diff --git a/doc/doxygen/thermoprops.dox b/doc/doxygen/thermoprops.dox index 6409d746c3..d20cab627c 100644 --- a/doc/doxygen/thermoprops.dox +++ b/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$. The thermodynamic functions * are specified via derived objects of the SpeciesThermoInterpType object class, and usually * consist of polynomials in temperature such as the NASA polynomial or the SHOMATE * polynomial. Calculators for these @@ -346,14 +346,14 @@ * * * - * The activity @f$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 diff --git a/include/cantera/equil/MultiPhase.h b/include/cantera/equil/MultiPhase.h index 1af0e38f0b..3617ed11c3 100644 --- a/include/cantera/equil/MultiPhase.h +++ b/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. diff --git a/include/cantera/kinetics/ChebyshevRate.h b/include/cantera/kinetics/ChebyshevRate.h index 536b71f633..a2235e53df 100644 --- a/include/cantera/kinetics/ChebyshevRate.h +++ b/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[ diff --git a/include/cantera/kinetics/Kinetics.h b/include/cantera/kinetics/Kinetics.h index c0ae09d7a2..75a05cfe34 100644 --- a/include/cantera/kinetics/Kinetics.h +++ b/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 diff --git a/include/cantera/kinetics/StoichManager.h b/include/cantera/kinetics/StoichManager.h index 997fa7303a..7d88ea683a 100644 --- a/include/cantera/kinetics/StoichManager.h +++ b/include/cantera/kinetics/StoichManager.h @@ -564,7 +564,7 @@ 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. @@ -572,8 +572,8 @@ inline static void _scale(InputIter begin, InputIter end, * 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) * diff --git a/include/cantera/numerics/Func1.h b/include/cantera/numerics/Func1.h index 4950cc2537..56725772ad 100644 --- a/include/cantera/numerics/Func1.h +++ b/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& 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& params); diff --git a/include/cantera/numerics/FuncEval.h b/include/cantera/numerics/FuncEval.h index 064bc8cc99..84f50eca3c 100644 --- a/include/cantera/numerics/FuncEval.h +++ b/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] diff --git a/include/cantera/numerics/IdasIntegrator.h b/include/cantera/numerics/IdasIntegrator.h index 0b8b14bca5..7096d9274b 100644 --- a/include/cantera/numerics/IdasIntegrator.h +++ b/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 diff --git a/include/cantera/numerics/polyfit.h b/include/cantera/numerics/polyfit.h index bb7ace77f1..3ad3572c17 100644 --- a/include/cantera/numerics/polyfit.h +++ b/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. diff --git a/include/cantera/thermo/BinarySolutionTabulatedThermo.h b/include/cantera/thermo/BinarySolutionTabulatedThermo.h index d751a2785f..0cd99dcfc8 100644 --- a/include/cantera/thermo/BinarySolutionTabulatedThermo.h +++ b/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: @@ -65,7 +65,7 @@ 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$, and standard * state thermo variables for species in any other phases are calculated * according to the rules specified in that phase definition. * @@ -73,7 +73,7 @@ namespace Cantera * thermodynamics for binary solutions where the tabulated species is * incorporated via an electrochemical reaction, such that the open circuit * voltage can be measured, relative to a counter electrode species with - * standard state thermo properties @f$ h^{\rm o} = 0@f$. + * standard state thermo properties @f$ h^{\rm o} = 0 @f$. * It is possible