Galerkin Approximation of Weak Solutions of the Drift Diffusion Model for Semiconductors Coupled with Maxwell's Equations

1996 ◽  
Vol 19 (18) ◽  
pp. 1471-1488
Author(s):  
F. Jochmann
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Galerkin Approximation ◽  
Drift Diffusion Model ◽  
Drift Diffusion

scholarly journals Bounded weak solutions to a matrix drift–diffusion model for spin-coherent electron transport in semiconductors

2015 ◽  
Vol 25 (05) ◽  
pp. 929-958 ◽  
Author(s):  
Ansgar Jüngel ◽  
Claudia Negulescu ◽  
Polina Shpartko
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Spin Vector ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Vector Density ◽  
Cross Diffusion ◽  
Electron Density Matrix ◽  
Finite Volume Discretization ◽  
Bounded Weak Solutions

The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift–diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and spin-vector density) satisfy a parabolic 4 × 4 cross-diffusion system. The key idea of the existence proof is to work with different variables: the spin-up and spin-down densities as well as the parallel and perpendicular components of the spin-vector density with respect to the precession vector. In these variables, the diffusion matrix becomes diagonal. The proofs of the L∞ estimates are based on Stampacchia truncation as well as Moser- and Alikakos-type iteration arguments. The monotonicity of the entropy (or free energy) is also proved. Numerical experiments in one-space dimension using a finite-volume discretization indicate that the entropy decays exponentially fast to the equilibrium state.

The Global Existence and Semiclassical Limit of Weak Solutions to Multidimensional Quantum Drift-diffusion Model

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
Xiuqing Chen
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Semiclassical Limit ◽  
Periodic Boundary Conditions ◽  
Drift Diffusion Model ◽  
Global Weak Solutions ◽  
Drift Diffusion ◽  
Initial Value ◽  
Fourth Order Parabolic System ◽  
Entropy Estimate

AbstractWe establish the global weak solutions to quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions with large initial value and periodic boundary conditions and furthermore obtain the semiclassical limit by entropy estimate and compactness argument.

scholarly journals Informing cognitive abstractions through neuroimaging: The neural drift diffusion model.

2015 ◽  
Vol 122 (2) ◽  
pp. 312-336 ◽  
Author(s):  
Brandon M. Turner ◽  
Leendert van Maanen ◽  
Birte U. Forstmann
Keyword(s):  
Diffusion Model ◽  
Drift Diffusion Model ◽  
Drift Diffusion

Incorporating photon recycling into the analytical drift-diffusion model of high efficiency solar cells

2014 ◽  
Vol 116 (19) ◽  
pp. 194504 ◽  
Author(s):  
Matthew P. Lumb ◽  
Myles A. Steiner ◽  
John F. Geisz ◽  
Robert J. Walters
Keyword(s):  
Solar Cells ◽  
Diffusion Model ◽  
High Efficiency ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
High Efficiency Solar Cells ◽  
Photon Recycling
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