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Annual Review of Chemical and Biomolecular Engineering

Volume 11, 2020

Cellular Automata in Chemistry and Chemical Engineering

Abstract

We review the modern state of cellular automata (CA) applications for solving practical problems in chemistry and chemical technology. We consider the problems of material structure modeling and prediction of materials’ morphology-dependent properties. We review the use of the CA approach for modeling diffusion, crystallization, dissolution, erosion, corrosion, adsorption, and hydration processes. We also consider examples of hybrid CA-based models, which are combinations of various CA with other computational approaches and modeling methods. Finally, we discuss the use of high-performance parallel computing to increase the efficiency of CA.

Keyword(s): cellular automata, chemical engineering, chemistry
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2020-06-07
2024-04-19
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Literature Cited

  1. 1. 
    Ilachinski A. 2001. Cellular Automata: A Discrete Universe Singapore: World Sci844 pp.
  2. 2. 
    Wolfram S. 2002. A New Kind of Science Champaign, IL: Wolfram Media
  3. 3. 
    Chopard B, Droz M. 2005. Cellular Automata Modeling of Physical Systems Cambridge, UK: Cambridge Univ. Press358 pp.
  4. 4. 
    von Neumann J. 1951. The general and logical theory of automata. Cerebral Mechanisms in Behavior LA Jeffress 1–41 Oxford, UK: Wiley
     [Google Scholar]
  5. 5. 
    Von Neumann J, Aspray W, Burks AW 1987. Papers of John von Neumann on Computing and Computer Theory Cambridge, MA/Los Angeles, CA: MIT Press, Tomash Publ624 pp.
  6. 6. 
    Raabe D. 2002. Cellular automata in materials science with particular reference to recrystallization simulation. Annu. Rev. Mater. Res. 32:53–76
     [Google Scholar]
  7. 7. 
    Toffoli T, Margolus NH. 1990. Invertible cellular automata: a review. Phys. Nonlinear Phenom. 45:1–3229–53
     [Google Scholar]
  8. 8. 
    Vanag VK. 1999. Study of spatially extended dynamical systems using probabilistic cellular automata. Phys.-Uspekhi 42:5413–34
     [Google Scholar]
  9. 9. 
    Toffoli T. 1984. Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Phys. Nonlinear Phenom. 10:1–2117–27
     [Google Scholar]
  10. 10. 
    D'Souza RM, Margolus NH, Smith MA 2002. Dimension-splitting for simplifying diffusion in lattice-gas models. J. Stat. Phys. 107:1–2401–22
     [Google Scholar]
  11. 11. 
    Lis M, Pintal L, Swiatek J, Cwiklik L 2012. GPU-based massive parallel Kawasaki kinetics in the dynamic Monte Carlo simulations of lipid nanodomains. J. Chem. Theory Comput. 8:114758–65
     [Google Scholar]
  12. 12. 
    Hallberg H. 2011. Approaches to modeling of recrystallization. Metals 1:116–48
     [Google Scholar]
  13. 13. 
    Humphreys FJ, Hatherly M. 2004. Recrystallization and Related Annealing Phenomena Amsterdam/Boston: Elsevier628 pp, 2nd ed..
  14. 14. 
    Rollett AD. 1997. Overview of modeling and simulation of recrystallization. Prog. Mater. Sci. 42:1–479–99
     [Google Scholar]
  15. 15. 
    Lee HW, Im Y-T. 2010. Cellular automata modeling of grain coarsening and refinement during the dynamic recrystallization of pure copper. Mater. Trans. 51:91614–20
     [Google Scholar]
  16. 16. 
    Yazdipour N, Davies CHJ, Hodgson PD 2008. Microstructural modeling of dynamic recrystallization using irregular cellular automata. Comput. Mater. Sci. 44:2566–76
     [Google Scholar]
  17. 17. 
    Kugler G, Turk R. 2004. Modeling the dynamic recrystallization under multi-stage hot deformation. Acta Mater 52:154659–68
     [Google Scholar]
  18. 18. 
    Zhu MF, Hong CP. 2002. A three dimensional modified cellular automaton model for the prediction of solidification microstructures. ISIJ Int 42:5520–26
     [Google Scholar]
  19. 19. 
