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Home All issues Volume 711 (July 2026) A&A, 711 (2026) A163 References
Open Access
Issue
A&A
Volume 711, July 2026
Article Number A163
Number of page(s) 23
Section Numerical methods and codes
DOI https://doi.org/10.1051/0004-6361/202558713
Published online 14 July 2026
  1. Adachi, I., Hayashi, C., & Nakazawa, K. 1976, Prog. Theor. Phys., 56, 1756 [CrossRef] [Google Scholar]
  2. A’Hearn, M. F. 2011, ARA&A, 49, 281 [Google Scholar]
  3. Akimkin, V. V., Ivlev, A. V., & Caselli, P. 2020, ApJ, 889, 64 [NASA ADS] [CrossRef] [Google Scholar]
  4. Alexopoulos, A. H., Roussos, A., & Kiparissides, C. 2009, Chem. Eng. Sci., 64, 3260 [Google Scholar]
  5. Alfonso, L., Raga, G. B., & Baumgardner, D. 2008, Atmos. Chem. Phys., 8, 969 [Google Scholar]
  6. Barnes, J., & Hut, P. 1986, Nature, 324, 446 [NASA ADS] [CrossRef] [Google Scholar]
  7. Beutel, M., Dullemond, C. P., & Strzodka, R. 2024, A&A, 684, A2 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  8. Birnstiel, T., Dullemond, C. P., & Brauer, F. 2010, A&A, 513, A79 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  9. Birnstiel, T., Klahr, H., & Ercolano, B. 2012, A&A, 539, A148 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  10. Blum, J., & Wurm, G. 2000, Icarus, 143, 138 [NASA ADS] [CrossRef] [Google Scholar]
  11. Blum, J., & Wurm, G. 2008, ARA&A, 46, 21 [CrossRef] [Google Scholar]
  12. Brauer, F., Dullemond, C. P., & Henning, T. 2008, A&A, 480, 859 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  13. Capuzzo-Dolcetta, R., & Miocchi, P. 1998, J. Comput. Phys., 143, 29 [Google Scholar]
  14. Chakraborty, J., & Kumar, S. 2007, Chem. Eng. Sci., 62, 4112 [Google Scholar]
  15. Chaudhury, A., Kapadia, A., Prakash, A. V., Barrasso, D., & Ramachandran, R. 2013, Adv. Powder Technol., 24, 962 [Google Scholar]
  16. Chauhan, S. S., Chiney, A., & Kumar, S. 2012, Chem. Eng. Sci., 70, 135 [Google Scholar]
  17. Cheng, H., Greengard, L., & Rokhlin, V. 1999, J. Comput. Phys., 155, 468 [Google Scholar]
  18. Ciesla, F. J., & Cuzzi, J. N. 2006, Icarus, 181, 178 [NASA ADS] [CrossRef] [Google Scholar]
  19. Dehnen, W. 2000, ApJ, 536, L39 [NASA ADS] [CrossRef] [Google Scholar]
  20. Dehnen, W. 2014, ComAC, 1, 1 [Google Scholar]
  21. Drążkowska, J., Windmark, F., & Dullemond, C. P. 2013, A&A, 556, A37 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  22. Drążkowska, J., Windmark, F., & Dullemond, C. P. 2014, A&A, 567, A38 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Dullemond, C. P., & Dominik, C. 2005, A&A, 434, 971 [CrossRef] [EDP Sciences] [Google Scholar]
  24. Dyachenko, R. R., Matveev, S. A., & Valiakhmetov, B. I. 2025, arXiv e-prints [arXiv:2501.10206] [Google Scholar]
  25. Ernst, M. H., Ziff, R. M., & Hendriks, E. M. 1984, J. Colloid Interface Sci., 97, 266 [Google Scholar]