that this can be generalized such that this assumption about * the counter-electrode is not required. At present, this is left as future * work. @@ -81,21 +81,21 @@ namespace Cantera * The user therefore provides a table of three equally-sized vectors of * tabulated data: * - * - @f$ 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$. */ virtual void calcDensity(); diff --git a/include/cantera/thermo/ConstCpPoly.h b/include/cantera/thermo/ConstCpPoly.h index de8c2e8d6e..7c0459d236 100644 --- a/include/cantera/thermo/ConstCpPoly.h +++ b/include/cantera/thermo/ConstCpPoly.h @@ -34,7 +34,7 @@ namespace Cantera * @f] * * This parameterization takes 4 input values. These are: - * - c[0] = @f$ 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) diff --git a/include/cantera/thermo/DebyeHuckel.h b/include/cantera/thermo/DebyeHuckel.h index 539bf83fc1..05ade683d2 100644 --- a/include/cantera/thermo/DebyeHuckel.h +++ b/include/cantera/thermo/DebyeHuckel.h @@ -65,7 +65,7 @@ class PDSS_Water; * * For an incompressible, stoichiometric substance, the molar internal energy is * independent of pressure. Since the thermodynamic properties are specified by - * giving the standard-state enthalpy, the term @f$ P_0 \hat v@f$ is subtracted + * giving the standard-state enthalpy, the term @f$ P_0 \hat v @f$ is subtracted * from the specified molar enthalpy to compute the molar internal energy. The * entropy is assumed to be independent of the pressure. * @@ -78,7 +78,7 @@ class PDSS_Water; * * For an incompressible, stoichiometric substance, the molar internal energy is * independent of pressure. Since the thermodynamic properties are specified by - * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v@f$ is + * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v @f$ is * subtracted from the specified reference molar enthalpy to compute the molar * internal energy. * @@ -110,7 +110,7 @@ class PDSS_Water; * @f] * * where @f$ \gamma_k^{\triangle} @f$ is the molality based activity coefficient - * for species @f$k@f$. + * for species @f$ k @f$. * * Individual activity coefficients of ions can not be independently measured. * Instead, only binary pairs forming electroneutral solutions can be measured. @@ -118,7 +118,7 @@ class PDSS_Water; * ### Ionic Strength * * Most of the parameterizations within the model use the ionic strength as a - * key variable. The ionic strength, @f$ I@f$ is defined as follows + * key variable. The ionic strength, @f$ I @f$ is defined as follows * * @f[ * I = \frac{1}{2} \sum_k{m_k z_k^2} @@ -155,7 +155,7 @@ class PDSS_Water; * @f[ * z_k = z_{k1} + z_{k2} * @f] - * Then, we may only need to specify one charge value, say, @f$ z_{k1}@f$, the + * Then, we may only need to specify one charge value, say, @f$ z_{k1} @f$, the * cation charge number, in order to get both numbers, since we have already * specified @f$ z_k @f$ in the definition of original species. Then, the * stoichiometric ionic strength may be calculated via the following formula. @@ -166,7 +166,7 @@ class PDSS_Water; * @f] * * The specification of which species are weakly associated acids is made in YAML - * input files by specifying the corresponding charge @f$k1@f$ as the `weak-acid-charge` + * input files by specifying the corresponding charge @f$ k1 @f$ as the `weak-acid-charge` * parameter of the `Debye-Huckel` block in the corresponding species entry. * * Because we need the concept of a weakly associated acid in order to calculate @@ -211,7 +211,7 @@ class PDSS_Water; * @f[ * \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I} * @f] - * where @f$ I@f$ is the ionic strength + * where @f$ I @f$ is the ionic strength * @f[ * I = \frac{1}{2} \sum_k{m_k z_k^2} * @f] @@ -289,7 +289,7 @@ class PDSS_Water; * @f] * * In the current treatment the binary interaction coefficients, @f$ - * \beta_{j,k}@f$, are independent of temperature and pressure. + * \beta_{j,k} @f$, are independent of temperature and pressure. * * @f[ * \ln(a_o) = \frac{X_o - 1.0}{X_o} @@ -390,7 +390,7 @@ class PDSS_Water; * @f$ C_k^a @f$ is the activity concentration of species k. @f$ C_o @f$ * is the concentration of water at 298 K and 1 atm. @f$ a_j @f$ is the activity * of species j at the current temperature and pressure and concentration of the - * liquid phase. @f$k^1 @f$ has units of m3 kmol-1 s-1. + * liquid phase. @f$ k^1 @f$ has units of m3 kmol-1 s-1. * * The reverse rate constant can then be obtained from the law of microscopic * reversibility and the equilibrium expression for the system. @@ -409,7 +409,7 @@ class PDSS_Water; * k^{-1} = k^1 K^{o,1} C_o * @f] * - * @f$k^{-1} @f$ has units of s-1. + * @f$ k^{-1} @f$ has units of s-1. */ class DebyeHuckel : public MolalityVPSSTP { @@ -475,9 +475,9 @@ class DebyeHuckel : public MolalityVPSSTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T,P)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity, //! which depends only on temperature and the pressure. Activity is assumed //! to be molality-based here. //! @{ diff --git a/include/cantera/thermo/GibbsExcessVPSSTP.h b/include/cantera/thermo/GibbsExcessVPSSTP.h index fc69e2a60a..00a656d360 100644 --- a/include/cantera/thermo/GibbsExcessVPSSTP.h +++ b/include/cantera/thermo/GibbsExcessVPSSTP.h @@ -51,7 +51,7 @@ namespace Cantera * @f] * * where @f$ \gamma_k^{\triangle} @f$ is a molar based activity coefficient for - * species @f$k@f$. + * species @f$ k @f$. * * GibbsExcessVPSSTP contains an internal vector with the current mole fraction * vector. That's one of its primary usages. In order to keep the mole fraction @@ -104,8 +104,8 @@ class GibbsExcessVPSSTP : public VPStandardStateTP * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the pure species molar volumes. We @@ -121,9 +121,9 @@ class GibbsExcessVPSSTP : public VPStandardStateTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T,P)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity, //! which depends only on temperature and pressure. //! @{ diff --git a/include/cantera/thermo/HMWSoln.h b/include/cantera/thermo/HMWSoln.h index 955ece3831..989ac39bea 100644 --- a/include/cantera/thermo/HMWSoln.h +++ b/include/cantera/thermo/HMWSoln.h @@ -91,7 +91,7 @@ class WaterProps; * * For these incompressible, standard states, the molar internal energy is * independent of pressure. Since the thermodynamic properties are specified by - * giving the standard-state enthalpy, the term @f$ P_0 \hat v@f$ is subtracted + * giving the standard-state enthalpy, the term @f$ P_0 \hat v @f$ is subtracted * from the specified molar enthalpy to compute the molar internal energy. The * entropy is assumed to be independent of the pressure. * @@ -104,7 +104,7 @@ class WaterProps; * * For an incompressible, stoichiometric substance, the molar internal energy is * independent of pressure. Since the thermodynamic properties are specified by - * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v@f$ is + * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v @f$ is * subtracted from the specified reference molar enthalpy to compute the molar * internal energy. * @@ -136,7 +136,7 @@ class WaterProps; * @f] * * where @f$ \gamma_k^{\triangle} @f$ is the molality based activity coefficient - * for species @f$k@f$. + * for species @f$ k @f$. * * Individual activity coefficients of ions can not be independently measured. * Instead, only binary pairs forming electroneutral solutions can be measured. @@ -150,7 +150,7 @@ class WaterProps; * ### Ionic Strength * * Most of the parameterizations within the model use the ionic strength as a - * key variable. The ionic strength, @f$ I@f$ is defined as follows + * key variable. The ionic strength, @f$ I @f$ is defined as follows * * @f[ * I = \frac{1}{2} \sum_k{m_k z_k^2} @@ -211,7 +211,7 @@ class WaterProps; * the theory of unsymmetrical mixing of electrolytes with different charges. * This theory depends on the total ionic strength of the solution, and * therefore, @f$ \Phi_{c{c'}} @f$ and @f$ \Phi_{a{a'}} @f$ will depend on - * *I*, the ionic strength. @f$ B_{ca}@f$ is a strong function of the + * *I*, the ionic strength. @f$ B_{ca} @f$ is a strong function of the * total ionic strength, *I*, of the electrolyte. The rest of the coefficients * are assumed to be independent of the molalities or ionic strengths. However, * all coefficients are potentially functions of the temperature and pressure @@ -220,7 +220,7 @@ class WaterProps; * *A* is the Debye-Huckel constant. Its specification is described in its * own section below. * - * @f$ I@f$ is the ionic strength of the solution, and is given by: + * @f$ I @f$ is the ionic strength of the solution, and is given by: * * @f[ * I = \frac{1}{2} \sum_k{m_k z_k^2} @@ -238,7 +238,7 @@ class WaterProps; * Z = \sum_i m_i \left| z_i \right| * @f] * - * The value of @f$ B_{ca}@f$ is given by the following function + * The value of @f$ B_{ca} @f$ is given by the following function * * @f[ * B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha^{(1)}_{ca} \sqrt{I}) @@ -251,7 +251,7 @@ class WaterProps; * g(x) = 2 \frac{(1 - (1 + x)\exp[-x])}{x^2} * @f] * - * The formulation for @f$ B_{ca}@f$ combined with the formulation of the Debye- + * The formulation for @f$ B_{ca} @f$ combined with the formulation of the Debye- * Huckel term in the eqn. for the excess Gibbs free energy stems essentially * from an empirical fit to the ionic strength dependent data based over a wide * sampling of binary electrolyte systems. @f$ C_{ca} @f$, @f$ \lambda_{nc} @f$, @@ -263,17 +263,17 @@ class WaterProps; * more complicated. @f$ b @f$ is a universal constant defined to be equal to * @f$ 1.2\ kg^{1/2}\ gmol^{-1/2} @f$. The exponential coefficient @f$ * \alpha^{(1)}_{ca} @f$ is usually fixed at @f$ \alpha^{(1)}_{ca} = 2.0\ - * kg^{1/2} gmol^{-1/2}@f$ except for 2-2 electrolytes, while other parameters + * kg^{1/2} gmol^{-1/2} @f$ except for 2-2 electrolytes, while other parameters * were fit to experimental data. For 2-2 electrolytes, @f$ \alpha^{(1)}_{ca} = - * 1.4\ kg^{1/2}\ gmol^{-1/2}@f$ is used in combination with either @f$ - * \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2}@f$ or @f$ \alpha^{(2)}_{ca} = k + * 1.4\ kg^{1/2}\ gmol^{-1/2} @f$ is used in combination with either @f$ + * \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2} @f$ or @f$ \alpha^{(2)}_{ca} = k * A_\psi @f$, where *k* is a constant. For electrolytes other than 2-2 * electrolytes the @f$ \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) @f$ term * is not used in the fitting procedure; it is only used for divalent metal * solfates and other high-valence