    Gandin Ch-A, Rappaz M. 1994. A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes. Acta Metall. Mater. 42:72233–46
     [Google Scholar]
  20. 20. 
    Miller W, Succi S, Mansutti D 2001. Lattice Boltzmann model for anisotropic liquid-solid phase transition. Phys. Rev. Lett. 86:163578–81
     [Google Scholar]
  21. 21. 
    Krivovichev SV. 2012. Algorithmic crystal chemistry: a cellular automata approach. Crystallogr. Rep. 57:110–17
     [Google Scholar]
  22. 22. 
    Raabe D. 2004. Mesoscale simulation of spherulite growth during polymer crystallization by use of a cellular automaton. Acta Mater 52:92653–64
     [Google Scholar]
  23. 23. 
    Svyetlichnyy DS. 2014. A three-dimensional frontal cellular automaton model for simulation of microstructure evolution—initial microstructure module. Model. Simul. Mater. Sci. Eng. 22:8085001
     [Google Scholar]
  24. 24. 
    Raabe D. 1999. Introduction of a scalable three-dimensional cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena. Philos. Mag. A 79:102339–58
     [Google Scholar]
  25. 25. 
    Raabe D, Godara A. 2005. Mesoscale simulation of the kinetics and topology of spherulite growth during crystallization of isotactic polypropylene (iPP) by using a cellular automaton. Model. Simul. Mater. Sci. Eng. 13:5733
     [Google Scholar]
  26. 26. 
    Burbelko A, Falkus J, Kapturkiewicz W, Sołek K, Drożdż P, Wróbel M 2012. Modeling of the grain structure formation in the steel continuous ingot by Cafe Method. Arch. Metall. Mater. 57:1379–84
     [Google Scholar]
  27. 27. 
    Szeliga D, Kubiak K, Burbelko AA, Cygan R, Ziaja W 2013. Modelling of grain microstructure of IN-713C castings. Solid State Phenom 197:83–88
     [Google Scholar]
  28. 28. 
    Zhu MF, Kim JM, Hong CP 2001. Modeling of globular and dendritic structure evolution in solidification of an Al–7mass%Si alloy. ISIJ Int 41:9992–98
     [Google Scholar]
  29. 29. 
    Ivanova TB, Erdakova NN, Vaskin VV 2006. Cellular automatic model for modelling phase structure of the undercooled binary alloy. Vestnik Udmurtskogo Universiteta in Russian )
     [Google Scholar]
  30. 30. 
    Hurley PJ, Humphreys FJ. 2003. Modelling the recrystallization of single-phase aluminium. Acta Mater 51:133779–93
     [Google Scholar]
  31. 31. 
    Qian M, Guo ZX. 2004. Cellular automata simulation of microstructural evolution during dynamic recrystallization of an HY-100 steel. Mater. Sci. Eng. A 365:1–2180–85
     [Google Scholar]
  32. 32. 
    Chen F, Qi K, Cui Z, Lai X 2014. Modeling the dynamic recrystallization in austenitic stainless steel using cellular automaton method. Comput. Mater. Sci. 83:331–40
     [Google Scholar]
  33. 33. 
    Svyetlichnyy DS. 2010. Modelling of the microstructure: from classical cellular automata approach to the frontal one. Comput. Mater. Sci. 50:192–97
     [Google Scholar]
  34. 34. 
    Zheng C, Raabe D, Li D 2012. Prediction of post-dynamic austenite-to-ferrite transformation and reverse transformation in a low-carbon steel by cellular automaton modeling. Acta Mater 60:124768–79
     [Google Scholar]
  35. 35. 
    Zheng C, Raabe D. 2013. Interaction between recrystallization and phase transformation during intercritical annealing in a cold-rolled dual-phase steel: a cellular automaton model. Acta Mater 61:145504–17
     [Google Scholar]
  36. 36. 
    Song KJ, Wei YH, Dong ZB, Zhan XH, Zheng WJ, Fang K 2013. Numerical simulation of β to α phase transformation in heat affected zone during welding of TA15 alloy. Comput. Mater. Sci. 72:93–100
     [Google Scholar]
  37. 37. 
