Page 1 Next

Displaying 1 – 20 of 56

Showing per page

2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Mouhcine Tilioua (2011)

Applications of Mathematics

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

3D-2D asymptotic analysis for micromagnetic thin films

Roberto Alicandro, Chiara Leone (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Γ -convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure Ω ε = ω × ( - ε , ε ) , ω 2 , whose energy is given by ε ( m ¯ ) = 1 ε Ω ε W ( m ¯ , m ¯ ) + 1 2 u ¯ · m ¯ d x subject to div ( - u ¯ + m ¯ χ Ω ε ) = 0 on 3 , and to the constraint | m ¯ | = 1 on Ω ε , where W is any continuous function satisfying p -growth assumptions with p > 1 . Partial results are also obtained in the case p = 1 , under an additional assumption on W .

3D-2D Asymptotic Analysis for Micromagnetic Thin Films

Roberto Alicandro, Chiara Leone (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Γ-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure Ω ε = ω × ( - ε , ε ) , ω 2 , whose energy is given by ε ( m ¯ ) = 1 ε Ω ε W ( m ¯ , m ¯ ) + 1 2 u ¯ · m ¯ d x subject to div ( - u ¯ + m ¯ χ Ω ε ) = 0 on 3 , and to the constraint | m ¯ | = 1 on Ω ε , where W is any continuous function satisfying p-growth assumptions with p> 1. Partial results are also obtained in the case p=1, under an additional assumption on W.

Currently displaying 1 – 20 of 56

Page 1 Next