In this free e-book we provide a collection of deterministic and Monte-Carlo solutions to multiple-scattering problems in linear transport theory. Over 2000 references to literature containing derivations and related work are provided to help the reader discover further detail. Reference Monte Carlo code, solutions and Mathematica worksheets comparing the deterministic solutions to Monte Carlo are provided on github. We also include sections on:

  • Fredholm and Wiener-Hopf integral equations / pseudo problems / H-functions
  • Non-classical transport in stochastic (non-exponential) media
  • Stationary point processes, Renewal processes, Cox processes

Book – 2022 release v0.3.2 (pdf)

New results for transport in stochastic media (1D rod), sampling procedures for Draine and Cornette-Shanks phase functions, and additional corrections.

Book – 2021 release v0.3.0.1 (pdf)

New in this release: the same book is available in three different notations (\sigma_t, \mu_t, and \Sigma_t, respectively, plus a few other changes):


Github repo

For each of the major problems we provide C++ code that produces Monte Carlo reference output. The deterministic solutions are all implemented and cross-checked against Monte Carlo in Mathematica worksheets, which you can download and use to interactively explore the various simulations. Each Mathematica worksheet is also saved as a PDF (convenient if you don’t have Mathematica).

Previous versions (pdf)