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Hierarchies of transport equations for nanopores

Equations derived from the Boltzmann equation and the modeling of confined structures

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University (ASU), Phoenix, AZ, USA

    Clemens Heitzinger & Christian Ringhofer

  2. Institute for Analysis and Scientific Computing, Vienna University of Technology (TU Vienna), Wien, Austria

    Clemens Heitzinger

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  1. Clemens Heitzinger
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  2. Christian Ringhofer
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Correspondence to Clemens Heitzinger.

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Heitzinger, C., Ringhofer, C. Hierarchies of transport equations for nanopores. J Comput Electron 13, 801–817 (2014). https://doi.org/10.1007/s10825-014-0586-8

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  • DOI: https://doi.org/10.1007/s10825-014-0586-8

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