  We present a population control method with sampling and regulation steps for
Monte Carlo particles involved in the numerical simulation of a transport
equation. We recall in the first section the difficulties related to the
variance reduction methods in the general framework of transport equations; we
continue with a brief presentation of the mathematical tools invoked when
solving the radiative transport equations and we focus on the importance of the
emission and control of existing Monte Carlo particles.
  The next part discusses several novel methods based on the cell-based
population control method proposed earlier. To this end, we analyze
theoretically two types of splitting: one is conservative in energy (at the
particle level) and the other is not. Thanks to these results, a new algorithm
is introduced that uses the cell-based population control method and a spatial
distribution. A numerical comparison of the different types of splitting is
proposed in a simplified framework, then the various algorithms presented are
compared against two benchmarks : the propagation of a Marshak wave and the
propagation of two waves having different intensity and speed scales. To carry
out these last tests, we use the multi-physics code FCI2.
