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

Abstract

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.

Persistence Atlas for Critical Point Variability in Ensembles

“…However, many more topological constructions could benefit from a similar variability analysis based on such tailored clustering strategies. For instance, the separatrices of the Morse-Smale complex [32,71] have been shown to excel at representing filament structures in various applications, such as chemistry [10,28] or astrophysics [78,79], and studying their trend and spatial variabilities would be of tremedous help for the understanding of non-deterministic models in these applications. By first focusing on critical points, we believe we made a first step in this direction, which will be helpful and inspirational for future generalizations to other topological constructions.…”

“…While this overall strategy has been successfully instantiated for simple objects, such as level sets [27,86] or streamlines [26], it is necessary to extend it to more advanced constructions, such as topological features. Topological data analysis (TDA) [22,35] has demonstrated its ability over the last two decades to capture in a generic, robust and efficient manner the features of interest in scalar data in a variety of applications: turbulent combustion [15,31,41], material sciences [25,33,34], computational fluid dynamics [39], chemistry [10,28] or astrophysics [78,79] to name a few. In these applications, domain-specific features of interest are easily expressed in terms of the critical points [6] of the data (points where the gradient vanishes), which are robustly extracted by topological methods.…”

The Effect of Data Transformations on Scalar Field Topological Analysis of High-Order FEM Solutions

“…The structures have seen direct usage in visualization of scalar fields, for example in selecting isosurfaces [70], topologically-guided simplification [68], feature tracking [61], transfer function design [73], isosurface simplification [11], and similarity estimation [65]. Even though topological analysis is a purely mathematical framework, a key reason for its success has been the mapping of these mathematical abstractions to applicationspecific features, as demonstrated by its use across a wide variety of domains, including astrophysics [59,62], battery design [33], combustion [7,18,31], chemistry [12,29], porous media [34], turbulence [42], and vortex extraction [41].…”

Visual Analysis of Charge Flow Networks for Complex Morphologies

“…Shivashankar et al . [SPN*16] use similar abstractions to find filament structures within density fields from the cosmology domain. Aboulhassan et al .…”