary network thus forms an intricate part of the cosmic web. In this paper, we describe Felix, a topology based framework for visual exploration of filaments in the cosmic web. The filamentary structure is represented by the ascending manifold geometry of the 2-saddles in the Morse-Smale complex of the density field. We generate a hierarchy of Morse-Smale complexes and query for filaments based on the density ranges at the end points of the filaments. The query is processed efficiently over the entire hierarchical Morse-Smale complex, allowing for interactive visualization. We apply Felix to computer simulations based on the heuristic Voronoi kinematic model and the standard ΛCDM cosmology, and demonstrate its usefulness through two case studies. First, we extract cosmic filaments within and across cluster like regions in Voronoi kinematic simulation datasets. We demonstrate that we produce similar results to existing structure finders. Second, we extract different classes of filaments based on their density characteristics from the ΛCDM simulation datasets. Filaments that form the spine of the cosmic web, which exist in high density regions in the current epoch, are isolated using Felix. Also, filaments present in void-like regions are isolated and visualized. These filamentary structures are often over shadowed by higher density range filaments and are not easily characterizable and extractable using other filament extraction methodologies.Index Terms-Morse-Smale complexes, tessellations, cosmology theory, cosmic web, large-scale structure of the universe.

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Section: Resultsmentioning

confidence: 99%

“…They use Voronoi tessellations as a template for distribution of matter and related galaxy population [76], [77], [74], and its subsequent evolution.…”

Section: Voronoi Evolution Modelsmentioning

confidence: 99%

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Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Shivashankar

Pranav

Natarajan

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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“…Voronoi Clustering Models are a class of heuristic models for cellular distributions of matter which use the Voronoi tessellation as the skeleton of the cosmic matter distribution [30], [31], [32].…”

Section: Voronoi Clustering Modelsmentioning

confidence: 99%

“…This concerns not only the values and range over which β 2 reaches a maximum, as for the pure filament and wall models, but even entirely different systematic behaviour in the case of the more elaborate and complex Voronoi kinematic models (see e.g. the review by Van de Weygaert 2010 [34] and [32]). …”

Section: Number Of Holes: βmentioning

confidence: 99%

Alpha Shape Topology of the Cosmic Web

Weygaert

Platen

Vegter

et al. 2010

2010 International Symposium on Voronoi Diagrams in Science and Engineering

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We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers (β k , k = 1, . . . , D), which represent a complete characterization of the topology of a manifold. This forms a useful extension of the geometry and topology of the galaxy distribution by Minkowski functionals, of which three specify the geometrical structure of surfaces and one, the Euler characteristic, represents merely a summary of its topology. In order to develop an intuitive understanding for the relation between Betti numbers and the running α parameter of the alpha shapes, and thus in how far they may discriminate between different topologies, we study them within the context of simple heuristic Voronoi clustering models. These may be tuned to consist of a few or even only one specific morphological element of the Cosmic Web, ie. clusters, filaments or sheets.

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Stochastic Geometry and Its Applications

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Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe

Abstract: Abstract

Cited by 14 publications

References 13 publications

Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Alpha Shape Topology of the Cosmic Web

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