    Svyetlichnyy DS, Mikhalyov AI. 2014. Three-dimensional frontal cellular automata model of microstructure evolution—phase transformation module. ISIJ Int 54:61386–95
     [Google Scholar]
  38. 38. 
    Palmiere EJ 2002. Conference Proceedings—International Conference on Thermomechanical Processing: Mechanics, Microstructure & Control: 23–26 June 2002, the University of Sheffield, England Sheffield, UK: Dep. Eng. Mater486 pp.
     [Google Scholar]
  39. 39. 
    Svyetlichnyy D, Majta J, Muszka K, Łach Ł 2011. Modeling of microstructure evolution of BCC metals subjected to severe plastic deformation. AIP Conf. Proc. 1315:1473
     [Google Scholar]
  40. 40. 
    Svyetlichnyy DS. 2013. Modeling of grain refinement by cellular automata. Comput. Mater. Sci. 77:408–16
     [Google Scholar]
  41. 41. 
    Körner C, Singer RF. 1999. Numerical simulation of foam formation and evolution with modified cellular automata. Metal Foams and Porous Metal Structures J Banhart, MF Ashby, NA Fleck 91–96 Bremen, Ger.: Verlag MIT Publ.
     [Google Scholar]
  42. 42. 
    Meakin P. 1999. A historical introduction to computer models for fractal aggregates. J. Sol-Gel Sci. Technol. 15:297–117
     [Google Scholar]
  43. 43. 
    Fry D, Mohammad A, Chakrabarti A, Sorensen CM 2004. Cluster shape anisotropy in irreversibly aggregating particulate systems. Langmuir 20:187871–79
     [Google Scholar]
  44. 44. 
    Sander LM. 2000. Diffusion-limited aggregation: A kinetic critical phenomenon. ? Contemp. Phys. 41:4203–18
     [Google Scholar]
  45. 45. 
    D'Souza RM, Margolus NH. 1998. A thermodynamically reversible generalization of diffusion limited aggregation. Phys. Rev. E 60:1264–74
     [Google Scholar]
  46. 46. 
    Eden M. 1961. A two-dimensional growth process. Proc. Fourth Berkeley Symp. Math Stat. Prob. 4:223–39
     [Google Scholar]
  47. 47. 
    Meakin P. 1983. Formation of fractal clusters and networks by irreversible diffusion-limited aggregation. Phys. Rev. Lett. 51:131119–22
     [Google Scholar]
  48. 48. 
    Finegold L. 1976. Cell membrane fluidity: molecular modeling of particle aggregations seen in electron microscopy. Biochim. Biophys. Acta 448:2393–98
     [Google Scholar]
  49. 49. 
    Jullien R, Kolb M. 1984. Hierarchical model for chemically limited cluster-cluster aggregation. J. Phys. Math. Gen. 17:12L639–43
     [Google Scholar]
  50. 50. 
    Aegerter MA, Leventis N, Koebel MM 2011. Aerogels Handbook New York: Springer
  51. 51. 
    Brouwers HJH, de Korte ACJ 2016. Multi-cycle and multi-scale cellular automata for hydration simulation (of Portland-cement). Comput. Mater. Sci. 111:116–24
     [Google Scholar]
  52. 52. 
    Puchkov M, Tschirky D, Leuenberger H 2013. 3-D cellular automata in computer-aided design of pharmaceutical formulations: mathematical concept and F-CAD software. Formulation Tools for Pharmaceutical Development JE Aguilar 155–201 Woodhead Publ. Ser. Biomed Swaston, UK: Woodhead Publ.
     [Google Scholar]
  53. 53. 
    Mitrofanov I, Malysheva I, Kolnoochenko A, Menshutina N 2017. Modelling of aerogels structures using intelligent system “AeroGen Structure. .” Comput. Aided Chem. Eng. 40:469–74
     [Google Scholar]
  54. 54. 
    Brady RM, Ball RC. 1984. Fractal growth of copper electrodeposits. Nature 309:5965225–29
     [Google Scholar]
  55. 55. 
