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Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method

  • Alexander A. Cheremisin EMAIL logo
Published/Copyright: February 17, 2022

Abstract

A Monte Carlo algorithm based on the use of transfer matrices is developed to describe the stochastic dynamics of the rotational--translational motion of aerosol clusters taking into account fluctuations in the molecular fluxes of the gas medium. In the general case, the cluster is immersed into a rarefied gas medium, the temperatures of its surfaces may differ from the temperature of the surrounding gas, for example, due to absorption of visible and infrared radiation. The motion of the cluster is described based on Langevin motion equations. The algorithm allows one to calculate parameters of the probability distribution of a six-dimensional vector consisting of components of the momentum and angular momentum vectors transmitted to the cluster by molecular flows. The numerical method allows one to apply preliminary analytical averaging modulo velocities of molecules for both the average values of the components of momentum and angular momentum and their correlation characteristics, which significantly reduces the calculation time.

MSC 2010: 82C80; 82C70; 82C31

Acknowledgment

The author is grateful to Prof. G. A. Mikhailov and to his collaborators for a fruitful discussion of the work.

  1. funding: The work was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. 075-15-2020-781).

References

[1] A. Ansmann, H. Baars, A. Chudnovsky, I. Mattis, I. Veselovskii, M. Haarig, P. Seifert, R. Engelmann, and U. Wandinger}, Extreme levels of Canadian wildfire smoke in the stratosphere over central Europe on 21–22 August 2017. Atmospheric Chemistry and Physics 18 (2018), No. 16, 11831–11845.10.5194/acp-18-11831-2018Search in Google Scholar

[2] M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, Cambridge, 1999.10.1017/CBO9781139644181Search in Google Scholar

[3] A. A. Borovkov, Probability Theory. Editorial URSS, Moscow, 1999 (in Russian).Search in Google Scholar

[4] A. A. Cheremisin, L. V. Granitskii, V. M. Myasnikov, and N. V. Vetchinkin, Improved aerosol scattering in the upper atmosphere according to data of ultraviolet observations from space, with instrumental smoothing taken into account. In: Proc. of the 7th Int. Symp. on Atmospheric and Ocean Optics (Eds. G. G. Matvienko and M. V. Panchenko).International Society for Optics and Photonics, Vol. 4341. SPIE, 2000, pp. 383–389.10.1117/12.411970Search in Google Scholar

[5] A. A. Cheremisin, Yu. V. Vassilyev, and H. Horvath, Gravito-photophoresis and aerosol stratification in the atmosphere. J. Aerosol Sci. 36 (2005), No. 11, 1277–1299.10.1016/j.jaerosci.2005.02.003Search in Google Scholar

[6] A. A. Cheremisin, Transfer matrices and solution of the heat-mass transfer problem for aerosol clusters in a rarefied gas medium by the Monte Carlo method. Russ. J. Numer. Anal. Math. Modelling 25 (2010), No. 3, 209–233.10.1515/rjnamm.2010.014Search in Google Scholar

[7] A. A. Cheremisin, I. S. Shnipov, H. Horvath, and H. Rohatschek, The global picture of aerosol layers formation in the stratosphere and in the mesosphere under the influence of gravito-photophoretic and magneto-photophoretic forces. J. Geophys. Research Atmospheres 116 (2011), No. D19204.10.1029/2011JD015958Search in Google Scholar

[8] A. A. Cheremisin, P. V. Novikov, I. S. Shnipov, V. V. Bychkov, and B. M. Shevtsov, Lidar observations and formation mechanism of the structure of stratospheric and mesospheric aerosol layers over Kamchatka. Geomagnetism and Aeronomy 52 (2012), No. 5, 653–663.10.1134/S0016793212050027Search in Google Scholar

[9] A. A. Cheremisin and A. V. Kushnarenko, Photophoretic interaction of aerosol particles and its effect on coagulation in rarefied gas medium J. Aerosol Sci. 62 (2013), 26–39.10.1016/j.jaerosci.2013.03.011Search in Google Scholar

[10] A. A. Cheremisin, Photophoresis of aerosol particles with nonuniform gas–surface accommodation in the free molecular regime. J. Aerosol Sci. 136 (2019), 15–35.10.1016/j.jaerosci.2019.05.005Search in Google Scholar

[11] A. A. Cheremisin, V. N. Marichev, D. A. Bochkovsky, P. V. Novikov, and I. I. Romanchenko, Lidar observation of aerosol from Siberian forest fire events in the stratosphere over Tomsk in August 2019. In: Proc. of the 27th International Symposium on Atmospheric and Ocean Optics, Atmospheric Physics, Vol. 11916. SPIE, 2021, 1191635.10.1117/12.2603013Search in Google Scholar

[12] W. T. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin equation: with applications to stochastic problems in physics, chemistry and electrical engineering, 2nd edition. World Sci. Publ. Co. Pte Ltd., Singapore, 2004.10.1142/5343Search in Google Scholar

[13] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2. John Wiley & Sons, New York, 1991.Search in Google Scholar

[14] S. K. Friedlander, Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics. Oxford University Press, New York, 2000.Search in Google Scholar

[15] V. Yu. Korolev, V. E. Bening, and S. Ya. Shorgin, Mathematical Foundations of Risk Theory. Fizmatlit, Moscow, 2011 (in Russian).Search in Google Scholar

[16] G. I. Marchuk, G. A. Mikhailov, M. A. Nazraliev, P. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics. Nauka, Novosibirsk, 1976.Search in Google Scholar

[17] G. A. Mikhailov, Optimization of Weighted Monte Carlo Methods. Springer-Verlag, Berlin–Heidelberg, 1992.10.1007/978-3-642-75981-9Search in Google Scholar

[18] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modelling. Monte Carlo Methods. Akademiya, Moscow, 2006 (in Russian).Search in Google Scholar

[19] I. M. Sobol’, Numerical Monte Carlo Methods. Nauka, 1973 (in Russian).Search in Google Scholar

Received: 2021-09-30
Accepted: 2021-11-22
Published Online: 2022-02-17
Published in Print: 2022-02-23

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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