Научная статья на тему 'Using the modified superposition method in the computational system NMPUD'

Using the modified superposition method in the computational system NMPUD Текст научной статьи по специальности «Математика»

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Текст научной работы на тему «Using the modified superposition method in the computational system NMPUD»

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: [email protected]

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: [email protected]

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.

The main content of the bank of the NMPUD system is elementary densities (that is, those that are effec-

tively simulated by the inverse distribution function method; see Chapter 2.6 of the book [3]). These densities

can be obtained in sufficient quantities using the technology of sequential (inserted) integral substitutions; see

Chapter 14.2 of the book [3].

In this paper, the expediency of creating blocks within the NMPUD system for simulating distributions

with polynomial and piecewise polynomial densities using the modified superposition method (see Chapters

11.2, 11.3 of the book [3]) is substantiated.

This work was carried out under state contract with ICMMG SB RAS (0251-2021-0002).

References

1. Vasiliev T. V., Postovalov Ya. S., Cherkashin D. A. Project of a computer system for the selection and study of

simulated probability distributions // Proceedings of the 58th International Student Conference "Student and Scientific

and Technological Progress". Mathematics. Novosibirsk: NPTs NSU, 2020. P. 112 [in Russian].

2. Voytishek A. V., Postovalov Ya. S., Cherkashin D. A. The system of numerical modeling of one-dimensional random

variables NMPUD: formation of a bank of densities, automation of mathematical calculations and applications //

Proceedings of the XIX International Conference named after A. F. Terpugov �Information Technologies and Mathematical

Modelling� (Tomsk, December 2-5, 2020). Tomsk: Publishing house NTL, 2021. P. 363�368 [in Russian].

3. Voytishek A. V. Lectures on Computational Monte Carlo Methods. Novosibirsk: NPTs NSU, 2018 [in Russian].

Numerical modeling of boundary value problems for differential equations with random coefficients

B. S. Dobronets, O. A. Popova, A. M. Merko

Siberian Federal University, Krasnoyarsk

Email: [email protected]

DOI 10.24412/cl-35065-2021-1-00-75

The article is devoted to the numerical modeling of differential equations with coefficients in the form of

random fields. Using the Karunen-Loeve expansion, the coefficients are approximated by the sum of inde-

pendent random variables and real functions. This allows us to use computational probabilistic analysis and, in

particular, we apply the technique of probabilistic extensions to construct the probability density functions of

the processes under study. As a result, we present a comparison of our approach with the Monte Carlo meth-

od in terms of the number of operations and demonstrate the results of numerical experiments for boundary

value problems for differential equations of elliptic type.

References

1. Dobronets B.S. Popova O.A. Computational Probabilistic Analysis: Models and Methods. Krasnoyarsk: Siberian

Federal University, 2020.

2. Soong T. Random Differential Equations in Science and Engineering. New York and London: Academic Press, 1973.

3. Dobronets B., Popova O. Computational aspects of probabilistic extensions. // Tomsk State University J. of Control

and Computer Science, 2019 pp 41�48.

Markov chain based stochastic modelling of HIV-1 and SARS-CoV-2 intracellular replication cycles

D. S. Grebennikov1,2, I. A. Sazonov3, G. A. Bocharov1,2

1Marchuk Institute of Numerical Mathematics RAS, Moscow, Russia

2Sechenov First Moscow State Medical University, Moscow, Russia

3Swansea University, Swansea, UK

Email: [email protected]

DOI 10.24412/cl-35065-2021-1-00-76

Understanding the dynamics of the intracellular virus replication is crucial for antiviral drug development.

We present the detailed deterministic models of the life cycles of HIV-1 [1] and SARS-CoV-2 [2] in target cells.

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