    Niemeyer L, Pietronero L, Wiesmann HJ 1984. Fractal dimension of dielectric breakdown. Phys. Rev. Lett. 52:121033–36
     [Google Scholar]
  56. 56. 
    Daccord G, Nittmann J, Stanley HE 1986. Radial viscous fingers and diffusion-limited aggregation: fractal dimension and growth sites. Phys. Rev. Lett. 56:4336–39
     [Google Scholar]
  57. 57. 
    Daccord G, Lenormand R. 1987. Fractal patterns from chemical dissolution. Nature 325:609941–43
     [Google Scholar]
  58. 58. 
    Honjo H, Ohta S, Matsushita M 1986. Irregular fractal-like crystal growth of ammonium chloride. J. Phys. Soc. Jpn. 55:82487–90
     [Google Scholar]
  59. 59. 
    Radnoczi Gy, Vicsek T, Sander LM, Grier D 1987. Growth of fractal crystals in amorphous GeSe2 films. Phys. Rev. A 35:94012–15
     [Google Scholar]
  60. 60. 
    Calemczuk R, de Goer AM, Salce B, Maynard R, Zarembowitch A 1987. Low-temperature properties of silica aerogels. Europhys. Lett. 3:111205–11
     [Google Scholar]
  61. 61. 
    Vertyagina Y, Marrow TJ. 2017. A multi-scale three-dimensional cellular automata fracture model of radiolytically oxidised nuclear graphite. Carbon 121:574–90
     [Google Scholar]
  62. 62. 
    Vertyagina Y, Marrow TJ. 2016. 3D cellular automata fracture model for porous graphite microstructures. Nucl. Eng. Des. 323:202–8
     [Google Scholar]
  63. 63. 
    Ivanov S, Tyrtyshnikov A, Tsygankov P, Menshutina N 2016. Mathematical modelling of carbon nanotubes aerogel structure, electrical and thermal conductivity. Proceedings of the 16th International Multidisciplinary Scientific GeoConference, June 28–July 16, Book 6 Vol 1221–28 Sofia: Surv. Geol. Min. Ecol. Manag.
     [Google Scholar]
  64. 64. 
    Pan P-Z, Feng X-T, Hudson JA 2009. Study of failure and scale effects in rocks under uniaxial compression using 3D cellular automata. Int. J. Rock Mech. Miner. Sci. 46:4674–85
     [Google Scholar]
  65. 65. 
    Moiseenko DD, Panin VE, Maksimov PV, Panin SV, Berto F 2014. Material fragmentation as dissipative process of micro rotation sequence formation: hybrid model of excitable cellular automata. AIP Conf. Proc. 1623:427–30
     [Google Scholar]
  66. 66. 
    Smolin AY, Roman NV, Konovalenko IS, Eremina GM, Buyakova SP, Psakhie SG 2014. 3D simulation of dependence of mechanical properties of porous ceramics on porosity. Eng. Fract. Mech. 130:53–64
     [Google Scholar]
  67. 67. 
    Psakhie SG, Moiseyenko DD, Smolin AY, Shilko EV, Dmitriev AI et al. 1999. The features of fracture of heterogeneous materials and frame structures. Potentialities of MCA design. Comput. Mater. Sci. 16:1–4333–43
     [Google Scholar]
  68. 68. 
    Biggs MJ, Humby SJ. 1998. Lattice-gas automata methods for engineering. Chem. Eng. Res. Des. 76:2162–74
     [Google Scholar]
  69. 69. 
    Wells JT, Janecky DR, Travis BJ 1991. A lattice gas automata model for heterogeneous chemical reactions at mineral surfaces and in pore networks. Phys. Nonlinear Phenom. 47:1–2115–23
     [Google Scholar]
  70. 70. 
    Demontis P, Pazzona FG, Suffritti GB 2006. A lattice-gas cellular automaton to model diffusion in restricted geometries. J. Phys. Chem. B 110:2713554–59
     [Google Scholar]
  71. 71. 
    Toffoli T, Capobianco S, Mentrasti P 2008. When—and how—can a cellular automaton be rewritten as a lattice gas. ? Theor. Comput. Sci. 403:171–88
     [Google Scholar]
  72. 72. 
