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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,
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a size of a projection, an evacuation way. It gives a wide opportunities to state a simulation task and reproduce a real phenomena. Different approaches [3] from mathematically continuous models to pure discrete models are developed already. A discrete-continuous approach combines advantages of both approaches: people move in a continuous space, but there are only fixed number of directions where a person can move.
In the article one discrete-continuous model is considered. A validation of the SigmaEva evacuation module is given with respect to a very important case study - fundamental diagrams (flow-density dependence) under periodic boundary conditions.
References
1. Schadschneider A., Klingsch W., Kluepfel H., Kretz T., Rogsch C., Seyfried A. Evacuation Dynamics: Empirical Results, Modeling and Applications. Encyclopedia of Complexity and System Science. Springer, 2009 (3). P. 3142-3192.
2. Kirik E., Vitova T., Malyshev A., Popel E. On the Validation of Pedestrian Movement Models under Transition and Steady-state Conditions // Proceedings of the Ninth International Seminar on Fire and Explosion Hazards (21-26 April 2019 Saint Petersburg, Russia), edited by A. Snegirev, Vol. 2. P. 1271-1280.
Combined use of two methods for analysis of nonstationary time series for solving forecasting and control problems
S. I. Kolesnikova, A. D. Bogdanova
Saint-Petersburg State University of Aerospace Instrumentation
Email: skolesnikova@yandex.ru
DOI: 10.24411/9999-017A-2020-10251
Combined algorithm for time series analysis based on two following basic methods [1, 2]: the empirical mode decomposition and nuclear regression is considered. Essence of the presented algorithm is the sequential calculation of nuclear regressions and residues resulting in decomposition of the original series into an additive mixture of the number of regressions and residual series.
The paper provides a comparative review of three methods and their implementing algorithms for the analysis and forecasting of nonstationary time series, and also an algorithm is obtained on the basis of their combined application.
There are grounds for believing that the synthetic use of two popular nonparametric forecasting algorithms will lead to a more efficient forecasting algorithm, at least for solving a certain class of control problems [3, 4].
This work was (partially) supported by the Russian Foundation for Basic Research (grant 20-08-00747). References
1. Huang, H et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series. Analysis Proc. R. Soc. Lond. A. 1998. V. 454. P. 903-995.
2. Nadaraya E. On Estimating Regression. TV and its applications. 1964. V. 9(1). P. 141-142.
3. Kolesnikova S. Stochastic discrete nonlinear control system for minimum dispersion of the output variable n Advances in Intelligent Systems and Computing. 2019. V 986. P. 325-31.
4. Kolesnikova S. I. A multiple-control system for nonlinear discrete object under uncertainty.Optimization Methods and Software. 2019. Т. 34. № 3. P. 578-585. URL: https://doi.org/10.1080/10556788.2018.1472258.
Численные статистические алгоритмы решения обратных задач теории переноса излучения в атмосфере с учетом поляризации
А. С. Корда
Институт математики и математической геофизики СО РАН
Email: asc@osmf.sscc.ru
DOI: 10.24411/9999-017A-2020-30371
В данном докладе описывается ряд численных статистических методов, построенных авторами для решения обратных задачи теории переноса излучения в атмосфере с учетом поляризации. Рассматривается задача восстановления матрицы аэрозольного рассеяния атмосферы по наземным наблюдениям поляризационных характеристик излучения в альмукантарате Солнца, для ее решения предлагаются алгоритмы, основанные на адаптивном и комбинированном способах моделирования рассеяния в атмосфере при больших оптических толщах аэрозоля. С помощью численного статистического моделирования была исследована эффективность этих способов в ранее предложенном методе "предиктор-корректор" восстановления первых двух компонент матрицы рассеяния, позволяющем повысить точность восстановления индикатрисы рассеяния.
Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проект № 18-01-00356)
