Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

a ( X506 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationsgame (number of simulation particles), then the final score isM 1=kWi.e.,k = 1/qThe variance of the score in the biased game isD 2 = W 2 k(l - k) = Mfq 2 k(l - k) = M 2 (q - 1)In contrast, the expected number of particles transmitted in the analog game is M 1. eachhaving a weight of unity, and therefore the variance of the analog game isD 2 = M 1(I - M 1)The ratio of the two variances isD 2 /D 2 = M,(q - 1)/(1 - M 1) =e-~ ^ ~ 1for certain values of x and E. Now, if b is positive, then the kernels are nonphysical aroundthe preferred direction (p. ~ 1). At the same time, a second problem is faced in the oppositedirection, namely, the weights of the particles will strongly fluctuate. This can be demonstratedin the case of a homogeneous slab. In this case, the second moment of the weight