electrolytes which exhibit significant * association at low ionic strengths. * - * The @f$ \beta^{(0)}_{ca} @f$, @f$ \beta^{(1)}_{ca}@f$, @f$ \beta^{(2)}_{ca} + * The @f$ \beta^{(0)}_{ca} @f$, @f$ \beta^{(1)}_{ca} @f$, @f$ \beta^{(2)}_{ca} * @f$, and @f$ C_{ca} @f$ binary coefficients are referred to as ion- * interaction or Pitzer parameters. These Pitzer parameters may vary with * temperature and pressure but they do not depend on the ionic strength. Their @@ -485,23 +485,23 @@ class WaterProps; * and pressure * - PIZTER_TEMP_COMPLEX1 - string name "COMPLEX" or "COMPLEX1" * - Uses the full temperature dependence for the - * @f$\beta^{(0)}_{MX} @f$ (5 coeffs), - * the @f$\beta^{(1)}_{MX} @f$ (3 coeffs), + * @f$ \beta^{(0)}_{MX} @f$ (5 coeffs), + * the @f$ \beta^{(1)}_{MX} @f$ (3 coeffs), * and @f$ C^{\phi}_{MX} @f$ (5 coeffs) parameters described above. * - PITZER_TEMP_LINEAR - string name "LINEAR" * - Uses just the temperature dependence for the - * @f$\beta^{(0)}_{MX} @f$, the @f$\beta^{(1)}_{MX} @f$, + * @f$ \beta^{(0)}_{MX} @f$, the @f$ \beta^{(1)}_{MX} @f$, * and @f$ C^{\phi}_{MX} @f$ coefficients described above. * There are 2 coefficients for each term. * * The specification of the binary interaction between a cation and an anion is - * given by the coefficients, @f$ B_{MX}@f$ and @f$ C_{MX}@f$ The specification - * of @f$ B_{MX}@f$ is a function of @f$\beta^{(0)}_{MX} @f$, - * @f$\beta^{(1)}_{MX} @f$, @f$\beta^{(2)}_{MX} @f$, @f$\alpha^{(1)}_{MX} @f$, - * and @f$\alpha^{(2)}_{MX} @f$. @f$ C_{MX}@f$ is calculated from - * @f$C^{\phi}_{MX} @f$ from the formula above. + * given by the coefficients, @f$ B_{MX} @f$ and @f$ C_{MX} @f$ The specification + * of @f$ B_{MX} @f$ is a function of @f$ \beta^{(0)}_{MX} @f$, + * @f$ \beta^{(1)}_{MX} @f$, @f$ \beta^{(2)}_{MX} @f$, @f$ \alpha^{(1)}_{MX} @f$, + * and @f$ \alpha^{(2)}_{MX} @f$. @f$ C_{MX} @f$ is calculated from + * @f$ C^{\phi}_{MX} @f$ from the formula above. * - * The parameters for @f$ \beta^{(0)}@f$ fit the following equation: + * The parameters for @f$ \beta^{(0)} @f$ fit the following equation: * * @f[ * \beta^{(0)} = q_0^{{\beta}0} + q_1^{{\beta}0} \left( T - T_r \right) @@ -513,7 +513,7 @@ class WaterProps; * This same `COMPLEX1` temperature dependence given above is used for the * following parameters: * @f$ \beta^{(0)}_{MX} @f$, @f$ \beta^{(1)}_{MX} @f$, - * @f$ \beta^{(2)}_{MX} @f$, @f$ \Theta_{cc'} @f$, @f$\Theta_{aa'} @f$, + * @f$ \beta^{(2)}_{MX} @f$, @f$ \Theta_{cc'} @f$, @f$ \Theta_{aa'} @f$, * @f$ \Psi_{c{c'}a} @f$ and @f$ \Psi_{ca{a'}} @f$. * * ### Like-Charged Binary Ion Parameters and the Mixing Parameters @@ -660,7 +660,7 @@ class WaterProps; * - R T \frac{d \ln(a_o)}{dT} * @f] * - * The partial molar heat capacity, @f$ C_{p,k}(T,P)@f$: + * The partial molar heat capacity, @f$ C_{p,k}(T,P) @f$: * * @f[ * \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P) @@ -737,7 +737,7 @@ class WaterProps; * a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o} * @f] * - * @f$k^1 @f$ has units of m^3/kmol/s. + * @f$ k^1 @f$ has units of m^3/kmol/s. * * Therefore the generalized activity concentration of a solute species has the following form * @@ -882,8 +882,8 @@ class HMWSoln : public MolalityVPSSTP * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the pure species molar volumes. We @@ -899,16 +899,16 @@ class HMWSoln : public MolalityVPSSTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T,P)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity, //! which depends only on temperature and the