[docs] Add spaces between Doxygen and LaTeX commands

doc/doxygen/thermoprops.dox

@@ -48,7 +48,7 @@
  *
  *   The first type are those whose underlying species have a reference state associated
  *   with them. The reference state describes the thermodynamic functions for a
- *   species at a single reference pressure, @f$p_0@f$. The thermodynamic functions
+ *   species at a single reference pressure, @f$ p_0 @f$. The thermodynamic functions
  *   are specified via derived objects of the SpeciesThermoInterpType object class, and usually
  *   consist of polynomials in temperature such as the NASA polynomial or the SHOMATE
  *   polynomial.  Calculators for these
@@ -346,14 +346,14 @@
  *  </H3>
  *
  *
- * The activity @f$a_k@f$ and activity coefficient @f$ \gamma_k @f$ of a
+ * The activity @f$ a_k @f$ and activity coefficient @f$ \gamma_k @f$ of a
  * species in solution is related to the chemical potential by
  *
  * @f[
  *    \mu_k = \mu_k^0(T,P) + \hat R T \log a_k.= \mu_k^0(T,P) + \hat R T \log x_k \gamma_k
  * @f]
  *
- * The quantity @f$\mu_k^0(T,P)@f$ is
+ * The quantity @f$ \mu_k^0(T,P) @f$ is
  * the standard chemical potential at unit activity,
  * which depends on the temperature and pressure,
  * but not on the composition. The

include/cantera/equil/MultiPhase.h

@@ -550,7 +550,7 @@ class MultiPhase
     //! MultiPhaseEquil solver.
     /*!
      * @param XY   Integer flag specifying properties to hold fixed.
-     * @param err  Error tolerance for @f$\Delta \mu/RT @f$ for all reactions.
+     * @param err  Error tolerance for @f$ \Delta \mu/RT @f$ for all reactions.
      *             Also used as the relative error tolerance for the outer loop.
      * @param maxsteps Maximum number of steps to take in solving the fixed TP
      *                 problem.

include/cantera/kinetics/ChebyshevRate.h

@@ -65,7 +65,7 @@ struct ChebyshevData : public ReactionData
  *     \log k(T,P) = \sum_{t=1}^{N_T} \sum_{p=1}^{N_P} \alpha_{tp}
  *                       \phi_t(\tilde{T}) \phi_p(\tilde{P})
  * @f]
- * where @f$\alpha_{tp}@f$ are the constants defining the rate, @f$\phi_n(x)@f$
+ * where @f$ \alpha_{tp} @f$ are the constants defining the rate, @f$ \phi_n(x) @f$
  * is the Chebyshev polynomial of the first kind of degree *n* evaluated at
  * *x*, and
  * @f[

