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GEOMETRICAL APPROACH TO THE SIMULATION OF PARTICLE FLIGHT DIRECTION. N. N. CHENTSOV FORMULAE AND THEIR GENERALIZATION FOR POLARIZED RADIATION COMPUTATIONS

A. N. Subbotin
VANT. Ser.: Mat. Mod. Fiz. Proc 2006. Вып.4. С. 66-79.

The method of polarized radiation transport description is proposed; it consists in the kinetic scalar equation with extended phase space of particles, and a specific form of collision term. The new equation is an ordinary Kolmogorov equation for transient probabilities of Markovian process. To substantiate the validity of Monte Carlo method for polarized radiation computation it is proved that vector Chandrasekhar equation for 4D Stokes vector-parameter of polarized radiation is the system of equations for four-dimensional functionals of the new scalar equation solution. Thus, Monte Carlo solution of vector equation is reduced to functional estimation using the path of Markovian process. We have considered the geometrical approach proposed by N. N. Chentsov to the derivation of failure-proof algorithms of particle scattering simulation based on the use of discontinuous functions for arraying of the transfer from one coordinate system to another. The choice of the coordinate system for the count of Stokes parameters of polarized radiation agrees with construction of moving coordinate system for simulation of new flight direction during the collision event, which allows economical algorithms of simulation of polarized radiation transport paths.










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