Branching processes Simulations Cosmic Rays Multi-type Branching Process Immigration
Issue Date:
2017
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 27, No 1, (2017), 103p-114p
Abstract:
The cosmic rays (CR) cascades are one of the most famous examples of branching processes in physics. They consist of many different types of secondary high energy particles which are offsprings of leading primary one, usually high energy nucleon or gamma photon after collision with atmosphere. The rate of expansion of cascade depends on multiple different conditional probabilities as the chance of survival in atmosphere without interactions, particle lifetime, the number of daughter particles, etc. The paper presents quantitative simulated results with a specially written in R software for parallel simulation of distributions of multiple types of daughter particles. The processes are based on simplified models of Hadron cascades simulated by age-dependent and imbedded Markov Galton-Watson branching processes. For the sake of simplicity in modelling the probability dependencies on particles energy and free path in atmosphere are not always constrained strictly to the available experimental results. Moreover, the scattering angles also are not considered in this version of software. 2010 Mathematics Subject Classification: 60-04.
