1. Eric Gjerde, origamitessellations.com ORIGAMI: Structure finding with phase-space folds Mark Neyrinck Johns Hopkins University ORIGAMI: Structure finding with phase-space folds Mark Neyrinck Johns Hopkins University

2. Some collaborators: Bridget Falck, Miguel Aragón-Calvo, Guilhem Lavaux, Alex Szalay Johns Hopkins University Some collaborators: Bridget Falck, Miguel Aragón-Calvo, Guilhem Lavaux, Alex Szalay Johns Hopkins University

3. Outline - The Universe as Origami - Lagrangian coordinates: perhaps underappreciated for simulation analysis - Finding stream-crossings/caustics: a parameter-free morphology classifier - Stretching/contraction of the “origami sheet” in position space also useful for halo finding Mark Neyrinck, JHU

4. Spherical collapse in phase space (e.g. Bertschinger 1985) Mark Neyrinck, JHU

5. A simulation in phase space: a 2D simulation slice Mark Neyrinck, JHU x vxvx y x z y

6. - 1d: particle in a halo if its order wrt any another particle is swapped compared to the original Lagrangian ordering - 3d: particle in a halo if this condition holds along 3 orthogonal axes (2 axes=filament, 1 axis=wall, 0 axes=void) - Need some diagonal axes as well - Finds places where streams have crossed Order-ReversIng Gravity, Apprehended Mangling Indices ORIGAMI Mark Neyrinck, JHU

7. 200 Mpc/h simulation, 0.8 Mpc/h cells δ initial

8. log(1+δ final ) (measured using Voronoi tessellation) plotted on Lagrangian grid

9. 200 Mpc/h simulation: # axes along which particle has crossed another particle (on Lagrangian grid) blue: 0 (void) cyan: 1 (sheet) yellow: 2 (filament) red: 3 (halo)

10. Morphology of particles, showing Eulerian position.

11. A 200 Mpc/h simulation: final- conditions morphology of particles, showing Eulerian position.

12. Lines between initial, final positions, colored according to morphology.

13. Fraction of dark matter in various structures. a walls+filaments+halo es walls+filaments walls

14. How to group halo particles once they’re identified? - Eulerian: group adjacent particles in Voronoi tessellation (Lagrangian grouping better?) - Halo mass function (Knebe et al, Halo-finder comparison): Mark Neyrinck, JHU

15. How much does the origami sheet stretch? - Look at spatial part, ∇ L ⋅ ψ. Lagrangian displacement ψ = x f - x i. ∇ L ⋅ ψ ~ -δ L. - ∇ L ⋅ ψ = -3: halo formation, where ∇ L ⋅ x f = 0. Mark Neyrinck, JHU

16. Duality between structures in Eulerian, Lagrangian coordinates Mark Neyrinck, JHU - Blobs become “points” (haloes) - Discs between blobs become filaments - Haloes look like voids in Lagrangian space! - Duality in Kofman et al. 1991, adhesion approx.

17. Filaments often stretched out. - Could allow access to smaller-scale initial fluctuations than naively you would think?

18. Eric Gjerde, origamitessellations.com - An interesting method to detect structures, independent of density Origami Mark Neyrinck, JHU