{"title":"随机介质中平均粒子流的超指数增长与倍增研究","authors":"G. Z. Lotova, G. A. Mikhailov","doi":"10.1134/s1995423923040055","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new correlative-grid approximation for a homogeneous isotropic random field of density is introduced for effective numerical-analytical investigation of overexponential growth of the mean flux of particles with multiplication in a random medium. In this case, the complexity of realization of a particle trajectory is independent of the correlation scale. For the correlative-grid approximation, the possibility of a Gaussian asymptotics of the average rate of particle multiplication is proved for a random field of limited density. It ensures a superexponential growth of the flux in some initial time interval. An estimate of further overexponential flux growth is constructed based on some test computations.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"82 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Investigation of Overexponential Growth of Mean Particle Flux with Multiplication in Random Medium\",\"authors\":\"G. Z. Lotova, G. A. Mikhailov\",\"doi\":\"10.1134/s1995423923040055\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>A new correlative-grid approximation for a homogeneous isotropic random field of density is introduced for effective numerical-analytical investigation of overexponential growth of the mean flux of particles with multiplication in a random medium. In this case, the complexity of realization of a particle trajectory is independent of the correlation scale. For the correlative-grid approximation, the possibility of a Gaussian asymptotics of the average rate of particle multiplication is proved for a random field of limited density. It ensures a superexponential growth of the flux in some initial time interval. An estimate of further overexponential flux growth is constructed based on some test computations.</p>\",\"PeriodicalId\":43697,\"journal\":{\"name\":\"Numerical Analysis and Applications\",\"volume\":\"82 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995423923040055\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423923040055","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Investigation of Overexponential Growth of Mean Particle Flux with Multiplication in Random Medium
Abstract
A new correlative-grid approximation for a homogeneous isotropic random field of density is introduced for effective numerical-analytical investigation of overexponential growth of the mean flux of particles with multiplication in a random medium. In this case, the complexity of realization of a particle trajectory is independent of the correlation scale. For the correlative-grid approximation, the possibility of a Gaussian asymptotics of the average rate of particle multiplication is proved for a random field of limited density. It ensures a superexponential growth of the flux in some initial time interval. An estimate of further overexponential flux growth is constructed based on some test computations.
期刊介绍：
Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998.
The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields.
The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.
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