One symbol table for the project, with the equivalents in the thesis, in Dullemond’s notes and coag_py, and the identifier planned for the Rust code. Units are SI (ADR 0003 ).
Project Thesis Dullemond Rust Meaning
i, j i, j i, j (or i_l, j_l for samples) i, jColliding bins. With several properties, a flattened multi-index (ADR 0004 ). k k k kReceiving bin. k̄ k̄ k̄ k_lowBin with m_k̄ ≤ m_i + m_j < m_k̄+1. s l sSample index, s = 1..S. n m (time step, clashes with mass) stepTime step index.
Project Thesis Dullemond / coag_py Rust Unit Meaning
N_m 𝒩_m N_m, nm n_massMass bins. N_φ 𝒩_p N_φ n_fillFilling factor bins (M9). m_k m_k^c mgrain[k]mass.center(k)kg Bin center (geometric mean on log grid). m_{k±1/2} m_k^b migrainmass.edge(k)kg Bin edges. Δm_k Δm_k dmgrainmass.width(k)kg Bin width. q_m mass.ratio()m_{k+1}/m_k; must be < 2 for cancellation handling (coag_py assert). r, Δr r, 𝒩_r radiusm Radial grid. t_n, Δt t, Δt time, dtt, dts Time.
Symbol Thesis value / definition Unit
M_, L_ M_⊙, L_⊙ kg, W q_disk M_disk/M_* = 0.01 ε_dg M_dust/M_gas = 0.01 μ, m_g 2.3, μ m_p , kg φ_f flaring angle 0.05 rad T_mid(r) (φ_f/2 · L_*/(4π r² σ_SB))^{1/4} K c_s sqrt(k_B T / m_g) m s⁻¹ Ω_K sqrt(G M_*/r³) s⁻¹ H_p c_s/Ω_K m Σ_g(r) Σ₀ r^{-σ}, σ = 0.8 (thesis), 1 (diskmodel.py) kg m⁻² ρ_g^mid Σ_g / (sqrt(2π) H_p) kg m⁻³ u_th sqrt(8/π) c_s m s⁻¹ λ_mfp 1/(n_g σ_H₂), σ_H₂ = 2·10⁻¹⁹ m² m ν_mol ½ u_th λ_mfp m² s⁻¹ ν_t α c_s H_p, α = 10⁻³ m² s⁻¹ Re α c_s H_p / ν_mol u_g -3/(Σ_g sqrt r) ∂_r(Σ_g ν_t sqrt r) (must use ν_t, see thesis review F6) m s⁻¹ u_n -E_d ∂_r P_g / (2 ρ_g Ω_K), E_d = 1 m s⁻¹ v_t sqrt(α) c_s (turbulent velocity of largest eddies) m s⁻¹
Project Thesis coag_pyUnit Meaning
ρ_s ρ_s = 1600 rhosolidkg m⁻³ Material density. a_k a_k m Radius, (3 m / (4π ρ_s φ))^{1/3}. St_k St_i ts*omkStokes number. Δv_ij Δv_ij dvm s⁻¹ Total relative velocity, RMS of components BR, RD, AZ, TU, (DS). v_frag 1 m s⁻¹ Fragmentation threshold. v_bounce m s⁻¹ Bouncing threshold (M3).
Project Thesis coag_py / notesUnit Meaning
C_ij R^coll_ij Cij, C(m₁,m₂)m³ s⁻¹ Collision rate coefficient σ_ij Δv_ij. P^x_ij P^x_ij Outcome probability, x ∈ {coag, bounce, frag}. R^x_ij R^x_ij m³ s⁻¹ C_ij P^x_ij. X_kij X_kij Per-collision change in N_k (recipe weights). K_kij K_kij Kkijm³ s⁻¹ Σ_x R^x_ij X^x_kij (symmetrized in i, j). F_k(N) ∂N_k/∂t compute_kernel_summ⁻³ s⁻¹ Σ_ij K_kij N_i N_j. J_kl matrix='J's⁻¹ ∂F_k/∂N_l. p_ij P^sample_ij F_i F_j Pair proposal probability. π_ij Inclusion probability (sampling without replacement). S ρ_sample N_m² NranNumber of draws. F̂_k Eq. 1.70 m⁻³ s⁻¹ MC estimate of F_k. ΔM^net_ij ΔM^net_ij kg m³ s⁻¹ Σ_k m_k |K_kij|, mass throughput of pair (i, j).
Symbol Definition Meaning
δ_M(t) (Σ m_k N_k(t) − Σ m_k N_k(0)) / Σ m_k N_k(0) Global mass error (thesis Δ_stab, chapter 3 definition). ΔX^rel sqrt(Σ_ij (Σ_k m_k X_kij/(m_i+m_j))²) Kernel mass error. e_acc(t) mass-weighted error vs reference, see verification Replaces the thesis Δ_acc, which divides by zero where the reference bin is empty. B_k, V_k E[F̂_k] − F_k, Var[F̂_k] Estimator bias and variance. η 1/(e² · cost) Work-normalized efficiency.