Hierarchies of transport equations for nanopores
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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.
KeywordsBoltzmann 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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