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Pol Grasland-Mongrain added section_Simulation_study_Additionally_to__.tex
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\section{Simulation study}
Additionally to the experiments, a three dimensional simulation of the experiments was performed using Matlab (Matlab 2010, The MathWorks, Natick, MA, USA). The simulation was performed by (1) calculating the electrical current induced by the coil, (2) simulating the magnetic field created by the permanent magnet, (3) calculating the resulting Lorentz force inside the medium, and finally (4) calculating the displacement along space and time due to the Lorentz force.
Using Equation \ref{Equation1} with two 75 mm diameter coils crossed by an half cycle of 0.4 ms electrical current, representing the butterfly coil used in the experiment, and Ohm's law, the electrical current $\mathbf{j}$ was estimated in a 4x8x8 sample with an electrical conductivity $\sigma$ = 1 S.m$^{-1}$ inside and 0 outside. No border effects have been taken into account. Electrical current in a XY plane at a depth of 2 cm is illustrated in Figure \ref{Figure3}-(A).
A finite element software (Finite Element Magnetic Method \cite{FEMM}) was used to produce a two dimensional simulation of the magnetic field $\mathbf{B}$. The magnetic field was supposed to be approximately constant in the sample along the Y axis. The software simulated a N48 NdFeB permanent magnet of 5x5 cm$^2$ placed in a 19x27 cm$^2$ surface of air, and resulting magnetic field is illustrated in Figure \ref{Figure3}-(B).