    Toffoli T, Margolus N. 1987. Cellular Automata Machines: A New Environment for Modeling Cambridge, MA: MIT Press284 pp.
  73. 73. 
    Bandman OL. 2007. A cellular automata convection-diffusion model of flows through porous media. Optoelectron. Instrum. Data Process. 43:6524–29
     [Google Scholar]
  74. 74. 
    Di Maio FP, Lignola PG, Di Gregorio S 2000. Cellular automata simulation of coal combustion. Phys. Chem. Chem. Phys. 2:183–89
     [Google Scholar]
  75. 75. 
    Roussel MR, Lim C. 1995. Dynamic model of lignin growing in restricted spaces. Macromolecules 28:1370–76
     [Google Scholar]
  76. 76. 
    Gurikov P, Kolnoochenko A, Golubchikov M, Menshutina N, Smirnova I 2016. A synchronous cellular automaton model of mass transport in porous media. Comput. Chem. Eng. 84:446–57
     [Google Scholar]
  77. 77. 
    Raabe D, Hantcherli L. 2005. 2D cellular automaton simulation of the recrystallization texture of an IF sheet steel under consideration of Zener pinning. Comput. Mater. Sci. 34:4299–313
     [Google Scholar]
  78. 78. 
    Lin JX, Wang CY, Zheng YY 2008. Prediction of isothermal crystallization parameters in monomer cast nylon 6. Comput. Chem. Eng. 32:123023–29
     [Google Scholar]
  79. 79. 
    Libbrecht KG. 2008. Physically derived rules for simulating faceted crystal growth using cellular automata. arXiv:0807.2616
  80. 80. 
    Burbelko A, Fraś E, Kapturkiewicz W, Olejnik E 2004. Cellular automata diffusion-kinetic model of dendritic growth. Cell. Autom. 2004:355–64
     [Google Scholar]
  81. 81. 
    Krane MJM, Johnson DR, Raghavan S 2009. The development of a cellular automaton-finite volume model for dendritic growth. Appl. Math. Model. 33:52234–47
     [Google Scholar]
  82. 82. 
    Krivovichev SV. 2010. Actinyl compounds with hexavalent elements (S, Cr, Se, Mo)—structural diversity, nanoscale chemistry, and cellular automata modeling. Eur. J. Inorg. Chem. 2010 18:2594–603
     [Google Scholar]
  83. 83. 
    Kimber JA, Kazarian SG, Štěpánek F 2011. Microstructure-based mathematical modelling and spectroscopic imaging of tablet dissolution. Comput. Chem. Eng. 35:71328–39
     [Google Scholar]
  84. 84. 
    Laaksonen TJ, Laaksonen HM, Hirvonen JT, Murtomäki L 2009. Cellular automata model for drug release from binary matrix and reservoir polymeric devices. Biomaterials 30:101978–87
     [Google Scholar]
  85. 85. 
    Jia X, Williams RA. 2007. A hybrid mesoscale modelling approach to dissolution of granules and tablets. Chem. Eng. Res. Des. 85:71027–38
     [Google Scholar]
  86. 86. 
    Gan M, Gopinathan N, Jia X, Williams RA 2004. Predicting packing characteristics of particles of arbitrary shapes. KONA Powder Part. J. 22:82–93
     [Google Scholar]
  87. 87. 
    Succi S. 2001. The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond Oxford, UK: Oxford Univ. Press308 pp.
  88. 88. 
    Bertrand N, Leclair G, Hildgen P 2007. Modeling drug release from bioerodible microspheres using a cellular automaton. Int. J. Pharm. 343:1–2196–207
     [Google Scholar]
  89. 89. 
    Bezbradica M, Ruskin HJ, Crane M 2014. Comparative analysis of asynchronous cellular automata in stochastic pharmaceutical modelling. J. Comput. Sci. 5:5834–40
     [Google Scholar]
  90. 90. 
    Campiñez MD, Caraballo I, Puchkov M, Kuentz M 2016. Novel polyurethane matrix systems reveal a particular sustained release behavior studied by imaging and computational modeling. AAPS PharmSciTech 18:1544–53
     [Google Scholar]
  91. 91. 
    Eberle VA, Häring A, Schoelkopf J, Gane PAC, Huwyler J, Puchkov M 2016. In silico and in vitro methods to optimize the performance of experimental gastroretentive floating mini-tablets. Drug Dev. Ind. Pharm. 42:5808–17
     [Google Scholar]
  92. 92. 
    Fathi M, Mohebbi M, Varshosaz J, Shahidi F 2012. Cellular automata modeling of hesperetin release phenomenon from lipid nanocarriers. Food Bioprocess Technol 6:113134–42
     [Google Scholar]
  93. 93. 
    Bezbradica M, Barat A, Ruskin H, Crane M 2010. Probabilistic models for dissolution of ethylcellulose coated microspheres Presented at ESM 2010—European Simulation and Modeling Conference, Hasselt, Belg., Oct25–27
  94. 94. 
    Gurikov PA, Kolnoochenko AV, Menshutina NV 2009. 3D reversible cellular automata for simulation of the drug release from aerogel-drug formulations. Comput. Aided Chem. Eng. 26:943–47
     [Google Scholar]
  95. 95. 
    Ivanov SI, Lovskaya DD, Menshutina NV 2013. Cellular automata modeling of dissolution of solid-dosage forms. Comput. Aided Chem. Eng. 32:883–88
     [Google Scholar]
  96. 96. 
    Ivanov SI, Tiptsova IA, Menshutina NV 2015. Modeling dissolution of solids based on cellular automata with changing sizes of cells. Comput. Aided Chem. Eng. 37:605–10
     [Google Scholar]
  97. 97. 
    Pérez-Brokate CF, di Caprio D, Féron D, De Lamare J, Chaussé A 2014. Overview of cellular automaton models for corrosion. Cellular Automata J Wąs, GC Sirakoulis, S Bandini 8751187–96 Cham, Switz.: Springer Int. Publ.
     [Google Scholar]
  98. 98. 
    Meakin P, Jøssang T, Feder J 1993. Simple passivation and depassivation model for pitting corrosion. Phys. Rev. E 48:42906–16
     [Google Scholar]
  99. 99. 
    Taleb A, Chaussé A, Dymitrowska M, Stafiej J, Badiali JP 2004. Simulations of corrosion and passivation phenomena:diffusion feedback on the corrosion rate. J. Phys. Chem. B 108:3952–58
     [Google Scholar]
  100. 100. 
    Córdoba-Torres P, Nogueira RP, de Miranda L, Brenig L, Wallenborn J, Fairén V 2001. Cellular automaton simulation of a simple corrosion mechanism: mesoscopic heterogeneity versus macroscopic homogeneity. Electrochim. Acta 46:192975–89
     [Google Scholar]
  101. 101. 
    Kortlüke O. 1998. A general cellular automaton model for surface reactions. J. Phys. Math. Gen. 31:469185
     [Google Scholar]
  102. 102. 
    Van der Weeën P, Zimer AM, Pereira EC, Mascaro LH, Bruno OM, De Baets B 2014. Modeling pitting corrosion by means of a 3D discrete stochastic model. Corros. Sci. 82:133–44
     [Google Scholar]
  103. 103. 
    Sun B, Fan W, Chakraborty A 2017. Adsorption kinetics emulation with lattice gas cellular automata. Heat Transf. Eng. 38:4409–16
     [Google Scholar]
  104. 104. 
    Bullard JW. 2008. A determination of hydration mechanisms for tricalcium silicate using a kinetic cellular automaton model. J. Am. Ceram. Soc. 91:72088–97
     [Google Scholar]
  105. 105. 
    Bonchev D, Thomas S, Apte A, Kier LB 2010. Cellular automata modelling of biomolecular networks dynamics. SAR QSAR Environ. Res. 21:1–277–102
     [Google Scholar]
  106. 106. 
    Markova VP, Sharifulina AE. 2011. Parallel implementation of the asynchronous cellular automata modelling CO oxidation on palladium. Prikl. Diskretn. Mat. 1:11116–26 in Russian )
     [Google Scholar]
  107. 107. 
