deletions | additions       diff --git a/Simulation_study.tex b/Simulation_study.tex  index 7fa026d..f7491b1 100644  --- a/Simulation_study.tex  +++ b/Simulation_study.tex 
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Using Equation \ref{Equation1} with two 75 mm diameter coils crossed by a 149.10$^6$ A.s$^{-1}$ electrical current, representing the TMS coil used in the experiment, electrical field $E$ was calculated in a 5x10x10 cm$^2$ volume (see \cite{Grandori_1991} for details on mathematical solving). Using Ohm's law, the electrical current $\mathbf{j}$ was estimated assuming an electrical conductivity $\sigma$ = 5 S.m$^{-1}$ inside a a 4x8x8 cm$^2$ medium and 0 outside. No border effects have been taken into account. Induced electrical current in a XY plane at a depth of 2 cm with 2x2 mm$^2$ pixels is illustrated in Figure \ref{Figure3}-(A), with colors indicating the absolute magnitude and arrows the direction.  A finite element software (Finite Element Magnetic Method \cite{FEMM}) was used to produce a two dimensional simulation of the magnetic field $\mathbf{B}$. Magnetostatic problem was solved from equations $\nabla \times H = \nabla \times M$, $\nabla B = 0$ and $B=\mu H$, with $H$ magnetic field intensity, $M$ magnetization of the medium, $B$ magnetic flux density and $\mu$ medium permeability. Medium was considered as linear, and space was meshed with approximately 0.5 cm$^2$ triangles. 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 20x20 cm$^2$ surface of air. Resulting magnetic field in a 19x27 cm$^2$ area  is illustrated in Figure \ref{Figure3}-(B), with colors indicating the absolute magnitude and arrows the direction. Body Lorentz force $\mathbf{f}$ was computed from the cross-product of $\mathbf{j}$ and $\mathbf{B}$. As the electrical current is induced in the XY plane and the magnetic field essentially along X direction, Lorentz force is mainly along Z direction. Z component of the Lorentz force is illustrated in Figure \ref{Figure3}-C, with arrows indicating the Lorentz force vector and color its amplitude along Z.