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A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation

O. Awono, J. Tagoudjeu (2010)

Mathematical Modelling of Natural Phenomena

We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...

Coulomb Interaction Effects on the Spin Polarization and Currents in Quantum Wires with Spin Orbit Interaction

Anton Heidar Thorolfsson, Andrei Manolescu, D.C. Marinescu, Vidar Gudmundsson (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

We analyze the charge and spin distributions induced in an interacting electron system confined inside a semiconductor quantum wire with spin orbit interaction in the presence of an external magnetic field. The wire, assumed to be infinitely long, is obtained through lateral confinement in three different materials: GaAs, InAs, and InSb. The spin-orbit coupling, linear in the electron momentum is of both Rashba and Dresselhaus type. Within the Hartree-Fock approximation the many-body Hamiltonian...

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