Homogenization of Boundary Layers in the Boltzmann--Poisson System

Simple item page
dc.contributor.authorHeitzinger, Clemens
dc.contributor.authorMorales Escalante, José A.
dc.date.accessioned2023-06-06T16:27:59Z
dc.date.available2023-06-06T16:27:59Z
dc.date.issued2021
dc.descriptionCopyright is held by the Society for Industrial and Applied Mathematics.en_US
dc.description.abstractWe homogenize the Boltzmann--Poisson system where the background medium is given by a periodic permittivity and a periodic charge concentration. The domain is the half-space with a periodic charge concentration on the boundary. Hence the domain consists of cells in R3 that are periodically repeated in two dimensions and unbounded in the third dimension. We obtain formal results for this homogenization problem. We prove the existence and uniqueness of the solution of the Laplace and Poisson problems in the fast variables with periodic and surface charge boundary conditions generating an electric field at infinity, obtaining formal solutions for the potential in terms of Magnus expansions for the case where the diagonal permittivity matrix depends on the vertical fast variable. Further on, splitting the potential into a stationary part and a self-consistent part, performing the two-scale homogenization expansions for the Poisson and the Boltzmann equations, and applying a solvability condition, we arrive at the drift-diffusion equations for the boundary-layer problem.en_US
dc.description.departmentMathematicsen_US
dc.description.departmentPhysics and Astronomyen_US
dc.description.sponsorshipAustrian Science Funden_US
dc.identifier.citationHeitzinger, C., & Morales Escalante, J. A. (2021). Homogenization of Boundary Layers in the Boltzmann--Poisson System. Multiscale Modeling & Simulation, 19(1), 506-532. doi:10.1137/18m1193888en_US
dc.identifier.issn1540-3467
dc.identifier.otherhttps://doi.org/10.1137/18M1193888
dc.identifier.urihttps://hdl.handle.net/20.500.12588/1873
dc.language.isoen_USen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.subjecthomogenizationen_US
dc.subjectBoltzmann--Poisson systemen_US
dc.subjectnanowire sensorsen_US
dc.titleHomogenization of Boundary Layers in the Boltzmann--Poisson Systemen_US
dc.typeArticleen_US

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
Morales Escalante 2021 - Homogenization of Boundary Layers in the Boltzmann-Poisson System.pdf
Size:
514.1 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.86 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

College of Sciences Faculty Research