Eric Gjerde, origamitessellations
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Eric Gjerde, origamitessellations.com
ORIGAMI:Structure finding with phase-
space foldsMark NeyrinckJohns Hopkins University
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Some collaborators:Bridget Falck, Miguel Aragón-Calvo, Guilhem Lavaux, Alex
SzalayJohns Hopkins University
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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
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Spherical collapse in phase space
(e.g. Bertschinger 1985)
Mark Neyrinck, JHU
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A simulation in phase space: a 2D simulation
slice
Mark Neyrinck, JHU
xvx
y
xz
y
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- 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
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200 Mpc/h simulation, 0.8 Mpc/h cells
δinitial
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log(1+δfinal)
(measured using Voronoi tessellation)
plotted on Lagrangian grid
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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)
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Morphology of particles, showing Eulerian position.
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A 200 Mpc/h simulation: final-conditions morphology of particles, showing Eulerian position.
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Lines between initial, final positions, colored according to morphology.
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Fraction of dark matter in various structures.
a
walls+filaments+haloes
walls+filaments
walls
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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
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How much does the origami sheet stretch?
- Look at spatial part, ∇L⋅ψ. Lagrangian displacement ψ = xf - xi. ∇L⋅ψ ~ -δL.- ∇L⋅ψ = -3: halo formation, where ∇L⋅xf = 0.
Mark Neyrinck, JHU
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Duality between structures inEulerian, 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.
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Filaments often stretched out.
- Could allow access to smaller-scale initial fluctuations than naively you would think?
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Eric Gjerde, origamitessellations.com
- An interesting method to detect structures, independent of density
Origami
Mark Neyrinck, JHU