    Kireeva A. 2015. Two-layer CA for simulation of catalytic reaction at dynamically varying surface temperature. J. Comput. Sci. 11:317–25
     [Google Scholar]
  108. 108. 
    Van der Weeën P, Baetens JM, Verwaeren J, Van Doorslaer X, Heynderickx PM et al. 2012. Modeling the photocatalytic degradation of moxifloxacin by means of a stochastic cellular automaton. Chem. Eng. J. 188:181–90
     [Google Scholar]
  109. 109. 
    Scalise D, Schulman R. 2016. Emulating cellular automata in chemical reaction-diffusion networks. Nat. Comput. 15:2197–214
     [Google Scholar]
  110. 110. 
    Bandman O. 2001. A hybrid approach to reaction-diffusion processes simulation. Parallel Computing Technologies V Malyshkin 1–16 Berlin/Heidelberg: Springer
     [Google Scholar]
  111. 111. 
    Van der Weeen P. 2014. Meso-scale modeling of reaction-diffusion processes using cellular automata PhD Thesis, Dep. Math. Model., Ghent Univ Ghent, Belg:.
  112. 112. 
    Bandman O. 2002. Cellular-neural automaton: a hybrid model for reaction-diffusion simulation. Futur. Gener. Comput. Syst. 18:6737–45
     [Google Scholar]
  113. 113. 
    Ziff RM, Fichthorn K, Gulari E 1991. Cellular automaton version of the AB2 reaction model obeying proper stoichiometry. J. Phys. Math. Gen. 24:153727
     [Google Scholar]
  114. 114. 
    Mai J, Kuzovkov VN, von Niessen W 1994. Stochastic model for the A+B2 surface reaction: island formation and complete segregation. J. Chem. Phys. 100:86073–81
     [Google Scholar]
  115. 115. 
    Clementi E, Corongiu G. 2005. Comments on computational chemistry: from diatomic molecules to large biochemical systems. Int. J. Quantum Chem. 105:6709–30
     [Google Scholar]
  116. 116. 
    Wolfram S. 1986. Cellular automaton fluids 1: basic theory. J. Stat. Phys. 45:3–4471–526
     [Google Scholar]
  117. 117. 
    Liao Q, Wang Y-J, Wang Y-Z, Chen R, Zhu X et al. 2012. Two-dimension mathematical modeling of photosynthetic bacterial biofilm growth and formation. Int. J. Hydrog. Energy 37:2015607–15
     [Google Scholar]
  118. 118. 
    Picioreanu C, Van Loosdrecht MC, Heijnen JJ 1998. Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol. Bioeng. 58:1101–16
     [Google Scholar]
  119. 119. 
    Song J, Kinney KA. 2002. A model to predict long-term performance of vapor-phase bioreactors: a cellular automaton approach. Environ. Sci. Technol. 36:112498–507
     [Google Scholar]
  120. 120. 
    Fernando A. 2000. A cellular automata approach to CFD flame spread modelling. Fire Saf. Sci. 6:625–36
     [Google Scholar]
  121. 121. 
    Psakhie S, Shilko E, Smolin A, Astafurov S, Ovcharenko V 2013. Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials. Frat. Integrità Strutt. 7:2426–59
     [Google Scholar]
  122. 122. 
    Salazar R, Gelb LD. 2007. A computational study of the reconstruction of amorphous mesoporous materials from gas adsorption isotherms and structure factors via evolutionary optimization. Langmuir 23:2530–41
     [Google Scholar]
  123. 123. 
    Testa B, Kier LB, Cheng C-K, Mayer J 2001. A cellular automata study of constraints (dissolvence) in a percolating many-particle system. Entropy 3:227–57
     [Google Scholar]
  124. 124. 
    Chopard B, Masselot A, Dupuis A 2000. A lattice gas model for erosion and particles transport in a fluid. Comput. Phys. Commun. 129:1–3167–76
     [Google Scholar]
  125. 125. 
    Kari J, Taati S. 2015. Statistical mechanics of surjective cellular automata. J. Stat. Phys. 160:51198–243
     [Google Scholar]
  126. 126. 
    Kari J, Taati S. 2011. Conservation laws and invariant measures in surjective cellular automata Presented at the 17th International Workshop on Cellular Automata and Discrete Complex Systems Santiago, Chile:
  127. 127. 
