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

@@ -415,12 +415,10 @@ possible values or a numeric range.
         Jeans-length-based mesh refinement criterion allowing a
         systematic reduction of the Jeans threshold with increasing
         refinement level $l$ according to the expression 
-        Jeans length becomes gradually higher resolved with increasing $l$. 
-        `_C.amr_dJeans` must be positiv.   $y=10^{-7}$ $y=10^{-7}$ 
-
         `_C.amr_Jeans`$-l*$`_C.amr_dJeans`, i.e., the local  
+        Jeans length becomes gradually higher resolved with increasing $l$. 
+        `_C.amr_dJeans` must be positiv. 
 
-        $y=10^{-7}$
         **Important**: `_C.amr_dJeans` must be chosen with care such
         that the actual Jeans threshold never becomes too small or
         negative at some refinement level. Otherwise it will trigger
@@ -454,7 +452,6 @@ possible values or a numeric range.
 -   `06` (`_C.flag[0-7]`)
 
     -   `_C.flag[0-7]`: freely usable parameter of `int` type.
-        $y=10^{-7}$
 
 **SOLVER SPECIFICATIONS**:
 
@@ -540,7 +537,7 @@ possible values or a numeric range.
     -   `_C.reactions_max_changeX` (typical value: $<0.1$): allowed
         maximal relative change of species number densities (or total
         number density) in the time integration of the chemo-thermal
-        rate equations. $y=10^{-7}$
+        rate equations.
 
         **Important:** The macro `SXN` in module `solveNCCM.c` is a
         linear weight applying `_C.reactions_max_change` to a combined
@@ -580,8 +577,8 @@ possible values or a numeric range.
         from the momentum equation and the induction equation is not
         solved.
 
-    -   `_C.permeability_rel`: relative magnetic permeability
-        $\mu_{rel}$ ($=\mu/\mu_0,\,\mu_0=4\pi\cdot10^{-7}\mathtt{V}\cdot\mathtt{m}^{-1}\cdot\mathtt{A}^{-1}\cdot\mathtt{s}^{-1}$).
+    -   `_C.permeability_rel`: relative magnetic permeability $\mu_{rel}$ 
+        ($=\mu/\mu_0,\,\mu_0=4\pi\cdot10^{-7}\mathtt{V}\cdot\mathtt{m}^{-1}\cdot\mathtt{A}^{-1}\cdot\mathtt{s}^{-1}$).
 
         **Important:** The Gaussian unit system can be mimicked by
         choosing a value ${\tt \_C.permeability\_rel}=10^7$ so that
@@ -623,7 +620,7 @@ possible values or a numeric range.
         `_C.conduction_coeff` (and `_C.conduction_coeff_perp` in the
         anisotropic case) described below. U enables thermal conduction
         with a user-defined conduction coefficient as coded in the user
-        interface function **conductionCoeffUser()** (cf. [Thermal
+        interface function `conductionCoeffUser()` (cf. [Thermal
         conduction](#thermal-conduction)). S enables thermal conduction
         using the standard Spitzer conductivity model predefined in
         NIRVANA (cf. [physics
@@ -650,8 +647,7 @@ possible values or a numeric range.
         described below. U enables ambipolar diffusion with a
         user-defined anbipolar diffusion coefficient as coded in the
         user interface function **APdiffusionCoeffUser()** (cf.
-        [Ambipolar
-        diffusion](#user-defined-coefficient-for-ambipolar-diffusion)).
+        [Ambipolar diffusion](#user-defined-coefficient-for-ambipolar-diffusion)).
         N disables ambipolar diffusion.
 
     -   `_C.APdiffusion_coeff`: constant ambipolar diffusion
@@ -731,8 +727,8 @@ possible values or a numeric range.
         adiabatic index is not a freely selectable parameter but is
         approximated by the expression
 
-        $\gamma=\left[5(n_\mathrm{H}+n_\mathrm{He}+n_\mathrm{e})+7n_{\mathrm{H}_2}\right]
-        /\left[3(n_\mathrm{H}+n_\mathrm{He}+n_\mathrm{e})+5n_{\mathrm{H}_2}\right]$.
+        $$\gamma=\left[5(n_\mathrm{H}+n_\mathrm{He}+n_\mathrm{e})+7n_{\mathrm{H}_2}\right]
+        /\left[3(n_\mathrm{H}+n_\mathrm{He}+n_\mathrm{e})+5n_{\mathrm{H}_2}\right]$$.
 
     -   `_C.polytropic_constant`: polytropic constant in the polytropic
         EOS.
@@ -815,10 +811,10 @@ energy density $e$ is irrelevant since no energy equation is solved. In
 HD simulations, the assignment of the magnetic field is redundant, of
 course, and would lead to an error because arrays for the magnetic field
 components are not allocated in the HD case. Likewise, arrays for tracer
-and species, $C_\mc$ and $n_\ms$, are not declared unless the parameters
+and species, $C_c$ and $n_s$, are not declared unless the parameters
 `_C.tracer`$>0$ respective ${\tt\_C.species}>0$. If the TESTFIELDS
 infrastructure is used (`_C.testfields`$>0$) testfields fluctuation
-variables, $\mathbf{b}_\mt,\,\mt=0,{\tt\_C.testfields}-1$, are also
+variables, $\mathbf{b}_t,\,t=0,{\tt\_C.testfields}-1$, are also
 considered as primary variables and must be assigned by the user. The
 parameter `_C.testfields` denotes the number of testfields.
 
@@ -851,7 +847,7 @@ structure](#mesh-data-structure).
 
