3-NIRVANA-user-guide/3.2-User-interfaces.md

@@ -1445,9 +1445,6 @@ below category PHYSICS SPECIFICATIONS.
 
 ### User-defined coefficient for ambipolar diffusion
 
-The module `APdiffusionCoeffUser.c` serves as template for a
-user-defined ambipolar diffusion coefficient.
-
 Ambipolar diffusion enters the induction equation and energy equation as
 a field contribution given by
 
@@ -1455,8 +1452,7 @@ a field contribution given by
 
 where *η*<sub>*AD*</sub> in units \[V⋅m⋅A<sup>−1</sup>⋅T<sup>−2</sup>\] 
 denotes the ambipolar diffusion coefficient.
-
-The prefactor* *η*<sub>*AD*</sub>/*μ* has units 
+The prefactor *η*<sub>*AD*</sub>/*μ* has units 
 m<sup>2</sup>⋅s<sup>−1</sup>⋅T<sup>−2</sup>.
 
 A user-defined coefficients, *η*<sub>*AD*</sub>,
@@ -1490,8 +1486,8 @@ found in testproblem `/nirvana/testproblems/APDIFF/problem1`.
 ### User-defined body force
 
 The module `forceUser.c` serves as template for a user-defined
-*specific* body force $\mathbf{f}$ (force per mass in units
-N$\cdot$kg$^{-1}$). The body force enters the momentum equation and
+*specific* body force **f** (force per mass in units N⋅kg<sup>−1</sup>).
+The body force enters the momentum equation and
 energy equation as source term.
 
 A user body force has to be defined in the function
@@ -1526,12 +1522,13 @@ be found in testproblem `/nirvana/testproblems/MHD/problem21`.
 
 The modules `sourceCoolingUser.c` and `sourceHeatingUser.c` serve as
 templates for coding a user-defined cooling function,
-$L_\mathrm{cool}\le 0$, and heating function, $L_\mathrm{heat}\ge 0$,
-respectively. Both functions are allowed to depend on temperature $T$
-and density $\varrho$. The net heatloss, i.e. the sum
-$L_\mathrm{cool}(T,\varrho)+L_\mathrm{heat}(T,\varrho)$, enters as
-source term in the energy equation. $L_\mathrm{cool}$ and
-$L_\mathrm{heat}$ are measured in units J$\cdot$s$^{-1}\cdot$m$^{-3}$.
+*L*<sub>*cool*</sub>≤0, and heating function, *L*<sub>*heat*</sub>≥0,
+respectively. Both functions are allowed to depend on temperature 
+*T* and density 𝜚. The net heatloss, i.e. the sum
+*L*<sub>*cool*</sub>(*T*,𝜚)+*L*<sub>*heat*</sub>(*T*,𝜚), enters as
+source term in the energy equation. 
+*L*<sub>*cool*</sub> and *L*<sub>*heat*</sub> are measured
+in units J⋅s<sup>−1</sup>⋅m<sup>−3</sup>.
 
 User-defined cooling/heating rates are to be defined in the functions
 
@@ -1541,11 +1538,10 @@ User-defined cooling/heating rates are to be defined in the functions
 
 taking arguments `T`, the temperature, `rho`, the gas density, the
 pointer `deriv`, a flag to tell the calling function whether the user
-provides the derivatives $\partial L_\mathrm{cool}\partial\varrho$,
-$\partial L_\mathrm{cool}\partial T$ to be stored in the 2-element
-vector `dfc[0], dfc[1]` and the derivatives
-$\partial L_\mathrm{heat}\partial\varrho$,
-$\partial L_\mathrm{heat}\partial T$ to be stored in the 2-element
+provides the derivatives ∂*L*<sub>*cool*</sub>/∂𝜚,
+∂*L*<sub>*cool*</sub>/∂*T* to be stored in the 2-element
+vector `dfc[0], dfc[1]` and the derivatives ∂*L*<sub>*heat*</sub>/∂𝜚,
+∂*L*<sub>*heat*</sub>/∂*T* to be stored in the 2-element
 vector `dfh[0], dfh[1]`. The default value is preset to `deriv=YES` in
 both functions. The user may avoid to explicitely calculating
 derivatives by setting `deriv=NO`. Then, derivatives are computed by the