  26. Estrada, P. R., & Cuzzi, J. N. 2008, ApJ, 682, 515 [Google Scholar]
  27. Estrada, P. R., Cuzzi, J. N., & Umurhan, O. M. 2022, ApJ, 936, 42 [NASA ADS] [CrossRef] [Google Scholar]
  28. Fernández-Díaz, J. M., & Gómez-García, G. J. 2007, EPL, 78, 56002 [Google Scholar]
  29. Garaud, P. 2007, ApJ, 671, 2091 [NASA ADS] [CrossRef] [Google Scholar]
  30. Garcia, A. J., & Gonzalez, J.-F. 2020, MNRAS, 493, 1788 [Google Scholar]
  31. Gelbard, F. M., & Seinfeld, J. H. 1978, J. Colloid Interface Sci., 63, 472 [Google Scholar]
  32. Gelbard, F., & Seinfeld, J. H. 1980, J. Colloid Interface Sci., 78, 485 [Google Scholar]
  33. Golovin, A. M. 1963, Bulletin of the Academy of Sciences of the U.S.S.R., Geophysics Series, 5, 783 [Google Scholar]
  34. Greengard, L., & Rokhlin, V. 1987, J. Comput. Phys., 73, 325 [NASA ADS] [CrossRef] [Google Scholar]
  35. Gruy, F. 2011, Colloids Surf. A: Physicochem. Eng. Aspects, 374, 69 [Google Scholar]
  36. Gunawan, R., Fusman, I., & Braatz, R. D. 2004, AIChE J, 50, 2738 [Google Scholar]
  37. Gurrutxaga, N., Vaikundaraman, V., & Drazkowska, J. 2026, A&A, 709, A164 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  38. Güttler, C., Blum, J., Zsom, A., Ormel, C. W., & Dullemond, C. P. 2010, A&A, 513, A56 [Google Scholar]
  39. Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357 [NASA ADS] [CrossRef] [Google Scholar]
  40. Hayashi, C. 1981, Prog. Theor. Phys. Suppl., 70, 35 [Google Scholar]
  41. Hernquist, L. 1987, ApJS, 64, 715 [NASA ADS] [CrossRef] [Google Scholar]
  42. Hirashita, H., Il’in, V. B., Pagani, L., & Lefèvre, C. 2021, MNRAS, 502, 15 [NASA ADS] [CrossRef] [Google Scholar]
  43. Hulburt, H. M., & Katz, S. 1964, Chem. Eng. Sci., 19, 555 [Google Scholar]
  44. Hunter, J. D. 2007, CiSE, 9, 90 [Google Scholar]
  45. Johansen, A., Oishi, J. S., Low, M.-M. M., et al. 2007, Nature, 448, 1022 [NASA ADS] [CrossRef] [Google Scholar]
  46. Johansen, A., Brauer, F., Dullemond, C., Klahr, H., & Henning, T. 2008, A&A, 486, 597 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  47. Kataoka, A., Tanaka, H., Okuzumi, S., & Wada, K. 2013a, A&A, 557, L4 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  48. Kataoka, A., Tanaka, H., Okuzumi, S., & Wada, K. 2013b, A&A, 554, A4 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  49. Kazeev, V. A., Khoromskij, B. N., & Tyrtyshnikov, E. E. 2013, SIAM J. Sci. Comput., 35, A1511 [Google Scholar]
  50. Knuth, D. E. 1997, The Art of Computer Programming: Fundamental Algorithms, 1 (Addison-Wesley Professional) [Google Scholar]
  51. Kobayashi, H., & Tanaka, H. 2021, ApJ, 922, 16 [NASA ADS] [CrossRef] [Google Scholar]
  52. Kobayashi, M. I., Inutsuka, S.-i., Kobayashi, H., & Hasegawa, K. 2017, ApJ, 836, 175 [NASA ADS] [CrossRef] [Google Scholar]