 There are two types of mesh variables: cell-averaged variables and
 face-averaged variables. Cell-averaged variables are
-$\varrho,m_x,m_y,m_z,n_\ms,C_\mc$. It are described by cell-centroid
+$\varrho,m_x,m_y,m_z,n_s,C_c$. It are described by cell-centroid
 coordinates. Face-averaged variables are the magnetic field components
 $B_x,B_y,B_z$ (and testfields). It are described by cell face-centroid
 coordinates.
@@ -950,13 +946,13 @@ divergence-free setup:
 components by exact integration of given analytical expressions. For a
 grid cell (,,) on superblock `g` the discretized components would then
 read 
-$$\mathtt{g->bx[iz][iy][ix]}=\frac{1}{\d \mathcal{A}_x}\int
+$$\mathtt{g->bx[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_x}\int
 \limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]}
 \int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]} B_x(\mathtt{g->x[ix]},y,z)h_yh_zdydz$$
-$$\mathtt{g->by[iz][iy][ix]}=\frac{1}{\d \mathcal{A}_y}\int
+$$\mathtt{g->by[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_y}\int
 \limits_\mathtt{g->x[ix]}^\mathtt{g->x[ix+1]}
 \int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]} B_y(x,\mathtt{g->y[iy]},z)h_zdxdz$$
-$$\mathtt{g->bz[iz][iy][ix]}=\frac{1}{\d \mathcal{A}_z}\int
+$$\mathtt{g->bz[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_z}\int
 \limits_\mathtt{g->x[ix]}^\mathtt{g->x[ix+1]}
 \int\limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]} B_z(x,y,\mathtt{g->z[iz]})h_ydxdy$$
 where the numerical expressions for the cell faces are:
@@ -974,23 +970,23 @@ integration over cell faces turns out to be too complicated.
 The face-averaged magnetic field components are then obtained from the
 integral form of $\mathbf{B}=\nabla\times \mathbf{A}$:
 
-`g->bx[iz][iy][ix]`$=\left[h_y\Delta_\miy (h_{zy}\hat{A}_z)
--h_y\Delta_\miz \hat{A}_y\right]/\d \mathcal{A}_x$
+`g->bx[iz][iy][ix]`$=\left[h_y\Delta_{iy} (h_{zy}\hat{A}_z)
+-h_y\Delta_{iz} \hat{A}_y\right]/\delta \mathcal{A}_x$
 
-`g->by[iz][iy][ix]`$=\left[\Delta_\miz \hat{A}_x
--h_{zy}\Delta_\mix (h_y\hat{A}_z)\right]/\d \mathcal{A}_y$
+`g->by[iz][iy][ix]`$=\left[\Delta_{iz} \hat{A}_x
+-h_{zy}\Delta_{ix} (h_y\hat{A}_z)\right]/\delta \mathcal{A}_y$
 
-`g->bz[iz][iy][ix]`$=\left[\Delta_\mix (h_y\hat{A}_y)
--\Delta_\miy \hat{A}_x\right]/\d \mathcal{A}_z$
+`g->bz[iz][iy][ix]`$=\left[\Delta_{ix} (h_y\hat{A}_y)
+-\Delta_{iy} \hat{A}_x\right]/\delta \mathcal{A}_z$
 
-where the difference operators $\Delta_\mix$, $\Delta_\miy$ and
-$\Delta_\miz$ are given by
+where the difference operators $\Delta_{ix}$, $\Delta_{iy}$ and
+$\Delta_{iz}$ are given by
 
-$\Delta_{\mix}X=X(\mathtt{ix+1,iy,iz})-X(\mathtt{ix,iy,iz})$,
+$\Delta_{ix}X=X(\mathtt{ix+1,iy,iz})-X(\mathtt{ix,iy,iz})$,
 
-$\Delta_{\miy}X=X(\mathtt{ix,iy+1,iz})-X(\mathtt{ix,iy,iz})$,
+$\Delta_{iy}X=X(\mathtt{ix,iy+1,iz})-X(\mathtt{ix,iy,iz})$,
 
-$\Delta_{\miz}X=X(\mathtt{ix,iy,iz+1})-X(\mathtt{ix,iy,iz})$
+$\Delta_{iz}X=X(\mathtt{ix,iy,iz+1})-X(\mathtt{ix,iy,iz})$
 
 and $(\hat{A}_x,\hat{A}_y,\hat{A}_z)$ are the cell-edge integrals
 
@@ -1436,7 +1432,7 @@ by the appropriate choice of parameter `_C.conduction` in file
 Ohmic diffusion enters the induction equation and energy equation as a
 field contribution given by
 
-$\mathbf{E}_\mathrm{D}=\eta_\mathrm{D} \nabla\times\mathbf{B}$
+$$\mathbf{E}_\mathrm{D}=\eta_\mathrm{D} \nabla\times\mathbf{B}$$
 
 where $\eta_\mathrm{D}$ in units \[m$^2\cdot$s$^{-1}$\] is the diffusion
 coefficient.
@@ -1475,8 +1471,8 @@ user-defined ambipolar diffusion coefficient.
 Ambipolar diffusion enters the induction equation and energy equation as
 a field contribution given by
 
-$\mathbf{E}_\mathrm{AD}=\eta_\mathrm{AD}/\mu\mathbf{B}\times\left[(\nabla\times\mathbf{B})
-\times\mathbf{B}\right]$
+$$\mathbf{E}_\mathrm{AD}=\eta_\mathrm{AD}/\mu\mathbf{B}\times\left[(\nabla\times\mathbf{B})
+\times\mathbf{B}\right]$$
 
 where $\eta_\mathrm{AD}$ \[V$\cdot$m$\cdot$A$^{-1}\cdot$T$^{-2}$\]
 denotes the ambipolar diffusion coefficient. The prefactor