Literature and source map
Every source this project builds on, with its role, where it lives locally (if anywhere), and its reading status. Paths are relative to this file; related/ is the folder of symlinks at the project root.
Bibliographic details were checked against publisher or ADS records on 2026-11-10.
Status: read (studied for this plan), skimmed (abstract and relevant sections), to read (needed before the milestone named in brackets), cited (only known from the thesis bibliography).
1. Primary sources of this project
| Key | Source | Local | Role | Status |
|---|---|---|---|---|
mader_2024 | V. Mader, Investigating the Feasibility of utilizing Stochastic Sampling of Colliding Circumstellar Dust Particle Pairs for Computational Cost Optimization of the Smoluchowski Coagulation Equation’s Numerical Integration, M.Sc. thesis, Heidelberg University (ITA), supervisor C. P. Dullemond, Feb 2024 | PDF, TeX | The starting point. Reviewed in 01-thesis-review.md. | read |
msc-thesis.py | Thesis code (Python), github.com/vincentmader/msc-thesis.py | repo | Reference implementation for parity tests (disk, kinematics, kernels). | read (core modules) |
mc_coag | Rust/PyO3 stub crate from the thesis | crate | Only a skeleton (169 lines); nothing to port. | read |
dullemond_notes | C. P. Dullemond, Dust evolution with binning methods (lecture notes / draft, 19 pp.) | The research program we continue. Kovetz and Olund, near-cancellation, fragmentation models (pulverization, shattering, cratering, bouncing with mass loss), cost scaling N^{3p}, MC kernel sampling (Eq. 1.70), implicit form (Eq. 1.71), detailed balance per sample, open TODOs. | read | |
coag_py | C. P. Dullemond, coag_py (Python), incl. react_0d.py (Radau via scipy, Newton backward Euler), coag.py (Kovetz and Olund kernel), mc_sampling/ (2021 MC prototype) | repo | Reference for kernel parity (create_coag_kernel), integrator semantics, and the importance-sampling prototype (sample_kernel_sum). | read |
dullemond_sizedist | C. P. Dullemond, Dust physics: size distributions (notes, 2 pp.) | Conventions for n(a), n(m), dimensionless bin widths, m²f(m) plots. | skimmed | |
dullemond_diskmodel | diskmodel.py, natconst.py (Dullemond) | diskmodel.py | Minimal irradiated power-law disk; cross check for M2 (note: Σ ∝ r⁻¹ there, r⁻⁰·⁸ in thesis). | read |
2. Coagulation physics and dust evolution in disks
| Key | Reference | DOI / URL | Local | Role | Status |
|---|---|---|---|---|---|
smoluchowski_1916 | M. v. Smoluchowski, Drei Vorträge über Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen, Phys. Z. 17, 557 (1916) | ADS 1916ZPhy…17..557S | The equation; constant kernel solution. | cited | |
kovetz_olund_1969 | A. Kovetz, B. Olund, J. Atmos. Sci. 26, 1060 (1969) | 10.1175/1520-0469(1969)026<1060:TEOCAC>2.0.CO;2 | Mass and number conserving mapping of m_i+m_j onto a log grid. | cited (method read via dullemond_notes) | |
dullemond_dominik_2005 | C. P. Dullemond, C. Dominik, Dust coagulation in protoplanetary disks: a rapid depletion of small grains, A&A 434, 971 (2005) | arXiv:astro-ph/0412117 | Brownian Δv, need for fragmentation to sustain small grains. The thesis bib entry dullemond_dominik_2004 carries a different title (the settling paper); fix in the paper. | skimmed | |
brauer_2008 | F. Brauer, C. P. Dullemond, Th. Henning, Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks, A&A 480, 859 (2008) | 10.1051/0004-6361:20077759 | Σ_g profile, modified Podolak algorithm (App. A), implicit differencing (App. C), 10⁴ speed-up. | skimmed (App. A, C read) | |
birnstiel_2010 | T. Birnstiel, C. P. Dullemond, F. Brauer, Gas- and dust evolution in protoplanetary disks, A&A 513, A79 (2010) | 10.1051/0004-6361/200913731 | Disk + kinematics recipes (St, radial drift, u_g with α viscosity, σ_H₂, ρ_s), fully implicit unsplit scheme (App. A), test cases (App. B). | skimmed; to read App. A, B [M6] | |
birnstiel_2011 | T. Birnstiel, PhD thesis (2011), arXiv | Long-form derivations. | cited | ||
ormel_cuzzi_2007 | C. W. Ormel, J. N. Cuzzi, Closed-form expressions for particle relative velocities induced by turbulence, A&A 466, 413 (2007); arXiv:astro-ph/0702303 | 10.1051/0004-6361:20066899 | Turbulent Δv regimes (their Eqs. 26 to 29). | to read [M3] | |
weidenschilling_1977 | S. J. Weidenschilling, MNRAS 180, 57 (1977) | 10.1093/mnras/180.2.57 | Maximum drift velocity u_n. | cited | |
nakagawa_1986 | Y. Nakagawa, M. Sekiya, C. Hayashi, Icarus 67, 375 (1986) | 10.1016/0019-1035(86)90121-1 | Azimuthal drift. | cited | |
lynden-bell_pringle_1974 | D. Lynden-Bell, J. E. Pringle, MNRAS 168, 603 (1974) | 10.1093/mnras/168.3.603 | Viscous radial gas velocity. | cited | |
stammler_birnstiel_2022 | S. M. Stammler, T. Birnstiel, DustPy, ApJ 935, 35 (2022) | 10.3847/1538-4357/ac7d58 | Maxwell-Boltzmann fragmentation probability; state-of-the-art 1D Smoluchowski code to benchmark against. Run as an external oracle at one radius with transport off (M3.6). | to read [M3, M6] | |
dominik_dullemond_2024 | C. Dominik, C. P. Dullemond, The bouncing barrier revisited, A&A 682, A144 (2024) | 10.1051/0004-6361/202347716, arXiv:2312.06000 | Sticking/bouncing/fragmentation probabilities, v_frag scaling; source for the bouncing model. The thesis cites it as “2003”. | to read [M3] | |
mathis_1977 | J. S. Mathis, W. Rumpl, K. H. Nordsieck, ApJ 217, 425 (1977) | 10.1086/155591 | MRN slope for fragment distribution (p = -11/6 in mass). | cited | |
kun_herrmann_1999 | F. Kun, H. J. Herrmann, Phys. Rev. E 59, 2623 (1999) | Alternative fragment slope p ≈ -3.27. | cited via dullemond_notes | ||
guettler_2010 | C. Güttler et al., A&A 513, A56 (2010) | Laboratory based collision outcome recipe. | to read [M3] | ||
blum_wurm_2008 | J. Blum, G. Wurm, ARA&A 46, 21 (2008) | Laboratory review. | to read [M3] | ||
wada_2009 | K. Wada et al., ApJ 702, 1490 (2009) | 10.1088/0004-637X/702/2/1490 | Collision growth conditions (BPCA). | cited | |
laibe_lombart_2021 | G. Laibe, M. Lombart, On the CFL condition for numerical solvers of the coagulation equation, MNRAS (2021) | 10.1093/mnras/stab3499 | Explicit time step limits; needed for the Euler/RK study. | to read [M5] |
3. Porosity and additional particle properties (the regime where sampling should pay off)
| Key | Reference | DOI / URL | Role | Status |
|---|---|---|---|---|
ormel_2007 | C. W. Ormel, M. Spaans, A. G. G. M. Tielens, Dust coagulation in protoplanetary disks: porosity matters, A&A 461, 215 (2007) | 10.1051/0004-6361:20065949 | Direct MC with mass + porosity; collision regimes (hit-and-stick, compaction, fragmentation). Thesis key ormel_2006. | to read [M9] |
okuzumi_2009 | S. Okuzumi, H. Tanaka, M. Sakagami, ApJ 707, 1247 (2009) | 10.1088/0004-637X/707/2/1247, arXiv:0911.0239 | Extended Smoluchowski with volume as second variable; volume-averaging method. | to read [M9] |