  53. Kornet, K., Stepinski, T. F., & Różyczka, M. 2001, A&A, 378, 180 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  54. Kostoglou, M. 2007, J. Colloid Interface Sci., 306, 72 [Google Scholar]
  55. Kostoglou, M., & Konstandopoulos, A. G. 2001, J. Aerosol Sci., 32, 1399 [Google Scholar]
  56. Kostoglou, M., Konstandopoulos, A. G., & Friedlander, S. K. 2006, J. Aerosol Sci., 37, 1102 [Google Scholar]
  57. Kovetz, A., & Olund, B. 1969, J. Atmos. Sci. [Google Scholar]
  58. Krijt, S., Ormel, C. W., Dominik, C., & Tielens, A. G. G. M. 2015, A&A, 574, A83 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  59. Krijt, S., Ormel, C. W., Dominik, C., & Tielens, A. G. G. M. 2016, A&A, 586, A20 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Krijt, S., Schwarz, K. R., Bergin, E. A., & Ciesla, F. J. 2018, ApJ, 864, 78 [Google Scholar]
  61. Kumar, S., & Ramkrishna, D. 1996, Chem. Eng. Sci., 51, 1311 [Google Scholar]
  62. Laibe, G., & Lombart, M. 2022, MNRAS, 510, 5220 [Google Scholar]
  63. Laibe, G., Gonzalez, J.-F., Fouchet, L., & Maddison, S. T. 2008, A&A, 487, 265 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  64. Laurenzi, I. J., Bartels, J. D., & Diamond, S. L. 2002, J. Comput. Phys., 177, 418 [Google Scholar]
  65. Lebreuilly, U., Vallucci-Goy, V., Guillet, V., Lombart, M., & Marchand, P. 2023, MNRAS, 518, 3326 [Google Scholar]
  66. Lee, M. H. 2000, Icarus, 143, 74 [Google Scholar]
  67. Liu, H., Gröpler, R., & Warnecke, G. 2019, SIAM J. Sci. Comput., 41, B448 [CrossRef] [Google Scholar]
  68. Lombart, M., & Laibe, G. 2021, MNRAS, 501, 4298 [Google Scholar]
  69. Lombart, M., Hutchison, M., & Lee, Y.-N. 2022, MNRAS, 517, 2012 [CrossRef] [Google Scholar]
  70. Lombart, M., Bréhier, C.-E., Hutchison, M., & Lee, Y.-N. 2024, MNRAS, 533, 4410 [CrossRef] [Google Scholar]
  71. Lushnikov, A. A. 1976, J. Colloid Interface Sci., 54, 94 [Google Scholar]
  72. Ma, D. L., Tafti, D. K., & Braatz, R. D. 2002, Ind. Eng. Chem. Res., 41, 6217 [Google Scholar]
  73. Matveev, S. A., Zheltkov, D. A., Tyrtyshnikov, E. E., & Smirnov, A. P. 2016, J. Comput. Phys., 316, 164 [Google Scholar]
  74. McLeod, J. B. 1964, Proc. Lond. Math. Soc., 3, 445 [Google Scholar]
  75. Melzak, Z. 1957, Trans. Am. Math. Soc., 85, 547 [CrossRef] [Google Scholar]
  76. Michoulier, S., & Gonzalez, J.-F. 2022, MNRAS, 517, 3064 [NASA ADS] [CrossRef] [Google Scholar]
  77. Michoulier, S., Gonzalez, J.-F., & Price, D. J. 2024, A&A, 688, A31 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  78. Müller, H. 1928, Kolloidchem Beih, 27, 223 [Google Scholar]
  79. Nakagawa, Y., Nakazawa, K., & Hayashi, C. 1981, Icarus, 45, 517 [NASA ADS] [CrossRef] [Google Scholar]
  80. Nandanwar, M. N., & Kumar, S. 2008, Chem. Eng. Sci., 63, 2198 [Google Scholar]
  81. Nomura, H., & Nakagawa, Y. 2006, ApJ, 640, 1099 [Google Scholar]
