English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We apply the Minkowski Tensor statistics to two dimensional slices of thethree dimensional density field. The Minkowski Tensors are a set of functionsthat are sensitive to directionally dependent signals in the data, andfurthermore can be used to quantify the mean shape of density peaks. We beginby introducing our algorithm for constructing bounding perimeters aroundsubsets of a two dimensional field, and reviewing the definition of MinkowskiTensors. Focusing on the translational invariant statistic $W^{1,1}_{2}$ - a $2\times 2$ matrix - we calculate its eigenvalues for both the entire excursionset ($\Lambda_{1},\Lambda_{2}$) and for individual connected regions and holeswithin the set ($\lambda_{1},\lambda_{2}$). The ratio of eigenvalues$\Lambda_{2}/\Lambda_{1}$ informs us of the presence of global anisotropies inthe data, and $\langle \lambda_{2}/\lambda_{1} \rangle$ is a measure of themean shape of peaks and troughs in the density field. We study these quantitiesfor a Gaussian field, then consider how they are modified by the effect ofgravitational collapse using the latest Horizon Run 4 cosmological simulation.We find $\Lambda_{1,2}$ are essentially independent of gravitational collapse,as the process maintains statistical isotropy. However, the mean shape of peaksis modified significantly - overdensities become relatively more circularcompared to underdensities of the same area. When applying the statistic to aredshift space distorted density field, we find a significant signal in theeigenvalues $\Lambda_{1,2}$, suggesting that they can be used to probe thelarge-scale velocity field.

Minkowski Tensors in Two Dimensions - Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields