A cellular automaton model for description of the free diffusion process at the initial stage of nanowire formation — Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki

1. Evsutin O.O., Rososhek S.K. [Use of cellular automatons for problems solving of information transformation]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2012, vol. 1, no. 25, part 1, рp. 173–174 (in Russ.).
2. Evsutin O.O., Shelupanov A.A. [Applications of cellular automata in the field of information security and data processing]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2012, vol. 1, no. 25, part 2, pp. 119–125 (in Russ.).
3. Evsutin O.O. [The complex of programmes for the construction and research of decorrelating cellular transformations and for the compression of digital images on the base of it]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2012, vol. 1, no. 25, part 2, pp. 220–224 (in Russ.).
4. Evsutin O.O., Milikhin M.M. [Compression of digital images, used in geo-information system of electronic general plan in an industrial enterprise]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2012, vol. 2, no. 26, part 1, pp. 224–229 (in Russ.).
5. Evsutin O.O., Negacheva E.V. [Steganographic embedding of information into digital images compressed with the use of block cellular automata]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2013, vol. 4, no. 30, pp. 130–135 (in Russ.).
6. Evsutin O.O., Shelupanov A.A. [Basic approaches to the use of mathematical apparatus of cellular automata theory for the tasks of encoding information]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2014, vol. 2, no. 32, pp. 60–65 (in Russ).
7. Bondarenko D.O., Evsutin O.O., Rashchupkina A.V. [Continuous optimization using cellular automata by choosing the evolution rule]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2015, vol. 4, no. 38, pp. 119–122 (in Russ.).
8. Evsutin O.O., Shelupanov A.A., Babishin V.D., Sosedko K.A. [Continuous optimization using a hybrid model of cellular automata and learning automata]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2019, vol. 1, no. 22, pp. 50–54 (in Russ.).
9. Achasova S.M. [Cellular automaton self-reproducing matrix from artificial biological cells]. Problemy informatiki, 2016, no. 3, pp. 13–25 (in Russ.).
10. Markov M.A. Ispol'zovanie kletochnyh avtomatov dlya modelirovaniya ontogeneza [The use of cellular automata for modeling ontogenesis]. Young scientist, 2010. vol. 1, no. 16, pp. 118–125.
11. Janssens K.G.F. An introductory review of cellular automata modeling of moving grain boundaries in polycrystalline materials. Mathematics and Computers in Simulation. 2010, vol. 80, pp. 1361–1381.
12. Gilpin W. Cellular automata as convolutional neural networks. Phys. Rev. E. 2019, vol. 100, pp. 032402–032413.
13. Comelli, T., Pinel F., Bouvry P. Comparing Elementary Cellular Automata Classifications with a Convolutional Neural Network. In Proceedings of the 13th International Conference on Agents and Artificial Intelligence. Science and Technology Publications, Lda, 2021, vol. 2, pp. 467–474.
14. Najarro E., Sudhakaran Sh., Risi S. Towards Self-Assembling Artificial Neural Networks through Neural Developmental Programs. Available at: https://arxiv.org/abs/2307.08197 (Аccessed: 19 January 2026).
15. Mokretsov N.S., Tatarnikova T.M. [Self-Organizing Neural Cellular Automata for Reinforcement Learning and Evolutionary Development]. LETI Transactions on Electrical Engineering & Computer Science, 2023, vol. 16, no. 7. pp. 68–75 (in Russ.).
16. Rollier M., Daly A.J., Baetens J.M. Convolutional Neural Networks for Automated Cellular Automaton Classification. Available at: https://arxiv.org/abs/2409.02740 (Аccessed: 19 January 2026).
17. Raboty po odnorodnym strukturam i kletochnym avtomatam, vypolnennye v SSSR, Rossii i byvshih respublikah SSSR [Works on homogeneous structures and cellular automata performed in the USSR, Russia and former Soviet republics – Virtual Computer Museum]. Available at: https://computer-museum.ru/articles/books/1066/?sphrase_id=1353857 (Аccessed: 19 January 2026) (in Russ.).
18. Matyushkin I.V., Zapletina M.A. [Cellular automata review based on modern domestic publications]. Computer Research and Modeling, 2019, vol. 11, no. 1, pp. 9–57.
