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@ARTICLE{Reiser:859038,
      author       = {Reiser, D. and Romazanov, J. and Linsmeier, Ch.},
      title        = {{O}n the possibility of track length based {M}onte-{C}arlo
                      algorithms for stationary drift-diffusion systems with
                      sources and sinks},
      journal      = {Journal of computational physics},
      volume       = {377},
      issn         = {0021-9991},
      address      = {Amsterdam},
      publisher    = {Elsevier},
      reportid     = {FZJ-2019-00007},
      pages        = {219 - 231},
      year         = {2019},
      abstract     = {The problem of constructing Monte-Carlo solutions of
                      drift-diffusion systems corresponding to Fokker–Planck
                      equations with sources and sinks is revisited. Firstly, a
                      compact formalism is introduced for the specific problem of
                      stationary solutions. This leads to identification of the
                      dwell time as the key quantity to characterize the system
                      and to obtain a proper normalization for statistical
                      analysis of numerical results. Secondly, the question of
                      appropriate track length estimators for drift-diffusion
                      systems is discussed for a 1D model system. It is found that
                      a simple track length estimator can be given only for pure
                      drift motion without diffusion. The stochastic nature of the
                      diffusive part cannot be appropriately described by the path
                      length of simulation particles. Further analysis of the
                      usual situation with inhomogeneous drift and diffusion
                      coefficients leads to an error estimate based on particle
                      trajectories. The result for limits in grid cell size and
                      time step used for the construction of Monte-Carlo
                      trajectories resembles the Courant-Friedrichs-Lewy and von
                      Neumann conditions for explicit methods.},
      cin          = {IEK-4},
      ddc          = {000},
      cid          = {I:(DE-Juel1)IEK-4-20101013},
      pnm          = {174 - Plasma-Wall-Interaction (POF3-174)},
      pid          = {G:(DE-HGF)POF3-174},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000450428900010},
      doi          = {10.1016/j.jcp.2018.07.051},
      url          = {https://juser.fz-juelich.de/record/859038},
}