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оценки методов Монте-Карло. Таким образом, учитывается нестационарность источника. Для построения взволнованной поверхности океана используется фацетная модель. Расчеты проводились для различных параметров приемника.
Работа выполнена в рамках государственного задания ИВМиМГ СО РАН (проект 0315-2019-0002). Список литературы
1. Марчук Г. И., Михайлов Г. А., Назаралиев М. А. и др. Метод Монте-Карло в атмосферной оптике // Новосибирск: Наука, 1976, с. 80.
2. Cox C., Munk W. H., The measurement of the roughness of the sea curface from photographs of the sun's glitter // J. Opt. Soc. America, 1954, 44, No. 11, p. 838-850.
3. K. B. Rakimgulov, S.A. Ukhinov, Local estimates in Monte Carlo method for the ocean-atmosphere system with random interface // Russ. J. Numer. Anal. Math. Modelling, Vol.9, No.6, pp.547-564 (1994).
Stochastic simulation of GaN island formation in molecular beam epitaxy
S. E. Kireev, K. K. Sabelfeld
Institute of Computational Mathematics and Mathematical Geophysics SBRAS
Email: kireev@ssd.sscc.ru
DOI: 10.24411/9999-017A-2020-10075
A stochastic simulation model for self-assembly formation of GaN (gallium nitride) islands under plasmaassisted molecular beam epitaxy is developed. Formation of precursors of stable GaN islands is a challenging and still not completely understood phenomenon which is crucial in the technology of nanowire growth in the molecular beam epitaxy [1, 2]. In the model we suggest and implemented, we combine a kinetic Monte Carlo approach and an Ising type model where a coarse-grained Hamiltonian can be mainly expressed in terms of two binary variables, Ga, and Ni, for the Ga and N densities. The process is simulated by an asynchronous cellular automaton (ACA) [3]. The nucleation and island formation processes are simulated on a surface represented by a rectangular cellular array of size Nx*Ny. The boundary conditions are periodic. The states of the cells are Ga (gallium), N (nitrogen), and E (empty surface). Transition rules of ACA describe the simulated processes which include diffusion of atoms, Ga and N atoms desorption and adsorption of the incoming Ga and N atoms. The simulation process is carried out as a sequence of iterations, each iteration being a sequence of Nx*Ny steps. At each step, one cell is randomly selected. For the selected cell, an action is randomly selected depending on its state: swap with a neighboring cell in a randomly selected direction, desorption, or adsorption of atoms from the incoming fluxes. The probabilities of adsorption and desorption are model parameters defined by the experiment conditions. If the selected action is sampled, then it is performed with Metropolis probability, p = min [1, exp(-AH/kBT)], kB is Boltzmanns constant, AH is the resulting change is energy of the system, where AH calculation is based on the change in local neighborhood of the cell, taking into account the attraction forces between neighboring atoms and islands. We present the results of simulation of the whole process in its time evolution, and search for a set of input parameters generating the model which produces the kinetics and patterns similar to that obtained in the experiments.
Support of the Russian Science Foundation under grant 19-11-00019 is gratefully acknowledged. References
1. K.K. Sabelfeld, E.G. Kablukova, Stochastic simulation of nanowire growth in plasma-assisted molecularbeam epitaxy, Computational Materials Science, 125 (2016), 284-296.
2. K.K. Sabelfeld, V Kaganer, F. Limbach et al. Height self-equilibration during the growth of dense nanowire ensembles: Order emerging from disorder, Applied Physics Letters, 103 (2013), 133105
3. Bandman O.L. Mapping physical phenomena onto CA-models // AUT0MATA-2008. In: Adamatzky A., AlonsoSanz R., Lawniczak A., Martinez G.J., Morita K., Worsch T. (eds.) Theory and Applications of Cellular Automata. - Luniver Press, UK, 2008. - P. 381-397.
Computer simulation of pedestrian movement
Е. С. Кирик, Т. Б. Витова, А. В. Малышев, Е. V. Popel Институт вычислительного моделирования СО РАН Email: kirik@icm.krasn.ru DOI: 10.24411/9999-017A-2020-10076
A simulation of pedestrian dynamics is used in many fields, from entertainment (e.g., cinema and computer games) to fire safety of buildings, ships, and aircrafts. The most attractive for application is so called microscopic models, when each person is considered separately and a model determines coordinates of each person. In a model every person can have individual properties, including a free movement speed, an evacuation start time,