    Mairesse J, Marcovici I. 2014. Around probabilistic cellular automata. Theor. Comput. Sci. 559:42–72
     [Google Scholar]
  128. 128. 
    An D, Chen S, Sun D, Pan S, Krakauer BW, Zhu M 2019. A cellular automaton model integrated with CALPHAD-based thermodynamic calculations for ferrite-austenite phase transformations in multicomponent alloys. Comput. Mater. Sci. 166:210–20
     [Google Scholar]
  129. 129. 
    Chen F, Cui Z, Liu J, Zhang X, Chen W 2009. Modeling and simulation on dynamic recrystallization of 30Cr2Ni4MoV rotor steel using the cellular automaton method. Model. Simul. Mater. Sci. Eng. 17:7075015
     [Google Scholar]
  130. 130. 
    Burbelko AA, Fraś E, Kapturkiewicz W, Gurgul D 2010. Modelling of dendritic growth during unidirectional solidification by the method of cellular automata. Mater. Sci. Forum. 649:217–22
     [Google Scholar]
  131. 131. 
    Salem JB, Wolfram S. 1985. Thermodynamics and hydrodynamics with cellular automata. Cellular Automata and Complexity: Collected Papers S Wolfram Boca Raton, FL: CRC Press
     [Google Scholar]
  132. 132. 
    Bagnoli F, Rechtman R. 2009. Thermodynamic entropy and chaos in a discrete hydrodynamical system. Phys. Rev. E 79:4041115
     [Google Scholar]
  133. 133. 
    Kolnoochenko A, Gurikov P, Menshutina N 2011. General-purpose graphics processing units application for diffusion simulation using cellular automata. Comput. Aided Chem. Eng. 29:166–70
     [Google Scholar]
  134. 134. 
    Bandman O. 2016. Parallelization efficiency versus stochasticity in simulation reaction-diffusion by cellular automata. J. Supercomput. 73:2687–99
     [Google Scholar]
  135. 135. 
    Bandman O. 2013. 3-D cellular automata model of fluid permeation through porous material. Parallel Computing Technologies V Malyshkin 278–90 Berlin/Heidelberg: Springer
     [Google Scholar]
  136. 136. 
    Brieger L, Bonomi E. 1992. Cellular automata—lattice gas models for PDE's. Comput. Phys. Commun. 73:1–347–60
     [Google Scholar]
  137. 137. 
    Hansen PB. 1993. Parallel cellular automata: a model program for computational science. Concurr. Pract. Exp. 5:5425–48
     [Google Scholar]
  138. 138. 
    Ferrando N, Gosálvez MA, Cerdá J, Gadea R, Sato K 2011. Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces. Comput. Phys. Commun. 182:3628–40
     [Google Scholar]
  139. 139. 
    Bezbradica M, Crane M, Ruskin HJ 2012. Parallelisation strategies for large scale cellular automata frameworks in pharmaceutical modelling Paper presented at the 2012 International Conference on High Performance Computing and Simulation (HPCS) Madrid:223–30 https://doi.org/10.1109/HPCSim.2012.6266916
    [Crossref]
  140. 140. 
    Rybacki S, Himmelspach J, Uhrmacher AM 2009. Experiments with single core, multi-core, and GPU based computation of cellular automata Paper presented at the 2009 First International Conference on Advances in System Simulation. Porto, Port:62–67 https://doi.org/10.1109/SIMUL.2009.36
    [Crossref] [Google Scholar]
  141. 141. 
    Kalgin K. 2010. Comparative study of parallel algorithms for asynchronous cellular automata simulation on different computer architectures. Cell. Autom. 6350:399–408
     [Google Scholar]
/content/journals/10.1146/annurev-chembioeng-093019-075250
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Cellular Automata in Chemistry and Chemical Engineering
Annual Review of Chemical and Biomolecular Engineering 11, 87 (2020); https://doi.org/10.1146/annurev-chembioeng-093019-075250
/content/journals/10.1146/annurev-chembioeng-093019-075250
/content/journals/10.1146/annurev-chembioeng-093019-075250
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