TY - JOUR
T1 - Hierarchies of transport equations for nanopores
T2 - Equations derived from the Boltzmann equation and the modeling of confined structures
AU - Heitzinger, Clemens
AU - Ringhofer, Christian
N1 - Funding Information:
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).
Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - 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.
AB - 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.
KW - Boltzmann equation
KW - Confined structure
KW - Drift-diffusion-Poisson system
KW - Model hierarchy
KW - Nanopore
KW - Navier–Stokes equation
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U2 - 10.1007/s10825-014-0586-8
DO - 10.1007/s10825-014-0586-8
M3 - Article
AN - SCOPUS:84927123360
SN - 1569-8025
VL - 13
SP - 801
EP - 817
JO - Journal of Computational Electronics
JF - Journal of Computational Electronics
IS - 4
ER -