19. Sabelfeld K.K., Kaganer V.M., Limbach F., Dogan P., Brandt O., Geelhaar L., Riechert H. Height self-equilibration during the growth of dense nanowire ensembles: order emerging from disorder. Applied Physics Letters, 2013, vol. 103, pp. 181–189.
20. Sabelfeld K.K., Kablukova E.G. A stochastic model of the nanowires growth by molecular beam epitaxy. Siberian J. Num. Math. Sib. Branch of Russ. Acad. of Sci, Novosibirsk, 2017, vol. 20, no. 2, pp. 181–199.
21. Lushnikov D.A., Shipulya M.A., Hervier Yu.Yu. Analiz fenomenologicheskikh modelei rosta nitevidnykh nanokristallov [Analysis of phenomenological models of the growth of filamentous nanocrystals]. Prospects of fundamental sciences development: Proceedings of the XXI International Conference of Students, Graduate Students and Young Scientists, Tomsk, Publishing House of TPU, 2023, vol. 1: Physics, pp. 258–260.
22. Kuznetsov K.A. Kinetika obrazovaniya i dvizheniya stupenej na bokovyh granyah nitevidnogo nanokristalla pri nalichii bar'era Erliha-Shvebelya [Kinetics of formation and movement of steps on the lateral faces of a filamentous nanocrystal in the presence of an Ehrlich-Schwebel barrier]. Bachelor's thesis, field of study: 03.03.02. Physics, Tomsk, 2016, 40 p. (in Russ.).
23. Urazbekov A.E. Soglasovannaya model' aksial'nogo i lateral'nogo rosta nitevidnykh nanokristallov [Coordinated model of axial and lateral growth of filamentous nanocrystals]. Bachelor's thesis, field of study: 03.03.02. Physics, Tomsk, 2018. 29 p. (in Russ.).
24. Nazarenko M.V. Modelirovanie rosta poluprovodnikovykh struktur A3B5 metodami teorii nukleatsii [Modeling the growth of A3B5 semiconductor structures by methods of nucleation theory]. PhD thesis, field of study: 01.04.10, St. Petersburg Academic University of the Russian Academy of Sciences, St. Petersburg, 2012, 108 p. (in Russ.).
25. Wagner R.S., Ellis, W.C. Vapor-liquid-solid mechanism of single crystal growth. Applied Physics Letters, 1964, vol. 4, p. 89–90.
26. Dubrovskii V.G. Criterion for Selective Area Growth of III-V Nanowires. Nanomaterials, 2022, vol. 12, P. 3698.
27. Yuan X., Pan D., Zhou Y., Zhang X., Peng K., Zhao B., Deng M., He J., Tan H. H., Jagadish C. Selective Area Epitaxy of III–V Nanostructure arrays and networks: Growth, applications, and future directions. Appl. Phys. Rev, 2021, vol. 8, pp. 021302.
28. Tomioka K., Ikejiri K., Tanaka T., Motohisa J., Hara S., Hiruma K., Fukui T. Selective area growth of III-V nanowires and their applications. J. Mater. Res., 2011, vol. 26, no. 17, pp. 2127–2141.
29. Tomioka K., Tanaka T., Hara S., Hiruma K., Fukui T. III–V Nanowires on Si Substrate: Selective Area Growth and Device Applications. IEEE J. Sel. Top. Quant. Electron, 2011, vol. 17, no. 4, pp. 1112–1129.
30. Pantle F., Becker F., Kraut M., Worle S., Hoffmann T., Artmeier S., Stutzmann M. Selective area growth of GaN nanowires and nanofins by molecular beam epitaxy on heteroepitaxial diamond (001) substrates. Nanoscale Adv., 2021, vol. 3, pp. 3835.
31. Adhikari S., Lysevych M., Jagadish C., Tan H.H. Selective Area Growth of GaN Nanowire: Partial Pressures and Temperature as the Key Growth Parameters. Cryst. Growth Des., 2022, vol. 22, no. 9, pp. 5345–5353.
32. Kruse J.E., Lymperakis L., Eftychis S., Adikimenakis A., Doundoulakis G., Tsagaraki K., Androulidaki M., Olziersky A., Dimitrakis P., Ioannou Sougleridis V., Normand P., Koukoula T., Kehagias Th., Komninou Ph., Konstantinidis G., Georgakilas A. Selective area growth of GaN nanowires on SiO masked Si (111) substrates by molecular beam epitaxy. Journal of Applied Physics, 2016, vol. 119, pp. 224305.
