相关论文: Geometry of the Cosmic Web: Minkowski Functionals …
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to…
Minkowski functionals (MFs) are a set of statistics that characterise the geometry and topology of the cosmic density field and contain complementary information to the standard two-point analyses. We present MEDUSA, an implementation of an…
The genus statistics of isodensity contours has become a well-established tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological descriptors. These are known as the Minkowski…
Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…
The density fields constructed by traditional mass assignment methods are susceptible to irritating discreteness, which hinders morphological measurements of cosmic large-scale structure (LSS) through Minkowski functionals (MFs). For…
We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogues generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We…
The lecture notes describe the Delaunay Tessellation Field Estimator for Cosmic Web analysis. The high sensitivity of Voronoi/Delaunay tessellations to the local point distribution is used to obtain estimates of density and related…
The application of Voronoi and Delaunay tessellation based methods for reconstructing continuous fields from discretely sampled data sets is discussed. The succesfull operation as ``multidimensional interpolation'' method is corroborated…
We present a first morphometric investigation of a preliminary sample from the SDSS of 154287 galaxies with apparent magnitude 14.5<m_r<17.5 and redshift 0.001<z<0.4. We measure the Minkowski Functionals, which are a complete set of…
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for…
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well…
Understanding the structure of the matter distribution in the Universe due to the action of the gravitational instability -- the cosmic web -- is complicated by lack of direct analytic access to the nonlinear domain of structure formation.…
We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of…
The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis…
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which…
The morphological properties of large scale structure of the Universe can be fully described by four Minkowski functionals (MFs), which provide important complementary information to other statistical observables such as the widely used…
Cosmic shear - the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure - is one of the most promising tools for current and future cosmological analyses. The…
In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales…
A novel method allowing to compute density, velocity and other fields in cosmological N--body simulations with unprecedentedly high spatial resolution is described. It is based on the tessellation of the three-dimensional manifold…
We present a new ansatz which can successfully be used to determine the morphological properties of the supercluster-void network. The ansatz is based on a surface modelling scheme SURFGEN, which generates a triangulated surface from a…