include/cantera/kinetics/Kinetics.h

@@ -733,8 +733,8 @@ class Kinetics
      * mole fractions at constant temperature, pressure and molar concentration.
      *
      * The method returns a matrix with nReactions rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$X_i@f$, all other @f$X_j@f$ are held
-     * constant, rather than enforcing @f$\sum X_j = 1@f$.
+     * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+     * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
      *
      * @warning  This method is an experimental part of the %Cantera API and
      *      may be changed or removed without notice.
@@ -751,7 +751,7 @@ class Kinetics
      * concentrations.
      *
      * The method returns a matrix with nReactions rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$c_i@f$, all other @f$c_j@f$ are held
+     * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
      * constant.
      *
      * @warning  This method is an experimental part of the %Cantera API and
@@ -806,8 +806,8 @@ class Kinetics
      * mole fractions at constant temperature, pressure and molar concentration.
      *
      * The method returns a matrix with nReactions rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$X_i@f$, all other @f$X_j@f$ are held
-     * constant, rather than enforcing @f$\sum X_j = 1@f$.
+     * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+     * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
      *
      * @warning  This method is an experimental part of the %Cantera API and
      *      may be changed or removed without notice.
@@ -824,7 +824,7 @@ class Kinetics
      * concentrations.
      *
      * The method returns a matrix with nReactions rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$c_i@f$, all other @f$c_j@f$ are held
+     * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
      * constant.
      *
      * @warning  This method is an experimental part of the %Cantera API and
@@ -879,8 +879,8 @@ class Kinetics
      * mole fractions at constant temperature, pressure and molar concentration.
      *
      * The method returns a matrix with nReactions rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$X_i@f$, all other @f$X_j@f$ are held
-     * constant, rather than enforcing @f$\sum X_j = 1@f$.
+     * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+     * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
      *
      * @warning  This method is an experimental part of the %Cantera API and
      *      may be changed or removed without notice.
@@ -897,7 +897,7 @@ class Kinetics
      * concentrations.
      *
      * The method returns a matrix with nReactions rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$c_i@f$, all other @f$c_j@f$ are held
+     * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
      * constant.
      *
      * @warning  This method is an experimental part of the %Cantera API and
@@ -940,8 +940,8 @@ class Kinetics
      * mole fractions at constant temperature, pressure and molar concentration.
      *
      * The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$X_i@f$, all other @f$X_j@f$ are held
-     * constant, rather than enforcing @f$\sum X_j = 1@f$.
+     * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+     * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
      *
      * @warning  This method is an experimental part of the %Cantera API and
      *      may be changed or removed without notice.
@@ -954,7 +954,7 @@ class Kinetics
      * species.
      *
      * The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$c_i@f$, all other @f$c_j@f$ are held
+     * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
      * constant.
      *
      * @warning  This method is an experimental part of the %Cantera API and
@@ -993,8 +993,8 @@ class Kinetics
      * mole fractions at constant temperature, pressure and molar concentration.
      *
      * The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$X_i@f$, all other @f$X_j@f$ are held
-     * constant, rather than enforcing @f$\sum X_j = 1@f$.
+     * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+     * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
      *
      * @warning  This method is an experimental part of the %Cantera API and
      *      may be changed or removed without notice.
@@ -1007,7 +1007,7 @@ class Kinetics
      * species.
      *
      * The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$c_i@f$, all other @f$c_j@f$ are held
+     * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
      * constant.
      *
      * @warning  This method is an experimental part of the %Cantera API and
@@ -1046,8 +1046,8 @@ class Kinetics
      * mole fractions at constant temperature, pressure and molar concentration.
      *
      * The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$X_i@f$, all other @f$X_j@f$ are held constant,
-     * rather than enforcing @f$\sum X_j = 1@f$.
+     * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held constant,
+     * rather than enforcing @f$ \sum X_j = 1 @f$.
      *
      * @warning  This method is an experimental part of the %Cantera API and
      *      may be changed or removed without notice.
@@ -1060,7 +1060,7 @@ class Kinetics
      * species.
      *
      * The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
-     * For a derivative with respect to @f$c_i@f$, all other @f$c_j@f$ are held
+     * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
      * constant.
      *
      * @warning  This method is an experimental part of the %Cantera API and

include/cantera/kinetics/StoichManager.h

@@ -564,16 +564,16 @@ inline static void _scale(InputIter begin, InputIter end,
  * @f[
  *     r_i = \sum_m^{M_i} s_{k_{m,i}}
  * @f]
- * To understand the operations performed by this class, let @f$ N_{k,i}@f$
+ * To understand the operations performed by this class, let @f$ N_{k,i} @f$
  * denote the stoichiometric coefficient of species k on one side (reactant or
  * product) in reaction i. Then \b N is a sparse K by I matrix of stoichiometric
  * coefficients.
  *
  * The following matrix operations may be carried out with a vector S of length
  * K, and a vector R of length I:
  *
- * - @f$ S = S + N R@f$   (incrementSpecies)
- * - @f$ S = S - N R@f$   (decrementSpecies)
+ * - @f$ S = S + N R @f$   (incrementSpecies)
+ * - @f$ S = S - N R @f$   (decrementSpecies)
  * - @f$ R = R + N^T S @f$ (incrementReaction)
  * - @f$ R = R - N^T S @f$ (decrementReaction)
  *

include/cantera/numerics/Func1.h

@@ -498,7 +498,7 @@ class Tabulated1 : public Func1
     Tabulated1(size_t n, const double* tvals, const double* fvals,
                const string& method="linear");
 
-    //! Constructor uses @f$ 2 n@f$ parameters in the following order:
+    //! Constructor uses @f$ 2 n @f$ parameters in the following order:
     //! @f$ [t_0, t_1, \dots, t_{n-1}, f_0, f_1, \dots, f_{n-1}] @f$
     Tabulated1(const vector<double>& params);
 
@@ -1302,7 +1302,7 @@ class Arrhenius1 : public Func1
         }
     }
 
-    //! Constructor uses @f$ 3 n@f$ parameters in the following order:
+    //! Constructor uses @f$ 3 n @f$ parameters in the following order:
     //! @f$ [A_1, b_1, E_1, A_2, b_2, E_2, \dots, A_n, b_n, E_n] @f$
     Arrhenius1(const vector<double>& params);
 

include/cantera/numerics/FuncEval.h

@@ -22,7 +22,7 @@ namespace Cantera
 /**
  *  Virtual base class for ODE/DAE right-hand-side function evaluators.
  *  Classes derived from FuncEval evaluate the right-hand-side function
- * @f$ \vec{F}(t,\vec{y})@f$ in
+ * @f$ \vec{F}(t,\vec{y}) @f$ in
  * @f[
  *  \dot{\vec{y}} = \vec{F}(t,\vec{y}).
  * @f]

include/cantera/numerics/IdasIntegrator.h

@@ -103,7 +103,7 @@ class IdasIntegrator : public Integrator
     void* m_linsol_matrix = nullptr; //!< matrix used by Sundials
     SundialsContext m_sundials_ctx; //!< SUNContext object for Sundials>=6.0
 
