GENERALIZED CASCADE-PROBABILITY FUNCTION FOR HOUR-TIME FLOWS AND ITS CONNECTION WITH THE BOLTZMAN EQUATION
https://doi.org/10.52676/1729-7885-2019-1-123-125
Abstract
An analytical solution is obtained for the integro-differential equation of a cascade process for particles (knocked out atoms, etc.) in a three-dimensional model of an elementary act, into which a generalized cascade-probability function (GCPF) leads. It is shown that after the Laplace transformation, the equation passes into an integral one, which is then solved by the method of successive approximations. The basic physical properties of this function are established. With the constancy of the path to the interaction and the angle of departure of the particle after the collision, the GCPF goes into the simplest CPF. With small depths of registration, the probability that a particle will pass this depth tends to zero (both without collisions and when testing i interactions). At greater depths, these probabilities tend to zero. With a large i GCPF goes into a Stirling type formula. As the interaction path increases, the probability without interaction tends to unity, and the probability with i-interactions tends to zero.
About the Authors
N. A. Voronova
Kazakh National Pedagogical University named after Abai
Kazakhstan
Almaty
Kazakhstan
Almaty
A. I. Kupchishin
Kazakh National Pedagogical University named after Abai;
Kazakh National University named after al-Farabi
Kazakhstan
Almaty
Kazakhstan
Almaty
T. A. Shmygaleva
Kazakh National Pedagogical University named after Abai
Kazakhstan
Almaty
Kazakhstan
Almaty
V. I. Kirdyashkin
Kazakh National Pedagogical University named after Abai
Kazakhstan
Almaty
Kazakhstan
Almaty
A. A. Kupchishin
Kazakh National Pedagogical University named after Abai
Kazakhstan
Almaty
Kazakhstan
Almaty
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Review
For citations:
Voronova N.A., Kupchishin A.I., Shmygaleva T.A., Kirdyashkin V.I., Kupchishin A.A. GENERALIZED CASCADE-PROBABILITY FUNCTION FOR HOUR-TIME FLOWS AND ITS CONNECTION WITH THE BOLTZMAN EQUATION. NNC RK Bulletin. 2019;(1):123-125. (In Russ.) https://doi.org/10.52676/1729-7885-2019-1-123-125
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