  82. Öberg, K. I., Facchini, S., & Anderson, D. E. 2023, ARA&A, 61, 287 [Google Scholar]
  83. Ohtsuki, K., Nakagawa, Y., & Nakazawa, K. 1990, Icarus, 83, 205 [NASA ADS] [CrossRef] [Google Scholar]
  84. Okuzumi, S. 2009, ApJ, 698, 1122 [Google Scholar]
  85. Okuzumi, S., Tanaka, H., & Sakagami, M.-a. 2009, ApJ, 707, 1247 [NASA ADS] [CrossRef] [Google Scholar]
  86. Okuzumi, S., Tanaka, H., Takeuchi, T., & Sakagami, M.-a. 2011, ApJ, 731, 95 [Google Scholar]
  87. Okuzumi, S., Tanaka, H., Kobayashi, H., & Wada, K. 2012, ApJ, 752, 106 [NASA ADS] [CrossRef] [Google Scholar]
  88. Ormel, C. W., Spaans, M., & Tielens, A. G. G. M. 2007, A&A, 461, 215 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  89. Oseledets, I. V. 2011, SIAM J. Sci. Comput., 33, 2295 [Google Scholar]
  90. Oshiro, H., Tatsuuma, M., Okuzumi, S., & Tanaka, H. 2025, ApJ, 983, 75 [Google Scholar]
  91. Ossenkopf, V. 1993, A&A, 280, 617 [NASA ADS] [Google Scholar]
  92. O’Sullivan, D., & Rigopoulos, S. 2022, Chem. Eng. Sci., 263, 117925 [Google Scholar]
  93. Otto, E., Ajalova, A., Bück, A., Tsotsas, E., & Kienle, A. 2024, Ind. Eng. Chem. Res., 63, 17545 [Google Scholar]
  94. Pfeil, T., Birnstiel, T., & Klahr, H. 2024, A&A, 691, A45 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  95. Planes, M. B., Millán, E. N., Urbassek, H. M., & Bringa, E. M. 2021, MNRAS, 503, 1717 [CrossRef] [Google Scholar]
  96. Rafikov, R. R., Silsbee, K., & Booth, R. A. 2020, ApJS, 247, 65 [Google Scholar]
  97. Safronov, V. S. 1962, Dokl. Akad. Nauk SSSR, 147, 64 [Google Scholar]
  98. Safronov, V. S. 1972, Evolution of the Protoplanetary Cloud and Formation of the Earth and Planets (Israel Program for Scientific Translations, Keter Publishing House) [Google Scholar]
  99. Sato, T., Okuzumi, S., & Ida, S. 2016, A&A, 589, A15 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  100. Schumann, T. E. W. 1940, Quart. J. Roy. Meteorol. Soc., 66, 195 [Google Scholar]
  101. Scott, W. T. 1968, J. Atmos. Sci., 25, 54 [Google Scholar]
  102. Seigneur, C., Hudischewskyj, A. B., Seinfeld, J. H., et al. 1986, Aerosol Sci. Technol., 5, 205 [Google Scholar]
  103. Shimaki, Y., & Arakawa, M. 2012, Icarus, 221, 310 [NASA ADS] [CrossRef] [Google Scholar]
  104. Shimaki, Y., & Arakawa, M. 2021, Icarus, 369, 114646 [NASA ADS] [CrossRef] [Google Scholar]
  105. Silk, J., & Takahashi, T. 1979, ApJ, 229, 242 [NASA ADS] [CrossRef] [Google Scholar]
  106. Singh, M. 2021, Stud. Appl. Math., 147, 955 [Google Scholar]
  107. Singh, M., Kaur, G., De Beer, T., & Nopens, I. 2018, Reac. Kinet. Mech. Cat., 123, 385 [Google Scholar]
  108. Smirnov, A. P., Matveev, S. A., Zheltkov, D. A., & Tyrtyshnikov, E. E. 2016, Proc. Comput. Sci., 80, 2141 [Google Scholar]
  109. Solsvik, J., & Jakobsen, H. A. 2015, J. Dispers. Sci. Technol., 36, 510 [Google Scholar]
