Neutral particles are fired at normal incidence into a purely absorbing slab of…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Monte Carlo and lattice simulation of physical systems

Error, Chance and the Machine, Ch Monte Carlo integration and variance reduction

Problem

Neutral particles are fired at normal incidence into a purely absorbing slab of thickness

L = 4

mean free paths

\ell

. Each particle's free path is sampled by

s = -\ell\ln u

with

u

uniform on

(0,1)

; if

s < L

the particle is absorbed, otherwise it is transmitted. In a run of

N = 1\times10^5

histories,

n_T = 1832

particles are transmitted. ((a)) Give the estimated transmission fraction and its standard error, treating each history as a Bernoulli trial. ((b)) Compare with the analytic transmission

e^{-L/\ell}

and state whether the simulation is consistent with it.

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