Journal of Computational Electronics

, Volume 13, Issue 4, pp 801–817 | Cite as

Hierarchies of transport equations for nanopores

Equations derived from the Boltzmann equation and the modeling of confined structures
  • Clemens Heitzinger
  • Christian Ringhofer


We review transport equations and their usage for the modeling and simulation of nanopores. First, the significance of nanopores and the experimental progress in this area are summarized. Then the starting point of all classical and semiclassical considerations is the Boltzmann transport equation as the most general transport equation. The derivation of the drift-diffusion equations from the Boltzmann equation is reviewed as well as the derivation of the Navier–Stokes equations. Nanopores can also be viewed as a special case of a confined structure and hence as giving rise to a multiscale problem, and therefore we review the derivation of a transport equation from the Boltzmann equation for such confined structures. Finally, the state of the art in the simulation of nanopores is summarized.


Boltzmann equation Model hierarchy Drift-diffusion-Poisson system Navier–Stokes equation Confined structure Nanopore 



The first author acknowledges support by the FWF (Austrian Science Fund) START project No. Y660 PDE Models for Nanotechnology. The second author acknowledges support by NSF Grant 11-07465 (KI-Net).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State University (ASU)PhoenixUSA
  2. 2.Institute for Analysis and Scientific ComputingVienna University of Technology (TU Vienna)WienAustria

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