minor corrections

MagneticForces/magnets.pro

@@ -2,7 +2,8 @@
    Tutorial 9 : 3D magnetostatic dual formulations and magnetic forces
 
    Features:
-   - Dual 3D magnetostatic formulations
+   - 3D Magnetostatics 
+   - Dual vector and scalar magnetic potentials formulations
    - Boundary condition at infinity with infinite elements
    - Maxwell stress tensor and rigid-body magnetic forces
 
@@ -24,12 +25,12 @@
  in the problem decription below, irresective of whether they are
  truly permanent magnets or ferromagnetic barrels. 
 
- The tutorial model proposes the both dual 3D magnetostatic formulations:
+ The tutorial model proposes both dual 3D magnetostatic formulations:
  the magnetic vector potential formulation with spanning-tree gauging,
  and the scalar magnetic potential formulation.
  The later is rather simple in this case since, as there are no conductors,
  the known coercive field hc[] is the only source field "hs" one needs 
- to represens the magnetic field:
+ to represent the magnetic field:
   
    h = hs - grad phi   ,  hs = -hc.
 
@@ -45,19 +46,22 @@
  which is a material dependent function of the magnetic induction "b" field. 
  Exactly like we computed the heat flux "q(S)" through a surface "S"
  using a special auxiliary function "g(S)" associated with that surface 
- in the tutorial "Tutorial 5 : thermal problem with contact resistances",
+ in "Tutorial 5 : thermal problem with contact resistances",
  the magnetic force acting on a rigid body in empty space can be evaluated
  as the flux of the Maxwell stress tensor through that surface.
  There is one auxiliary function "g(SkinMagnet~{i}) = un~{i}"
- for each magnet and the resultant magnetic force acting on "Magnet~{i}"
+ for each magnet, and the resultant magnetic force acting on "Magnet~{i}"
  is given by the integral:
 
  f~{i} = Integral [ TM[{b}] * {-grad un~{i}} ] ;
 
- It should be insisted on the fact that the Maxwell stress is discontinuous
- on material discontinuities, and that magnetic forces on rigid bodies
- only depend on the Maxwell stress tensor of empty space and 
- on the "b" and "h" field distribution on the outer side of "SkinMagnet~{i}".
+ It should be insisted on the fact that the Maxwell stress tensor
+ is always discontinuous on material discontinuities, 
+ and that magnetic forces acting on rigid bodies
+ only depend on the Maxwell stress tensor of empty space, 
+ and on the "b" and "h" field distribution, 
+ on the external side of "SkinMagnet~{i}" 
+ (the side of the surface in contact with air).
 
  "{-grad un~{i}}" in the above formula can be regarded 
  as the normal vector to "SkinMagnet~{i}"
@@ -69,7 +73,7 @@
  which is much smaller than "AirBox".
  To speed up the computation of forces, a special domain "Vol_Force"
  for force integrations is defined, which contains only
- the layers  "layer~{i}" of alla magnets.  
+ the layers  "layer~{i}" of all magnets.  
 */
 
 Include "magnets_common.pro"