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

@@ -1574,16 +1574,16 @@ by definition of the following macros:
 | `TUSR(rho,eth)`   | temperature            |
 | `ETUSR(rho,eth)`  | thermal energy density |
 
-The macros are in general functions of the mass density $\varrho$
-(`rho`) and thermal energy density $\varepsilon$ (`eth`). It are
+The macros are in general functions of the mass density 𝜚 (`rho`) 
+and thermal energy density *ε* (`eth`). It are
 declared in the header file `nirvanaUser.h`. In order to give an
 example, the following code fragment (taken from `nirvanaUser.h` in
 testproblem `/nirvana/testproblems/GRAVITY/problem4`) illustrates the
 definition of a barotropic EOS of the form
 
-$p(\varrho)=a^2\varrho \left[1+(\varrho/\varrho_0)^{4/3}\right]^{1/2}$
+*p*(𝜚) = *a*<sup>2</sup>𝜚\[1+(𝜚/𝜚<sub>0</sub>)<sup>4/3</sup>\]<sup>1/2</sup>
 
-with $a=200$ and $\varrho_0=10^{-10}$.
+with *a*=200 and 𝜚<sub>0</sub>=10<sup>−10</sup>.
 
     #define PUSR(rho,eth)   (40000.*(rho)*sqrt(1.+pow((rho)/1.e-10,4./3.))+0*(eth))
     #define CS2USR(rho,eth) (40000.*sqrt(1.+pow((rho)/1.e-10,4./3.)) \
@@ -1592,10 +1592,10 @@ with $a=200$ and $\varrho_0=10^{-10}$.
     #define TUSR(rho,eth)   (MOK*_C.mean_molecular_weight*PUSR(rho,eth)/rho)
     #define ETUSR(rho,eth)  (PUSR(rho,eth)/(_C.gamma-1.))
 
-Since $p$ solely depends on $\varrho$ the energy density parameter `eth`
+Since *p* solely depends on 𝜚 the energy density parameter `eth`
 is irrelevant is this case. The `ETUSR` definition makes use of the
 prior definition of `PUSR` and assumes the usual caloric EOS with ratio
-of specific heats $\gamma$ (code variable `_C.gamma`). A barotropic EOS
+of specific heats *γ* (code variable `_C.gamma`). A barotropic EOS
 is consistent with solving no energy equation.
 
 **Important:** If an energy equation is solved together with an analytic
@@ -1616,19 +1616,19 @@ An analytic EOS is enabled by appropriately choosing the parameter
 
 NIRVANA also permits the implementation of a tabulated EOS. However, the
 procedure is more involved and requires the creation of look-up tables
-for the logarithm of pressure, $\log p$, and logarithm of temperature,
-$\log T$, both as functions of the logarithm of mass density $\varrho$
-and the logarithm of thermal energy density $\varepsilon$. The look-up
-tables for a prescribed $(\log\varrho, \log\varepsilon)$-range are
-generated by cubic interpolation from user-specified data
-$\{(\log p)_{ij}\}$ and $\{(\log T)_{ij}\}$ on an rectilinear mesh
-$\{(\log\varrho)_i\}\times\{(\log\varepsilon)_j\}$, $i=0,{\tt n1}-1$ and
-$j=0,{\tt n2}-1$ with `n1`$\times$`n2` the number of mesh points.
+for the logarithm of pressure, log *p*, and logarithm of temperature,
+log *T*, both as functions of the logarithm of mass density log 𝜚
+and the logarithm of thermal energy density *ε*. 
+The look-up tables for a prescribed (log 𝜚, log *ε*)-range
+are generated by cubic interpolation from user-specified data
+{(log *p*)<sub>*ij*</sub>} and ({(log *T*)<sub>*ij*</sub>})
+on an rectilinear mesh {(log 𝜚)<sub>*i*</sub>} × {(log *ε*)<sub>*j*</sub>},
+*i*=0,n1-1 and *j*=0,n2-1, with n1 × n2 the number of mesh points.
 
 Data for the look-up tables has to be defined in the function
-`eosTabPressureUser()` in module `eosTabPressureUser.c` for $\log p$,
+`eosTabPressureUser()` in module `eosTabPressureUser.c` for log *p*,
 and in the function `eosTabTemperatureUser()` in module
-`eosTabTemperatureUser.c` for $\log T$.
+`eosTabTemperatureUser.c` for log *T*.
 
 In both, `eosTabPressureUser()` and `eosTabTemperatureUser()`, the user
 must assign and return a structure of type `UTAB` (declared in header
@@ -1646,7 +1646,7 @@ Denoting by `ut` an instance of `UTAB` the structure is accessed by
 
 Here is an example how to code `eosTabPressureUser()` taken from
 testproblem `/nirvana/testproblem/MHD/problem1B` which provides data for
-the standard EOS of caloric type, $p=(\gamma -1)\varepsilon$, in
+the standard EOS of caloric type, *p*=(*γ* − 1)*ε*, in
 tabulated form:
 
     UTAB eosTabPressureUser(void)
@@ -1713,14 +1713,14 @@ tabulated form:
 
 First, the number of mesh points, `ut.n1` and `ut.n2`, in
 $\log\varrho$-direction and $\log\varepsilon$-direction is set. It
-follows the range \[`ut.u1_lo`,`ut.u1_up`\] for $\log\varrho$ and
-\[`ut.u2_lo`,`ut.u2_up`\] for $\log\varepsilon$, respectively. Then, the
-2D array `ut.dt2` is allocated and $\{(\log p)_{ij}\}$ data is assigned.
-`ut` is returned and used by the code to finally create the look-up
-table `_TABLP`. Actually, `_TABLP` is a (global) pointer of struct type
-`TAB` (declared in the header file `tabular.h`) and represents the
-tabulated EOS $\log p(\log\varrho,\log\varepsilon)$. Correspondingly,
-coding `eosTabTemperatureUser()` for $\log T$ would provide the input
+follows the range \[`ut.u1_lo`,`ut.u1_up`\] for log 𝜚 and
+\[`ut.u2_lo`,`ut.u2_up`\] for  log *ε*, respectively. Then, the
+2D array `ut.dt2` is allocated and {(log *p*)<sub>*ij*</sub>} 
+data is assigned. `ut` is returned and used by the code to finally create 
+the look-up table `_TABLP`. Actually, `_TABLP` is a (global) pointer of 
+struct type `TAB` (declared in the header file `tabular.h`) and represents 
+the tabulated EOS log *p*(log 𝜚, log *ε*). Correspondingly,
+coding `eosTabTemperatureUser()` for log *T* would provide the input
 for the look-up table `_TABLT`. `_TABLP` and `_TABLT` are used in the
 code function `TDeos()` in module `utilTD.c`.