3-NIRVANA-user-guide/3.1-Code-basics.md

@@ -412,7 +412,7 @@ where
 is the grid spacing of the base level, i.e., there is a doubling of
 resolution from one refinement level to the next higher.
 
-Starting on the base level (*l* = 0) mesh refinements are realized by
+Starting on the base level (*l*=0) mesh refinements are realized by
 overlaying child grid blocks at locations which need refinement
 according to different refinement criteria discussed in more detail
 below. A child grid block covers one octant (a logical cube of 2 grid
@@ -432,7 +432,7 @@ The criterion is applied to primary (or related) physical variables
     computed along various spatial directions. The switch *α* ∈ \[0, 1\]
     (code parameter: `_C.amr_d1`) selects between a purely
     gradient-based criterion (*α*=1) and a purely
-    second-derivatives-based criterion (*α* = 0).
+    second-derivatives-based criterion (*α*=0).
     *U*<sub>*r**e**f*</sub> are reference values to avoid division by
     zero for indefinite variables. The exponent *ξ* ∈ \[0, 2\] (code
     parameter: `_C.amr_exp`) introduces a power law functional on the
@@ -458,7 +458,7 @@ The criterion is applied to primary (or related) physical variables
     *c*<sub>*s*</sub> the sound speed and *G* the gravitational
     constant, and where
     *δs* = min {*δx*, *h*<sub>*y*</sub>*δy*, *h*<sub>*z*</sub>*δz*}.
-    ℰ<sub>*J**e**a**n**s*</sub> is a user-specific threshold with the
+    ℰ<sub>*Jeans*</sub> is a user-specific threshold with the
     reciprocal value giving the minimum number of grid cells the local
     Jeans length should be resolved.
   
@@ -467,7 +467,7 @@ The criterion is applied to primary (or related) physical variables
 ![amr_Field](uploads/de458510a631f1c2c18766c32f92eff1/amr_Field.png)    
     where the first factor is the Field length with *L*(𝜚, *T*) the
     density- and temperature-dependent heatloss function and *κ* the
-    thermal conduction coefficient. ℰ<sub>*F**i**e**l**d*</sub> is a
+    thermal conduction coefficient. ℰ<sub>*Field*</sub> is a
     user-specific threshold with the reciprocal value giving the minimum
     number of grid cells the Field length should be resolved.