When do cosmic peaks, filaments or walls merge?A theory of critical events in a multi-scale landscape.

A complement to the paper : When do cosmic peaks, filaments or walls merge? A theory of critical events in a multi-scale landscape

by Corentin Cadiou, Christophe Pichon, Sandrine Codis, Marcello Musso, Dmitri Pogosyan, Yohan Dubois, Jean-Francois Cardoso, Simon Prunet

This web page contains two notebooks corresponding the functions plotted in Figure 6 of the paper togther with interactive version of Figures 1,2 and 5.

accompanying Mathematica notebook

accompanying Python notebook

	Name	Last modified	Size	Description

	1+1D.html	2020-03-02 18:45	24M	1+1D landscape of a 1D field smoothed at a scale R. Solid lines indicate maxima (red) and minima (blue). Smoothing length R is the small- est at the backplane and increases toward the viewer, critical point lines end at critical events (black dots).
	2+1D.html	2020-03-02 19:14	27M	2+1D landscape of a 2D field smoothed at a scale R. The density field (blue to red map) is smoothed at increasing (upward) R. For each scale, the critical points (red lines: peaks, green lines: saddle points, blue lines: minima) are found. At the tip of each branch a critical event is found (red: peak-saddle critical events, blue: saddle-minima). Isocontours of density in 2+1D are shown as transparent surfaces (blue for negative density and red for positive density).
	critical_point_2D.html	2020-01-22 16:05	89K	Critical points (triangles) and events (cubes) detected in a 2D Gaussian random field. Each critical point line either continue forever or merge with a neighbouring one in a critical event.
	critical_point_3D.html	2020-01-22 16:21	458K	Critical points detected at different smoothing scales (triangles) and events (cubes) detected in a 3D Gaussian random field. The drift of all critical point lines end up in a critical event, that records their merging with a neighbouring critical point.
	wall-merger.ogv	2020-01-22 16:21	68Mb	Two consecutive snapshots in a 100 Mpc/h simulation showing a F critical event (yellow ball) that encodes the disappearance of a filament (highlighted in red) separating two walls (red and blue wireframes). After the event, only one wall has survived (yellow wireframe).
	filament-merger.ogv	2020-01-22 16:21	98Mb	Two consecutive shapshots in a 500 Mpc/h simulation showing a W critical event (yellow ball) that encodes the merger of two voids separated by a wall (green wireframe). After the event, only one void subsists and the wall has disappeared. Individual DM particles are shown as black dots. The skeleton (green lines) and the walls (green and red surfaces) have been extracted using DISPERSE. Both critical events can be related to merger event in the evolved Universe.
	nucleation.html	2020-03-04 19:50	5.9M	2D slice, in the (x, R) plane, of the conditional mean density in 3+1D position-smoothing space, under constraint of a a nucleation critical event (red box, bottom panel) at R = 1, x = 0. The slice position is chosen to contain the events. Green lines show filament-type saddle points at each R and red lines show peaks. Density isocontours are represented as coloured lines (from red, high density to blue, low density).

C. Pichon