docs/2016-11-01-operativ.md

@@ -42,7 +42,7 @@ sections:
 - `<solver>euler</solver>`
      - The solver for the ODE. Only *Euler*. No other options.
 - `<stepsize>0.001</stepsize>`: 
-     - The time step for the solver. This should be choosed with care. For force-based model it is recommended to take a value between $$ 10^{-2} $$ and $$10^{-3}$$ s.
+     - The time step for the solver. This should be choosed with care. For force-based model it is recommended to take a value between $$ `10^{-2} `$$ and $$`10^{-3}`$$ s.
        For first-order models, a value of 0.05 s should be OK.
        A larger time step leads to faster simulations, however it is too risky and can lead to 
 numerical instability, collisions and overlapping among pedestrians.
@@ -52,7 +52,7 @@ numerical instability, collisions and overlapping among pedestrians.
      - This option is only implemented in *Tordeux2015* and is very geometry-specific (only for corridors) with predefined settings. See Utest/Validation/1test_1D/ for a use case.
      
 - `<exit_crossing_strategy>3</exit_crossing_strategy>`
-     - Positive values in $$[1, 9]$$. See [Direction strategies](2016-11-02-direction.html) for the definition of the strategies.
+     - Positive values in $$`[1, 9]`$$. See [Direction strategies](2016-11-02-direction.html) for the definition of the strategies.
      
 - `<linkedcells enabled="true" cell_size="2"/>`
      - Defines the size of the cells. This is important to get the neighbors of a pedestrians, which
@@ -84,19 +84,19 @@ The parameters that can be specified in this section are Gauss distributed (defa
     - Unit: m/s
 
 #### Shape of pedestrians
-Pedestrians are modeled as ellipses with two semi-axes: $$a$$ and $$b$$, where
+Pedestrians are modeled as ellipses with two semi-axes: $$`a`$$ and $$`b`$$, where
 
-$$
+$$`
 a= a_{min} + a_{\tau}v, 
-$$
+`$$
 
 and
 
-$$
+$$`
 b = b_{max} - (b_{max}-b_{min})\frac{v}{v^0}.
-$$
+`$$
 
-$$v$$ is the peed of a pedestrian.
+$$`v`$$ is the peed of a pedestrian.
 
 - `<bmax mu="0.15" sigma="0.0" />`
     - Maximal length of the shoulder semi-axis
@@ -105,7 +105,7 @@ $$v$$ is the peed of a pedestrian.
     - Minimal length of the shoulder semi-axis
     - Unit: m
 - `<amin mu="0.15" sigma="0.0" />`
-    - Minimal length of the movement semi-axis. This is the case when $$v=0$$.
+    - Minimal length of the movement semi-axis. This is the case when $$`v=0`$$.
     - Unit: m  
 - `<atau mu="0." sigma="0.0" />`  
     - (Linear) speed-dependency of the movement semi-axis  
@@ -114,7 +114,7 @@ $$v$$ is the peed of a pedestrian.
 Other parameters in this section are:
 
 - `<tau mu="0.5" sigma="0.0" />`
-    - Reaction time. This constant is used in the driving force of the force-based forces. Small $$\rightarrow$$ instantaneous acceleration.
+    - Reaction time. This constant is used in the driving force of the force-based forces. Small $$`\rightarrow`$$ instantaneous acceleration.
     - Unit: s
 - `<T mu="1" sigma="0.0" />`
     - Specific parameter for model 3 (Tordeux2015). Defines the slope of the speed function. 
@@ -151,10 +151,10 @@ Usage:
 Besides the options defined in [Mode_parameters](#model_parameters) the following options are necessary for this model:
 
 - `<force_ped  a="5" D="0.2"/>`
-     - The influence of other pedestrians is triggered by $$a$$ and $$D$$ where $$a$$ is the strength if the interaction and $$D$$ gives its range. The naming may be misleading, since the model is **not** force-based, but velocity-based. 
+     - The influence of other pedestrians is triggered by $$`a`$$ and $$`D`$$ where $$`a`$$ is the strength if the interaction and $$`D`$$ gives its range. The naming may be misleading, since the model is **not** force-based, but velocity-based. 
      - Unit: m
 - `<force_wall a="5" D="0.02"/>`: 
-     - The influence of  walls is triggered by $$a$$ and $$D$$ where $$a$$ is the strength if the interaction and $$D$$ gives its range. A larger value of $$D$$ may lead to blockades, especially when passing narrow bottlenecks.
+     - The influence of  walls is triggered by $$`a`$$ and $$`D`$$ where $$`a`$$ is the strength if the interaction and $$`D`$$ gives its range. A larger value of $$`D`$$ may lead to blockades, especially when passing narrow bottlenecks.
      - Unit: m
      
 The names of the aforementioned parameters might be misleading, since the model is *not* force-based. The naming will be changed in the future.
@@ -262,7 +262,7 @@ Valid exit strategies are {6, 8, 9}. Please see details below.
 ### Generalized Centrifugal Force Model with lateral swaying
 
 The [Generalized Centrifugal Force Model with lateral swaying][#Krausz] is mostly identical to the GCFM Model, 
-but instead of a variable semi-axis $$b$$ of the ellipse simulating the pedestrian, pedestrians perform an oscillation perpendicular to their direction of motion.
+but instead of a variable semi-axis $$`b`$$ of the ellipse simulating the pedestrian, pedestrians perform an oscillation perpendicular to their direction of motion.
 As a consequence the parameter `Bmax` is ignored. 
 
 Usage:
@@ -276,10 +276,10 @@ Four Parameters can be passed to control the lateral swaying, for example:
 `<sway ampA="-0.14" ampB="0.21" freqA="0.44" freqB="0.35" />`
 
 - `ampA` and `ampB` determine the amplitude of the oscillation according to the linear relation 
-   $$A = \texttt{ampA} \cdot \| v_i \| + \texttt{ampB}$$.
+   $$`A = \texttt{ampA} \cdot \| v_i \| + \texttt{ampB}`$$.
 
 - `freqA` and `freqB` determine the frequency of the oscillation according to 
-   $$f = \texttt{freqA} \cdot \| v_i \| + \texttt{freqB}$$.
+   $$`f = \texttt{freqA} \cdot \| v_i \| + \texttt{freqB}`$$.
 
 Setting `ampA` and `ampB` to 0 disables lateral swaying. If not specified, the empirical values given in [Krausz, 2012][#Krausz] are used, that is: