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Original file line number Diff line number Diff line change
Expand Up @@ -94,9 +94,9 @@ To get the average temperature on these two regions,
the sum of temperature nodal values is divided by the number
of unique nodes. In this example,
the average temperature is
\f$\f$
$$
(500 + 300 + 800 + 600 + 500 + 300) / 6 = 500 [K]
\f$\f$.
$$.

![Figure 6: Nodal intensive variable (temperature) values for the multi-region case with shared nodes](../images/MultiregionFigure6.png)
*Figure 6: Nodal intensive variable (temperature) values for the multi-region case with shared nodes*
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Expand Up @@ -35,7 +35,7 @@ elements. The meshes with default settings are shown in _Figure 1_.
_Figure 1: Default pipe meshes_

On each side, we initialize the nodal
solution data with a simple linear profile \f$f(x,y,z) = 1x + 2y + 3z + 4\f$. On the **quad** region, we initialize
solution data with a simple linear profile $f(x,y,z) = 1x + 2y + 3z + 4$. On the **quad** region, we initialize
**linear1** variable, and on the **tri** region, we initialize the **linear2** variable.

We then use the mapping capabilities within the Participant Library to transfer
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Expand Up @@ -42,14 +42,14 @@ _Figure 1: Structural solver geometry_
Since the purpose of this example is to demonstrate the use of Participant
Library APIs for a transient analysis, a simple damping force solver will be
used to couple with Mechanical via System Coupling. This solver receives nodal
displacements \f$\vec{X}\f$ from Mechanical and calculates the damping force
\f$\vec{F}\f$ using the following formula:
displacements $\vec{X}$ from Mechanical and calculates the damping force
$\vec{F}$ using the following formula:

\f$\f$
$$
\vec{F} = - c \frac{d\vec{X}}{dt}
\f$\f$
$$

where \f$c\f$ is the damping coefficient and \f$\frac{d\vec{X}}{dt}\f$ is the rate of change
where $c$ is the damping coefficient and $\frac{d\vec{X}}{dt}$ is the rate of change
of nodal positions with respect to time (nodal velocities).
The damping solver will then provide the calculated
forces to Mechanical via System Coupling, and these damping forces will cause the
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