Monday, 07/24: Writing a pm-code - AIP

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Setting up cosmological ICs 41 Thus, if we construct a realization of {k x,y,z c k } using a cosmological power spectrum on a grid in the Fourier space, its discrete FFT gives us components of the real space displacement vector S(q) for all particles.
Setting up cosmological ICs 42 Applying these equations in practice for N p particles on a cubic grid with N 3 g cells amounts to 1) distributing particles uniformly in the simulation volume (e.g., placing particles in the centers of appropriately spaced grid cells). 2) Computing the displacement vector for each particle position. Construct a realization of k x,y,z c k on three (each for one component of the wavevector) cubic grids. For example, for the x-component, the grid is initialized to k x c k where k x are running from −k Ny to k Ny (assume k Ny = N p,1 /2, k here is in units of the fundamental mode 2π/L box = 2π/Ng 1/3 ) and a k and b k are gaussian random numbers defined above. 3) FFT each of the three grids to get S x (q), S y (q), and S z (q) in real space. Apply ZA to displace particles from their Lagrangian positions (q → x).
Page 1 and 2: Writing a PM code Andrey Kravtsov a
Page 3 and 4: equations I 2 Cosmological simulati
Page 5 and 6: N-body approach 4 Cosmological simu
Page 7 and 8: particle initial conditions 6 Cosmo
Page 9 and 10: equations of gasdynamics 8 Cosmolog
Page 11 and 12: equations summary 10 • Baryonic g
Page 13 and 14: dissipationless simulations 12 Part
Page 15 and 16: Model equations 14 Model equations
Page 17 and 18: Model equations 16 The quantities w
Page 19 and 20: Model equations 18 In dimensionless
Page 21 and 22: PM: main code blocks 20 Density Ass
Page 23 and 24: PM: main code blocks 22 In practice
Page 25 and 26: PM: main code blocks 24 Implementin
Page 27 and 28: PM: main code blocks 26 Solving the
Page 29 and 30: PM: main code blocks 28 ⇒ Given a
Page 31 and 32: PM: main code blocks 30 After n tim
Page 33 and 34: Zeldovich approximation (ZA) 32 Zel
Page 35 and 36: A test problem: 1D collapse of a pl
Page 41: Setting up cosmological ICs 40 The
Page 45 and 46: project summary 44 Project summary
Page 47 and 48: References and links 46 PM in cosmo
Page 49 and 50: References and links 48 • Michael

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