33. Gridchina V.O., Kotlyar K.P., Reznik R.R., Dvoretskaya L.N., Parfen’eva A.V., Mukhina I.S., Cirlin G.E. Selective Area Growth of GaN Nan-owires on Patterned SiO/Si Substrates by Molecular Beam Epitaxy. Tech. Phys. Lett., 2020, vol. 46, no. 11, pp. 1080–1083.
34. Morassi M., Guan N., Dubrovskii V.G., Berdnikov Yu., Barbier C. et al. Selective Area Growth of GaN Nanowires on Graphene Nanodots. Crystal Growth & Design, 2019, vol. 20, no. 2, pp. 552–559.
35. Jung J., Schellingerhout S.G., Ritter M.F., ten Kate S.C., van der Molen O.A. H., de Loijer S., Verheijen M.A., Riel H., Nichele F., Bakkers E.P.A.M. Selective Area Growth of PbTe Nanowire Networks on InP. Adv. Funct. Mater., 2022, vol. 32, pp. 2208974.
36. Gao Q., Dubrovskii V.G., Caroff P., Wong Leung J., Li L., Guo Y., Fu L., Tan H.H., Jagadish C. Simultaneous Selective Area and Vapor-Liquid-Solid Growth of InP Nanowire Arrays. Nano Lett., 2016, vol. 16, pp. 4361–4367.
37. Dalacu D., Kam A., Austing D.G., Wu X., Lapointe J., Aers G.C., Poole P.J. Selective area vapor-liquid-solid growth of InP nanowires. Nanotechnology, 2009, vol. 20, pp. 395602.
38. Wang X., Luo Y., Liao J., Joselevich E., Xu J. Selective Area Growth of Aligned Organic Semiconductor Nanowires and Their Device Integration. Adv. Funct. Mater., 2024, vol. 34, pp. 2308708.
39. Grégoire G., Zeghouane M., Goosney C., Göktaş N.I., Staudinger P., Schmid H., Moselund K.E., Taliercio T., Tournié E., Trassoudaine A., Gil E., LaPierre R.R., André Y. Selective Area Growth by Hydride Vapor Phase Epitaxy and Optical Properties of InAs Nanowire Arrays. Cryst. Growth Des., 2021, vol. 21, pp. 5158–5163.
40. Zhang K., Ray V., Herrera Fierro P., Sink J.R., Toor F., Prineas J.P. Selective Area Growth of InAs Nanowire Arrays on SiN/Si (111) by Molecular Beam Epitaxy. Proc. SPIE, 2017, vol. 10114, pp. 1011419.
41. Dubrovskii V.G., Kim W., Piazza V., Güniat L., Fontcuberta i Morral A. Simultaneous Selective Area Growth of Wurtzite and Zincblende Self-Catalyzed GaAs Nanowires on Silicon. Nano Letters, 2021, vol. 21, no. 7, pp. 3139–3145.
42. Samarsky A.A., Andreev V.B. Raznostnye metody dlya ellipticheskih uravnenij [Difference methods for elliptic equations]. Moscow, Nauka, 1976. 352 p. (in Russ.).
43. LeVeque R.J. Finite Difference Methods for Ordinary and Partial Differential Equations. Philadelphia, Society for Industrial and Applied Mathematics, 2007, 340 p.
44. Tamoshkin M.A. Ispol'zovanie kletochnykh avtomatov dlya modelirovaniya processa obrazovaniya nitevidnykh nanokristallov v oblastyakh selektivnogo travleniya [Using cellular automata to model the formation of nanowires in selective etching areas]. Prospects of fundamental sciences development: Proceedings of the XXI International Conference of Students, Graduate Students and Young Scientists, edited by I.A. Kurzina et al. 2024, vol. 1: Physics, pp. 311–313 (in Russ.).
45. Toffoli T. Mashiny kletochnykh avtomatov [Machines of cellular automata], Moscow, Mir Publ., 1991, 283 p. (in Russ.).
46. John von Neumann. Teoriya samovosproizvodyashchikhsya avtomatov [Theory of self-reproducing automata]. M., Mir Publ., 1971, 384 p. (in Russ.).