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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Statistical Mechanics of Fragmentation-advection Processes and Nonlinear Measurements Problem. I

Discontinuity, Nonlinearity, and Complexity 1(1) (2012) 79--112 | DOI:10.5890/DNC.2012.03.002

Vladimir V. Uchaikin

Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk, Russia

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The random fragmentation-advection process is described in terms of generating functional and multiparticle densities. The aim of this article is to connect characteristics of a device performing the measurements of the process at a fixed time with characteristics of elementary fragmentation processes. The measurand is a random number being a symmetrical function of particles distribution at the moment of measurement. This function is assumed to be non-linear, and this part of the article is devoted to development of the general approach to computing of the mathematical expectation of such detector’s reading whereas the next one will discuss the adjoint function approach in connection with solving the inverse problem: defining characteristics of elementary processes by using results of non-linear measurements.


I am very indebted to my assistents Kozhemjakina E.V. and Shulezhko V.V. for preparing the manuscript, to Russian Foundation for Basic Research (grants 10-01-00608, 11-01-00747) and to Ministry of Education and Science of the Russian Federation (grant 2.1894.2011) for financial support.


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