  110. Spouge, J. L. 1985, J. Phys. A, Math. Gen., 18, 3063 [Google Scholar]
  111. Stammler, S. M., & Birnstiel, T. 2022, ApJ, 935, 35 [NASA ADS] [CrossRef] [Google Scholar]
  112. Steinpilz, T., Joeris, K., Jungmann, F., et al. 2020, Nat. Phys., 16, 225 [Google Scholar]
  113. Stepinski, T. F., & Valageas, P. 1996, A&A, 309, 301 [NASA ADS] [Google Scholar]
  114. Stepinski, T. F., & Valageas, P. 1997, A&A, 319, 1007 [NASA ADS] [Google Scholar]
  115. Tanaka, H., Inaba, S., & Nakazawa, K. 1996, Icarus, 123, 450 [Google Scholar]
  116. Tanaka, H., Himeno, Y., & Ida, S. 2005, ApJ, 625, 414 [NASA ADS] [CrossRef] [Google Scholar]
  117. Tange, O. 2026, https://doi.org/10.5281/zenodo.18735643 [Google Scholar]
  118. Teiser, J., Penner, J., Joeris, K., et al. 2025, Nat Astron, 9, 535 [Google Scholar]
  119. The pandas development team 2020, https://doi.org/10.5281/zenodo.3509134 [Google Scholar]
  120. Vaikundaraman, V., Gurrutxaga, N., & Drążkowska, J. 2025, arXiv e-prints [arXiv:2507.21239] [Google Scholar]
  121. Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nat. Methods, 17, 261 [Google Scholar]
  122. von Smoluchowski, M. 1916, Z. Phys., 17, 585 [Google Scholar]
  123. Wei, J., & Kruis, F. E. 2013, J. Comput. Phys., 249, 67 [Google Scholar]
  124. Weidenschilling, S. J. 1977, MNRAS, 180, 57 [Google Scholar]
  125. Wetherill, G. W. 1990, Icarus, 88, 336 [NASA ADS] [CrossRef] [Google Scholar]
  126. Windmark, F., Birnstiel, T., Güttler, C., et al. 2012, A&A, 540, A73 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  127. Winn, J. N., & Fabrycky, D. C. 2015, ARA&A, 53, 409 [NASA ADS] [CrossRef] [Google Scholar]
  128. Xu, Z., Zhao, H., & Zheng, C. 2014, J. Aerosol Sci., 74, 11 [Google Scholar]
  129. Xu, Z., Zhao, H., & Zheng, C. 2015, J. Comput. Phys., 281, 844 [Google Scholar]
  130. Zagidullin, R., Smirnov, A., Matveev, S., & Tyrtyshnikov, E. 2019, in Supercomputing, eds. V. Voevodin & S. Sobolev (Cham: Springer International Publishing), 403 [Google Scholar]
  131. Zhang, W. 2014, in Nanomaterial: Impacts on Cell Biology and Medicine, eds. D. G. Capco, & Y. Chen (Dordrecht: Springer Netherlands), 19 [Google Scholar]
  132. Zhao, H., Kruis, F. E., & Zheng, C. 2010, J. Comput. Phys., 229, 6931 [Google Scholar]
  133. Ziff, R. M. 1980, J. Stat. Phys., 23, 241 [Google Scholar]
  134. Zsom, A., & Dullemond, C. P. 2008, A&A, 489, 931 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  135. Zsom, A., Ormel, C. W., Güttler, C., Blum, J., & Dullemond, C. P. 2010, A&A, 513, A57 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  136. Zsom, A., Ormel, C. W., Dullemond, C. P., & Henning, T. 2011, A&A, 534, A73 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]

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