Numerical-Statistical and Analytical Study of Asymptotics for the Average Multiplication Particle Flow in a Random Medium

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Numerical-Statistical and Analytical Study of Asymptotics for the Average Multiplication Particle Flow in a Random Medium. / Lotova, G. Z.; Mikhailov, G. A.

In: Computational Mathematics and Mathematical Physics, Vol. 61, No. 8, 08.2021, p. 1330-1338.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{9384f454078a415e82abd62e3f5e1183,

title = "Numerical-Statistical and Analytical Study of Asymptotics for the Average Multiplication Particle Flow in a Random Medium",

abstract = "It is well known that, under rather general conditions, the particle flux density in a multiplying medium is asymptotically exponential in time t with a parameter λ, i.e., with an exponent λ. If the medium is random, then λ is a random variable, and the time asymptotics of the average number of particles (over medium realizations) can be estimated in some approximation by averaging the exponent with respect to the distribution of λ. Assuming that this distribution is Gaussian, an asymptotic “superexponential” estimate for the average flux expressed by an exponential with the exponent tEλ + t2Dλ/2 can be obtained in this way. To verify this estimate in a numerical experiment, a procedure is developed for computing the probabilistic moments of λ based on randomizations of Fourier approximations of special nonlinear functionals. The derived new formula is used to study the COVID-19 pandemic.",

keywords = "COVID-19, particle flow, random medium, statistical modeling, time asymptotics",

author = "Lotova, {G. Z.} and Mikhailov, {G. A.}",

note = "Funding Information: This work was supported in part by the Russian Foundation for Basic Research, project nos. 18-01-00356, 18-01-00599. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = aug,

doi = "10.1134/S0965542521060075",

language = "English",

volume = "61",

pages = "1330--1338",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "PLEIADES PUBLISHING INC",

number = "8",

}

RIS

TY - JOUR

T1 - Numerical-Statistical and Analytical Study of Asymptotics for the Average Multiplication Particle Flow in a Random Medium

AU - Lotova, G. Z.

AU - Mikhailov, G. A.

PY - 2021/8

Y1 - 2021/8

N2 - It is well known that, under rather general conditions, the particle flux density in a multiplying medium is asymptotically exponential in time t with a parameter λ, i.e., with an exponent λ. If the medium is random, then λ is a random variable, and the time asymptotics of the average number of particles (over medium realizations) can be estimated in some approximation by averaging the exponent with respect to the distribution of λ. Assuming that this distribution is Gaussian, an asymptotic “superexponential” estimate for the average flux expressed by an exponential with the exponent tEλ + t2Dλ/2 can be obtained in this way. To verify this estimate in a numerical experiment, a procedure is developed for computing the probabilistic moments of λ based on randomizations of Fourier approximations of special nonlinear functionals. The derived new formula is used to study the COVID-19 pandemic.

AB - It is well known that, under rather general conditions, the particle flux density in a multiplying medium is asymptotically exponential in time t with a parameter λ, i.e., with an exponent λ. If the medium is random, then λ is a random variable, and the time asymptotics of the average number of particles (over medium realizations) can be estimated in some approximation by averaging the exponent with respect to the distribution of λ. Assuming that this distribution is Gaussian, an asymptotic “superexponential” estimate for the average flux expressed by an exponential with the exponent tEλ + t2Dλ/2 can be obtained in this way. To verify this estimate in a numerical experiment, a procedure is developed for computing the probabilistic moments of λ based on randomizations of Fourier approximations of special nonlinear functionals. The derived new formula is used to study the COVID-19 pandemic.

KW - COVID-19

KW - particle flow

KW - random medium

KW - statistical modeling

KW - time asymptotics

UR - http://www.scopus.com/inward/record.url?scp=85115198810&partnerID=8YFLogxK

U2 - 10.1134/S0965542521060075

DO - 10.1134/S0965542521060075

M3 - Article

AN - SCOPUS:85115198810

VL - 61

SP - 1330

EP - 1338

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 8

ER -

ID: 34256404