okuzumi_2012 | S. Okuzumi et al., Rapid coagulation of porous dust aggregates outside the snow line, ApJ 752, 106 (2012); 10.1088/0004-637X/752/2/106 | Porosity evolution recipe used widely. | to read [M9] | |
kataoka_2013 / kataoka_2017 | A. Kataoka et al. (2013, A&A 557, L4 (Fluffy dust forms icy planetesimals by static compression)); A. Kataoka, ASSL 445, 143 (2017) | 10.1007/978-3-319-60609-5_5 | Static compression, porosity evolution review. | to read [M9] |
schoell_2026 | Schöll, Dullemond, Dominik, The influence of the fractal dimension on dust evolution in protoplanetary disks (2026) | arXiv:2604.26794 | Same group. States that an independent filling-factor dimension is “often computationally too expensive” and uses φ(m,t) as a dependent variable instead. Direct motivation for our M9. | to read [M8] |
4. Numerical methods for the coagulation equation
| Key | Reference | DOI / URL | Role | Status |
|---|---|---|---|---|
hairer_wanner_1996 | E. Hairer, G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd ed., Springer (1996) | Radau IIA (RADAU5), simplified Newton, step control, W-methods. Basis of our own Radau implementation. | to read [M6] | |
radau5_f | E. Hairer, radau5.f reference code | https://www.unige.ch/~hairer/prog/stiff/radau5.f | Reference implementation, referenced by react_0d.py. | to read [M6] |
scipy_radau | SciPy solve_ivp(method='Radau') | scipy docs | Oracle for parity tests (what the thesis used). Order 5. | known |
filbet_laurencot_2004 | F. Filbet, P. Laurençot, SIAM J. Sci. Comput. (2004) | 10.1137/S1064827503429132 | Conservative finite volume scheme for Smoluchowski. | cited, to read [M5] |
lombart_laibe_2021 | M. Lombart, G. Laibe, Grain growth for astrophysics with discontinuous Galerkin schemes, MNRAS 501, 4298 (2021) | arXiv:2011.12298 | High-order DG coagulation, few bins, machine precision mass. Competing approach. | to read [M6] |
lombart_2024 | M. Lombart, C.-E. Bréhier, M. Hutchison, Y.-N. Lee, General non-linear fragmentation with discontinuous Galerkin methods, MNRAS (2024) | arXiv:2404.11851 | DG fragmentation, 0.1 to 1 % accuracy with 20 bins over 9 decades. Competing approach. | to read [M6] |
ohtsuki_1990 | K. Ohtsuki, Y. Nakagawa, K. Nakazawa, Icarus 83, 205 (1990) | 10.1016/0019-1035(90)90015-2 | Analytic solutions (constant, linear) and coarse-grid artificial acceleration. Used by coag_py tests. | to read [M5] |
wattis_2006 | J. A. D. Wattis, Physica D 222, 1 (2006) | 10.1016/J.PHYSD.2006.07.024 | Coagulation-fragmentation review, product kernel gelation. | to read [M5] |
safronov_1963/1972 | V. S. Safronov | Linear kernel solution. | cited | |
spouge_1985 | J. L. Spouge, J. Phys. A 18, 3063 (1985) | 10.1088/0305-4470/18/15/028 | Analytic solutions, combinatorial view. | cited |
dubovskii_1994 | P. B. Dubovskiǐ, Mathematical Theory of Coagulation (lecture notes, 164 pp.) | Existence, uniqueness, mass conservation, gelation theory. For the paper’s theory section. | to read [M8] | |
sekiyama_2017 | M. Sekiyama, T. Ohtsuki, H. Yamamoto, J. Phys. Soc. Jpn. (2017) | Analytic aggregation-fragmentation solutions: a benchmark with fragmentation. Thesis key ohtsuki_2017. | to read [M5] |
5. Stochastic and reduced-cost methods (positioning of the paper)
