CC BY
62. Aleksandrov A. V., Dorodnitsyn L. V., Duben A.P. Generation of three-dimensional homogeneous isotropic
turbulent velocity fields using the Randomized Spectral Method // Mathematical Models and Computer Simulations.
2020. V. 12, N. 3. P. 388�396.
3. Sabelfeld K. K., Kurbanmuradov O. Stochastic Lagrangian models for two-particle motion in turbulent flows //
Monte Carlo Methods Appl. 1997. V. 3, N. 1. P. 53�72.
Application of an economic algorithm for modeling of random variables for simulation of a Poisson point
process
T. A. Averina
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
Email: ata@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-71
Statistical solution of the problems of analysis, synthesis and filtration for systems of the diffusion-
discontinuous type, requires simulation of inhomogeneous Poisson point process [1]. In order to simulate the
latter, sometimes an algorithm based on the ordinariness property of the process is used. In this article, a
modification of the algorithm is being constructed by using an economic method for modeling of random vari-
ables [2�4]. The developed method is verified by solving test problems
This work was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
References
1. Averina T.A., Rybakov K.A. Using maximum cross section method for filtering jump-diffusion random processes //
Russian Journal of Numerical Analysis and Mathematical Modelling. 2020. V. 35. N. 2. P. 55-67.
2. Mikhailov G.A. Construction of economic Algorithms for the Simulation of Random Variables // U.S.S.R. Computa-
tional Mathematics and Mathematical Physics. 1966. V. 6. N. 6, P. 269--273.
3. Mikhailov G.A. and Voitishek A.V. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo (Numerical Sta-
tistical Simulation: Monte Carlo Methods). Moscow: Izd. Tsentr �Akademiya�. 2006. [in Russian]
4. Averina, T.A. New Algorithms for the Statistical Modeling of Inhomogeneous Poisson Ensembles // Computational
Mathematics and Mathematical Physics. 2010. V. 50. N 1. P. 16�23.
Double randomization method for estimating the moments of solution to the coagulation equation
A. V. Burmistrov1,2, M. A. Korotchenko1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: burm@osmf.sscc.ru, kmaria@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-72
The problem of estimating the probability moments of linear functionals from the solution to the Smolu-
chowski equation with random coagulation coefficients is considered. For this purpose, we modify the algo-
rithms previously proposed by the authors for solving kinetic problems [1, 2] using the double randomization
method. In addition, a splitting method is proposed to reduce the computational costs of the algorithms [3].
This work was created under the state contract with ICMMG SB RAS (0315-2019-0002).
References
1. Burmistrov A., Korotchenko M. Double Randomization Method for Estimating the Moments of Solution to
Vehicular Traffic Problems with Random Parameters // Russian J. of Numerical Analysis and Mathematical Modelling.
2020. V. 35, N. 3. P. 143-152.
2. Burmistrov A.V., Korotchenko M.A. Weight Monte Carlo algorithms for estimation and parametric analysis of the
solution to the kinetic coagulation equation // Numerical Analysis and Applications. 2014. V.7, N. 2. P. 104-116.
3. Mikhailov G.A. Improvement of Multidimensional Randomized Monte Carlo Algorithms with �Splitting� //
Computational Mathematics and Mathematical Physics. 2019. V. 59, N. 5. P. 775�781.
Application of the Monte Carlo method to study the features of aerosol cluster motion
A. A. Cheremisin1, A. V. Kushnarenko1,2
1Voevodsky Institute of Chemical Kinetics and Combustion SB RAS
2Siberian Federal University, Krasnoyarsk
Email: avkushnarenko@gmail.com
DOI 10.24412/cl-35065-2021-1-00-73
In this work we applied the previously developed Monte-Carlo algorithm [1] designed to calculate photo-
phoretic and viscous forces acting on the aerosol cluster in the rarified gas medium to study sedimentation of
clusters.
According to calculations, the photophoretic force significantly changes the qualitative and quantitative
characteristics of the cluster motion. It is shown that in the absence of light, the sedimentation velocity of clus-
ter consisting of equal-sized spherical particles is close to the sedimentation velocity of a single spherical parti-
cle. The relationship between the cluster velocity and its fractal dimension and the number of spherical parti-
cles in the cluster is revealed. Light significantly changes the character of sedimentation. The vertical velocities
of clusters are distributed within a broad range. Some of them move up against gravity. This is an effect of
photophoretic (gravito-photophoretic) levitation. The computer model simulates the characteristic movement
of the aerosol cluster at gravito-photophoresis, the upward spiral movement, which was previously observed
in the experiments.
References
1. Cheremisin A. A. Transfer matrices and solution of the heat-mass transfer problem for aerosol clusters in a
rarefied gas medium by the Monte Carlo method // Russian J. of Numerical Analysis and Mathematical Modelling. 2010.
V. 25, P. 209-233.
Using the modified superposition method in the computational system NMPUD
D. A. Cherkashin1, A. V. Voytishek2,3
1Lyceum No. 130 of the city Novosibirsk
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
3Novosibirsk State University
Email: vav@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-74
The computational system NMPUD (Numerical Modelling of Probabilistic Univariate Distributions) was de-
veloped in the Laboratory of Mathematical modelling of Lyceum No. 130 of the city Novosibirsk, Russia, in
2020 [1, 2]. The NMPUD system is used primarily as a helpful (or even necessary) tool for choosing the neces-
sary economically simulated probability distributions for researchers involved in the elaboration and (or) use
of computational stochastic models for solving urgent applied problems.
