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

@@ -195,7 +195,7 @@ in that list the next superblock is given by the 'next grid' operator
 The list ends if the next grid pointer is a NULL pointer. The following
 image illustrates the linked list concept.
 
-![linked-list-concept](uploads/7e311eea207cfd20102f732360c219c5/linked-list-concept.png)
+![linked-list-concept](uploads/7e311eea207cfd20102f732360c219c5/linked-list-concept.png){width=80%}
 
 Assuming a serial run for the moment, looping over all superblocks `g`
 of mesh refinement level $l$ (index `il`) is as simple as
@@ -405,15 +405,9 @@ individually selected by the user. The standard implementation covers
 the following criteria:
 
 -   derivatives-based (most important in practice):
-    $$\left[\alpha\frac{|\delta U|}{|U|+U_\mathrm{ref}}+(1-\alpha)
-    \frac{|\delta^2U|}{|\delta U|+{\rm FILTER}\cdot(|U|+U_\mathrm{ref})}\right]
-    \left(\frac{\delta x^{(l)}}{\delta x^{(0)}}\right)^{\xi}
-    \left\{\begin{array}{ll}
-    >\mathcal{E}_{U}  &\exists U \quad\hbox{refinement}\\
-    <0.8\mathcal{E}_{U}  & \forall U \quad\hbox{derefinement}\\
-    \end{array}\right.$$
 
 ![amr_deriv](uploads/25c608e1a335aca4242b34afb9e4ffeb/amr_deriv.png){width=80%} 
+
     The criterion is applied to physical variables $U$
     ($=\{\varrho,\mathbf{m},e,\mathbf{B},C_\mathrm{c}\}$). Undivided
     first ($\delta U$) and second ($\delta^2U$) differences are computed along
@@ -438,13 +432,9 @@ the following criteria:
     side) to decide whether a child block is to be created.
 
 -   Jeans-length-based (important in simulations involving selfgravity):
-    $\left(\frac{\pi}{G}\frac{c_s^2}{\varrho}\right)^{1/2}
-    \cdot \mathcal{E}_\mathrm{Jeans}\left\{\begin{array}{ll}
-    <\delta s & \mbox{refinement}\\
-    >1.25\delta s & \mbox{derefinement}\\
-    \end{array}\right.$ 
 
 ![amr_Jeans](uploads/57691ce992d4c86be15b6e7b5637166b/amr_Jeans.png){width=80%}          
+
     where the first factor is the local Jeans
     length with $c_s$ the sound speed and $G$ the gravitational
     constant, and where $\delta s=\min\{\delta x,h_y\delta y, h_z\delta z\}$.
@@ -454,14 +444,9 @@ the following criteria:
 
 -   Field-length-based (potentially relevant for simulations involving a
     heatloss source but rarely used in practice):
-    $$2\pi \left(\frac{\kappa T}{\max\left\{T\left(\frac{\partial L}{\partial T}\right)_{\varrho}
-    -\varrho \left(\frac{\partial L}{\partial \varrho}\right)_{T},EPS\right\}}
-    \right)^{1/2}\cdot \mathcal{E}_\mathrm{Field}\left\{\begin{array}{ll}
-    <\delta s & \mbox{refinement}\\
-    >1.25\delta s & \mbox{derefinement}\\
-    \end{array}\right.$$ 
 
 ![amr_Field](uploads/de458510a631f1c2c18766c32f92eff1/amr_Field.png){width=80%}   
+
     where the first factor is the Field length with
     $L(\varrho, T)$ the density- and temperature-dependent heatloss
     function and $\kappa$ the thermal conduction coefficient.