| Key | Reference | DOI / URL | Role | Status |
|---|---|---|---|---|
ormel_2007 | see section 3 | Direct simulation Monte Carlo. | to read | |
zsom_dullemond_2008 | A. Zsom, C. P. Dullemond, A representative particle approach to coagulation and fragmentation of dust aggregates and fluid droplets, A&A 489, 931 (2008); 10.1051/0004-6361:200809921, arXiv:0807.5052 | Representative particle MC (original). | to read [M8] | |
beutel_2023 | M. Beutel, C. P. Dullemond, An improved Representative Particle Monte Carlo method, A&A 670, A134 (2023) | 10.1051/0004-6361/202244955 | RPMC; the group’s current particle method. Main “other” MC baseline. | to read [M8] |
gurrutxaga_2026 | N. Gurrutxaga, V. Vaikundaraman, J. Drążkowska, A Monte Carlo method for tracking dust properties during coagulation in protoplanetary disks, A&A (accepted, 2026) | arXiv:2604.24857 | Very recent particle MC with strict global conservation of tracked properties. Must be discussed in the paper. | to read [M8] |
drazkowska_2014 | J. Drążkowska, F. Windmark, C. Dullemond, Modeling dust growth in protoplanetary disks: the breakthrough case, A&A 567, A38 (2014); 10.1051/0004-6361/201423708 | Compares Smoluchowski integration and MC codes head-to-head. | to read [M8] | |
matveev_2015 | S. A. Matveev, A. P. Smirnov, E. E. Tyrtyshnikov, A fast numerical method for the Cauchy problem for the Smoluchowski equation, J. Comput. Phys. 282, 23 (2015) | Low-rank kernel + fast convolution, O(N log N). Deterministic competitor. | to read [M8] | |
matveev_2016 | S. A. Matveev, D. A. Zheltkov, E. E. Tyrtyshnikov, A. P. Smirnov, Tensor train versus Monte Carlo for the multicomponent Smoluchowski coagulation equation, J. Comput. Phys. 316, 164 (2016) | Closest prior art for the multi-property argument. TT beats MC in their tests; our paper must address this. | to read [M8] | |
matveev_tretyak_2024 | S. A. Matveev, I. Tretyak, Nonnegative tensor train for the multicomponent Smoluchowski equation (2024) | arXiv:2404.10898 | Positivity fix for TT. | to read [M8] |
tree_2026 | A fast tree algorithm for multi-component coagulation equation (2026) | arXiv:2605.18353 | Recent deterministic fast multi-component method. | to read [M8] |
eibeck_wagner_2001 | A. Eibeck, W. Wagner, Stochastic particle approximations for Smoluchowski’s coagulation equation, Ann. Appl. Probab. 11(4), 1137 (2001); 10.1214/aoap/1015345398 | Mass flow algorithm; theory of stochastic approximations. | to read [M8] |
6. Context references from the thesis introduction (not needed for the paper)
andrews_2007, kitamura_2002, burton_2013, natta_2006, kant_1755, laplace_1799, newton_1687, courant_friedrichs_lewy_1928, schumann_1940, ALMA/ESO/Hubble image credits. Full entries: references.bib.
7. Local material that turned out not to be relevant
| File | Why not |
|---|---|
| Bani-Hashemian 2011, Accurate and Efficient Solution of the Smoluchowski Equation | Treats the diffusion Smoluchowski equation (Brownian pair PDFs for reaction-diffusion simulations, GFRD), not the coagulation equation. Same name, different equation. |
related/M.Sc. Thesis/Reading/ | Empty folder. |
Oral exam scripts in ~/Documents/org/Projects/Education/Acquire Physics M.Sc. from UHD./Sem_13/M.Sc. Oral Exam/Reading/ (Simulation Methods, Computational Physics, Computational Astrophysics) | General background; may help for ODE stiffness and MC variance chapters. |