-    //! Object implementing the DAE residual function @f$ f(t, y, \dot{y}) = 0@f$
+    //! Object implementing the DAE residual function @f$ f(t, y, \dot{y}) = 0 @f$
     FuncEval* m_func = nullptr;
 
     double m_t0 = 0.0; //!< The start time for the integrator

include/cantera/numerics/polyfit.h

@@ -17,7 +17,7 @@ namespace Cantera
  * evaluated at those points, this function computes the weighted least-squares
  * polynomial fit of degree *deg*:
  *
- * @f[ f(x) = p[0] + p[1]*x + p[2]*x^2 + \cdots + p[deg]*x^deg @f]
+ * @f[ f(x) = p[0] + p[1] x + p[2] x^2 + \cdots + p[deg] x^deg @f]
  *
  * @param n    The number of points at which the function is evaluated
  * @param deg  The degree of the polynomial fit to be computed. deg <= n - 1.

include/cantera/thermo/BinarySolutionTabulatedThermo.h

@@ -39,7 +39,7 @@ namespace Cantera
  *  \Delta g_{\rm rxn} = -\frac{E_eq}{nF}
  *  @f]
  *
- *  where @f$ n@f$ is the charge number transferred to the phase, via the
+ *  where @f$ n @f$ is the charge number transferred to the phase, via the
  *  reaction, and @f$ F @f$ is Faraday's constant.  The gibbs energy of
  *  reaction, in turn, can be separated into enthalpy and entropy of reaction
  *  components:
@@ -65,37 +65,37 @@ namespace Cantera
  *  @f]
  *
  *  Where the 'reference' species is automatically assigned standard state
- *  thermo variables @f$ h^{\rm o} = 0@f$ and @f$ s^{\rm o} = 0@f$, and standard
+ *  thermo variables @f$ h^{\rm o} = 0 @f$ and @f$ s^{\rm o} = 0 @f$, and standard
  *  state thermo variables for species in any other phases are calculated
  *  according to the rules specified in that phase definition.
  *
  *  The present model is intended for modeling non-ideal, tabulated
  *  thermodynamics for binary solutions where the tabulated species is
  *  incorporated via an electrochemical reaction, such that the open circuit
  *  voltage can be measured, relative to a counter electrode species with
- *  standard state thermo properties @f$ h^{\rm o} = 0@f$.
+ *  standard state thermo properties @f$ h^{\rm o} = 0 @f$.
  *  It is possible that this can be generalized such that this assumption about
  *  the counter-electrode is not required. At present, this is left as future
  *  work.
  *
  *  The user therefore provides a table of three equally-sized vectors of
  *  tabulated data:
  *
- *  - @f$ x_{\rm tab}@f$ = array of mole fractions for the tabulated species
+ *  - @f$ x_{\rm tab} @f$ = array of mole fractions for the tabulated species
  *                         at which measurements were conducted and thermo
  *                         data are provided.
- *  - @f$ h_{\rm tab}@f$ = @f$ F\left(-E_{\rm eq}\left(x,T^{\rm o} \right) + T^{\rm o} \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT}\right) @f$
- *  - @f$ s_{\rm tab}@f$ = @f$ F \left(\frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} + s_{\rm counter}^{\rm o} \right) @f$
+ *  - @f$ h_{\rm tab} @f$ = @f$ F\left(-E_{\rm eq}\left(x,T^{\rm o} \right) + T^{\rm o} \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT}\right) @f$
+ *  - @f$ s_{\rm tab} @f$ = @f$ F \left(\frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} + s_{\rm counter}^{\rm o} \right) @f$
  *
  *  where @f$ E_{\rm eq}\left(x,T^{\rm o} \right) @f$ and @f$ \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} @f$
  *  are the experimentally-measured open circuit voltage and derivative in
  *  open circuit voltage with respect to temperature, respectively, both
  *  measured as a mole fraction of @f$ x @f$ for the tabulated species and at a
- *  temperature of @f$ T^{\rm o} @f$.  The arrays @f$ h_{\rm tab}@f$ and
- *  @f$ s_{\rm tab}@f$ must be the same length as the @f$ x_{\rm tab}@f$ array.
+ *  temperature of @f$ T^{\rm o} @f$.  The arrays @f$ h_{\rm tab} @f$ and
+ *  @f$ s_{\rm tab} @f$ must be the same length as the @f$ x_{\rm tab} @f$ array.
  *
  *  From these tabulated inputs, the standard state thermodynamic properties
- *  for the tabulated species (subscript @f$ k@f$, tab) are calculated as:
+ *  for the tabulated species (subscript @f$ k @f$, tab) are calculated as:
  *
  *  @f[
  *   h^{\rm o}_{k,\,{\rm tab}} =  h_{\rm tab}
@@ -109,7 +109,7 @@ namespace Cantera
  *  thermodynamic data for the tabulated species.
  *
  *  Furthermore, there is an optional feature to include non-ideal effects regarding
- *  partial molar volumes of the species, @f$ \bar V_k@f$. Being derived from
+ *  partial molar volumes of the species, @f$ \bar V_k @f$. Being derived from
  *  IdealSolidSolnPhase, the default assumption in BinarySolutionTabulatedThermo
  *  is that the species comprising the binary solution have constant partial molar
  *  volumes equal to their pure species molar volumes. However, this assumption only
@@ -121,11 +121,11 @@ namespace Cantera
  *  (XRD) measurements of the unit cell volume. Therefore, the user can provide an optional fourth vector of
  *  tabulated molar volume data with the same size as the other tabulated data:
  *
- *  - @f$ V_{\mathrm{m,tab}}@f$ = array of the molar volume of the binary solution phase at
+ *  - @f$ V_{\mathrm{m,tab}} @f$ = array of the molar volume of the binary solution phase at
  *  the tabulated mole fractions.
  *
- *  The partial molar volumes @f$ \bar V_1@f$ of the tabulated species and
- *  @f$ \bar V_2@f$ of the 'reference' species, respectively, can then be derived from
+ *  The partial molar volumes @f$ \bar V_1 @f$ of the tabulated species and
+ *  @f$ \bar V_2 @f$ of the 'reference' species, respectively, can then be derived from
  *  the provided molar volume:
  *
  *  @f[
@@ -148,8 +148,8 @@ namespace Cantera
  *  \rho = \frac{\sum_k{x_k W_k}}{V_\mathrm{m}}
  *  @f]
  *
- *  where @f$x_k@f$ are the mole fractions, @f$W_k@f$ are the molecular weights, and
- *  @f$V_\mathrm{m}@f$ is the molar volume interpolated from @f$V_{\mathrm{m,tab}}@f$.
+ *  where @f$ x_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular weights, and
+ *  @f$ V_\mathrm{m} @f$ is the molar volume interpolated from @f$ V_{\mathrm{m,tab}} @f$.
  *
  *  If the optional fourth input vector is not specified, the molar volume is calculated
  *  by using the pure species molar volumes, as in IdealSolidSolnPhase. Regardless if the
@@ -203,8 +203,8 @@ class BinarySolutionTabulatedThermo : public IdealSolidSolnPhase
      * \rho = \frac{\sum_k{X_k W_k}}{V_\mathrm{m}}
      * @f]
      *
-     * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular weights, and
-     * @f$V_\mathrm{m}@f$ is the molar volume interpolated from @f$V_{\mathrm{m,tab}}@f$.
+     * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular weights, and
+     * @f$ V_\mathrm{m} @f$ is the molar volume interpolated from @f$ V_{\mathrm{m,tab}} @f$.
      */
     virtual void calcDensity();
 

include/cantera/thermo/ConstCpPoly.h

@@ -34,7 +34,7 @@ namespace Cantera
  * @f]
  *
  * This parameterization takes 4 input values. These are:
- *       -   c[0] = @f$ T_0 @f$(Kelvin)
+ *       -   c[0] = @f$ T_0 @f$ (Kelvin)
  *       -   c[1] = @f$ H_k^o(T_0, p_{ref}) @f$ (J/kmol)
  *       -   c[2] = @f$ S_k^o(T_0, p_{ref}) @f$    (J/kmol K)
  *       -   c[3] = @f$ {Cp}_k^o(T_0, p_{ref}) @f$  (J(kmol K)
@@ -54,7 +54,7 @@ class ConstCpPoly: public SpeciesThermoInterpType
      * @param coeffs       Vector of coefficients used to set the parameters for
      *                     the standard state for species n. There are 4
      *                     coefficients for the ConstCpPoly parameterization.
-     *           -   c[0] = @f$ T_0 @f$(Kelvin)
+     *           -   c[0] = @f$ T_0 @f$ (Kelvin)
      *           -   c[1] = @f$ H_k^o(T_0, p_{ref}) @f$ (J/kmol)
      *           -   c[2] = @f$ S_k^o(T_0, p_{ref}) @f$    (J/kmol K)
      *           -   c[3] = @f$ {Cp}_k^o(T_0, p_{ref}) @f$  (J(kmol K)