English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This work develops entropy-stable positivity-preserving DG methods as acomputational scheme for Boltzmann-Poisson systems modeling the pdf ofelectronic transport along energy bands in semiconductor crystal lattices. Wepose, using spherical or energy-angular variables as momentum coordinates, thecorresponding Vlasov Boltzmann eq. with a linear collision operator with asingular measure modeling the scattering as functions of the energy band. Weshow stability results of semi-discrete DG schemes under an entropy norm for1D-position 2D-momentum, and 2D-position 3D-momentum, using the dissipativeproperties of the collisional operator given its entropy inequality, whichdepends on the whole Hamiltonian rather than only the kinetic energy. For the1D problem, knowledge of the analytic solution to Poisson and of theconvergence to a constant current is crucial to obtain full stability. For the2D problem, specular reflection BC are considered in addition to periodicity inthe estimate for stability under an entropy norm. Regarding positivitypreservation (1D position), we treat the collision operator as a source termand find convex combinations of the transport and collision terms whichguarantee the positivity of the cell average of our numerical pdf at the nexttime step. The positivity of the numerical pdf in the whole domain isguaranteed by applying the natural limiters that preserve the cell average butmodify the slope of the piecewise linear solutions in order to make thefunction non-negative. The use of a spherical coordinate system$\vec{p}(|\vec{p}|,\mu=cos\theta,\varphi)$ is slightly different to the choicein previous DG solvers for BP, since the proposed DG formulation gives simplerintegrals involving just piecewise polynomial functions for both transport andcollision terms, which is more adequate for Gaussian quadrature than previousapproaches.

Entropy-stable positivity-preserving DG schemes for Boltzmann-Poisson models of collisional electronic transport along energy bands