pressure. Activity is assumed //! to be molality-based here. //! @{ //! This method returns an array of generalized activity concentrations /*! - * The generalized activity concentrations, @f$ C_k^a@f$, are defined such + * The generalized activity concentrations, @f$ C_k^a @f$, are defined such * that @f$ a_k = C^a_k / C^0_k, @f$ where @f$ C^0_k @f$ is a standard * concentration defined below. These generalized concentrations are used * by kinetics manager classes to compute the forward and reverse rates of @@ -991,7 +991,7 @@ class HMWSoln : public MolalityVPSSTP * a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o} * @f] * - * @f$k^1 @f$ has units of m^3/kmol/s. + * @f$ k^1 @f$ has units of m^3/kmol/s. * * Therefore the generalized activity concentration of a solute species has * the following form diff --git a/include/cantera/thermo/IdealGasPhase.h b/include/cantera/thermo/IdealGasPhase.h index 6d771371f2..c47f58987c 100644 --- a/include/cantera/thermo/IdealGasPhase.h +++ b/include/cantera/thermo/IdealGasPhase.h @@ -144,7 +144,7 @@ namespace Cantera * * ## Application within Kinetics Managers * - * @f$ C^a_k@f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where @f$ + * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where @f$ * C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are * activities used in the thermodynamic functions. These activity (or * generalized) concentrations are used by kinetics manager classes to compute @@ -237,7 +237,7 @@ namespace Cantera * k^{-1} = k^1 K^1_c * @f] * - * @f$k^{-1} @f$ has units of s-1. + * @f$ k^{-1} @f$ has units of s-1. * * ## YAML Example * @@ -406,19 +406,19 @@ class IdealGasPhase: public ThermoPhase //! @} //! @name Chemical Potentials and Activities //! - //! The activity @f$a_k@f$ of a species in solution is + //! The activity @f$ a_k @f$ of a species in solution is //! related to the chemical potential by //! @f[ //! \mu_k(T,P,X_k) = \mu_k^0(T,P) //! + \hat R T \log a_k. //! @f] - //! The quantity @f$\mu_k^0(T,P)@f$ is the standard state chemical potential + //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard state chemical potential //! at unit activity. It may depend on the pressure and the temperature. //! However, it may not depend on the mole fractions of the species in the //! solution. //! - //! The activities are related to the generalized concentrations, @f$\tilde - //! C_k@f$, and standard concentrations, @f$C^0_k@f$, by the following + //! The activities are related to the generalized concentrations, @f$ \tilde + //! C_k @f$, and standard concentrations, @f$ C^0_k @f$, by the following //! formula: //! //! @f[ diff --git a/include/cantera/thermo/IdealMolalSoln.h b/include/cantera/thermo/IdealMolalSoln.h index 843a211894..a57ceb9dae 100644 --- a/include/cantera/thermo/IdealMolalSoln.h +++ b/include/cantera/thermo/IdealMolalSoln.h @@ -177,8 +177,8 @@ class IdealMolalSoln : public MolalityVPSSTP * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the pure species molar volumes. We @@ -216,9 +216,9 @@ class IdealMolalSoln : public MolalityVPSSTP //! @} //! @name Activities and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T) @f$ is the chemical potential at unit activity, //! which depends only on temperature and the pressure. //! @{ @@ -383,9 +383,9 @@ class IdealMolalSoln : public MolalityVPSSTP * * | model | ActivityConc | StandardConc | * | -------------------- | -------------------------------- | ------------------ | - * | unity | @f$ {m_k}/ { m^{\Delta}}@f$ | @f$ 1.0 @f$ | - * | species-molar-volume | @f$ m_k / (m^{\Delta} V_k)@f$ | @f$ 1.0 / V_k @f$ | - * | solvent-molar-volume | @f$ m_k / (m^{\Delta} V^0_0)@f$ | @f$ 1.0 / V^0_0@f$ | + * | unity | @f$ {m_k}/ { m^{\Delta}} @f$ | @f$ 1.0 @f$ | + * | species-molar-volume | @f$ m_k / (m^{\Delta} V_k) @f$ | @f$ 1.0 / V_k @f$ | + * | solvent-molar-volume | @f$ m_k / (m^{\Delta} V^0_0) @f$ | @f$ 1.0 / V^0_0 @f$ | */ void setStandardConcentrationModel(const std::string& model); diff --git a/include/cantera/thermo/IdealSolidSolnPhase.h b/include/cantera/thermo/IdealSolidSolnPhase.h index e8128a4deb..7ea6f5c03d 100644 --- a/include/cantera/thermo/IdealSolidSolnPhase.h +++ b/include/cantera/thermo/IdealSolidSolnPhase.h @@ -178,8 +178,8 @@ class IdealSolidSolnPhase : public ThermoPhase * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the pure species molar volumes. We @@ -191,19 +191,19 @@ class IdealSolidSolnPhase : public ThermoPhase //! @} //! @name Chemical Potentials and Activities //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by //! @f[ //! \mu_k(T,P,X_k) = \mu_k^0(T,P) //! + \hat R T \log a_k. //! @f] - //! The quantity @f$\mu_k^0(T,P)@f$ is the standard state chemical potential + //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard state chemical potential //! at unit activity. It may depend on the pressure and the temperature. //! However, it may not depend on the mole fractions of the species in the //! solid solution. //! - //! The activities are related to the generalized concentrations, @f$\tilde - //! C_k@f$, and standard concentrations, @f$C^0_k@f$, by the following + //! The activities are related to the generalized concentrations, @f$ \tilde + //! C_k @f$, and standard concentrations, @f$ C^0_k @f$, by the following //! formula: //! //! @f[ @@ -287,7 +287,7 @@ class IdealSolidSolnPhase : public ThermoPhase * @f[ * \mu_k = \mu^o_k(T,p) + R T ln(X_k) * @f] - * where @f$ \mu^o_k(T,p) = \mu^{ref}_k(T) + V_k * (p - p_o)@f$ + * where @f$ \mu^o_k(T,p) = \mu^{ref}_k(T) + V_k * (p - p_o) @f$ * * @param mu Output vector of chemical potentials. */ @@ -296,13 +296,13 @@ class IdealSolidSolnPhase : public ThermoPhase /** * Get the array of non-dimensional species solution * chemical potentials at the current T and P - * @f$\mu_k / \hat R T @f$. + * @f$ \mu_k / \hat R T @f$. * @f[ * \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k + RT ln(X_k) * @f] - * where @f$V_k@f$ is the molar volume of pure species *k*. - * @f$ \mu^{ref}_k(T)@f$ is the chemical potential of pure - * species *k* at the reference pressure, @f$P_{ref}@f$. + * where @f$ V_k @f$ is the molar volume of pure species *k*. + * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure + * species *k* at the reference pressure, @f$ P_{ref} @f$. * * @param mu Output vector of dimensionless chemical potentials. * Length = m_kk. @@ -400,9 +400,9 @@ class IdealSolidSolnPhase : public ThermoPhase * @f[ * h^0_k(T,P) = h^{ref}_k(T) + (P - P_{ref}) * V_k * @f] - * where @f$V_k@f$ is the molar volume of pure species *k*. - * @f$ h^{ref}_k(T)@f$ is the enthalpy of the pure species *k* at the - * reference pressure, @f$P_{ref}@f$. + * where @f$ V_k @f$ is the molar volume of pure species *k*. + * @f$ h^{ref}_k(T) @f$ is the enthalpy of the pure species *k* at the + * reference pressure, @f$ P_{ref} @f$. * * @param hrt Vector of length m_kk, which on return hrt[k] will contain the * nondimensional standard state enthalpy of species k. @@ -427,9 +427,9 @@ class IdealSolidSolnPhase : public ThermoPhase * @f[ * \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k * @f] - * where @f$V_k@f$ is the molar volume of pure species *k*. - * @f$ \mu^{ref}_k(T)@f$ is the chemical potential of pure species *k* - * at the reference pressure, @f$P_{ref}@f$. + * where @f$ V_k @f$ is the molar volume of pure species *k*. + * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure species *k* + * at the reference pressure, @f$ P_{ref} @f$. * * @param grt Vector of length m_kk, which on return sr[k] will contain the * nondimensional standard state Gibbs function for species k. @@ -443,9 +443,9 @@ class IdealSolidSolnPhase : public ThermoPhase * @f[ * \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k * @f] - * where @f$V_k@f$ is the molar volume of pure species *k*. - * @f$ \mu^{ref}_k(T)@f$ is the chemical potential of pure species *k* at - * the reference pressure, @f$P_{ref}@f$. + * where @f$ V_k @f$ is the molar volume of pure species *k*. + * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure species *k* at + * the reference pressure, @f$ P_{ref} @f$. * * @param gpure Output vector of Gibbs functions for species. Length: m_kk. */ @@ -459,9 +459,9 @@ class IdealSolidSolnPhase : public ThermoPhase * @f[ * Cp^0_k(T,P) = Cp^{ref}_k(T) * @f] - * where @f$V_k@f$ is the molar volume of pure species *k*. - * @f$ Cp^{ref}_k(T)@f$ is the constant pressure heat capacity of species - * *k* at the reference pressure, @f$p_{ref}@f$. + * where @f$ V_k @f$ is the molar volume of pure species *k*. + * @f$ Cp^{ref}_k(T) @f$ is the constant pressure heat capacity of species + * *k* at the reference pressure, @f$ p_{ref} @f$. * * @param cpr Vector of length m_kk, which on return cpr[k] will contain the * nondimensional constant pressure heat capacity for species k. diff --git a/include/cantera/thermo/IdealSolnGasVPSS.h b/include/cantera/thermo/IdealSolnGasVPSS.h index 103a0c889a..8eff554026 100644 --- a/include/cantera/thermo/IdealSolnGasVPSS.h +++ b/include/cantera/thermo/IdealSolnGasVPSS.h @@ -71,8 +71,8 @@ class IdealSolnGasVPSS : public VPStandardStateTP * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the species standard state molar diff --git a/include/cantera/thermo/IonsFromNeutralVPSSTP.h b/include/cantera/thermo/IonsFromNeutralVPSSTP.h index e1ae1ea28f..05b860978f 100644 --- a/include/cantera/thermo/IonsFromNeutralVPSSTP.h +++ b/include/cantera/thermo/IonsFromNeutralVPSSTP.h @@ -108,9 +108,9 @@ class IonsFromNeutralVPSSTP : public GibbsExcessVPSSTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is + //! The activity @f$ a_k @f$ of a species in solution is //! related to the chemical potential by @f[ \mu_k = \mu_k^0(T) - //! + \hat R T \log a_k. @f] The quantity @f$\mu_k^0(T,P)@f$ is + //! + \hat R T \log a_k. @f] The quantity @f$ \mu_k^0(T,P) @f$ is //! the chemical potential at unit activity, which depends only //! on temperature and pressure. //! @{ diff --git a/include/cantera/thermo/LatticePhase.h b/include/cantera/thermo/LatticePhase.h index 1367ff5ba3..035effc06c 100644 --- a/include/cantera/thermo/LatticePhase.h +++ b/include/cantera/thermo/LatticePhase.h @@ -39,7 +39,7 @@ namespace Cantera * no effect on any quantities, as the molar concentration is a constant. * * The standard state enthalpy function is given by the following relation, - * which has a weak dependence on the system pressure, @f$P@f$. + * which has a weak dependence on the system pressure, @f$ P @f$. * * @f[ * h^o_k(T,P) = @@ -125,7 +125,7 @@ namespace Cantera * * ## Application within Kinetics Managers * - * @f$ C^a_k@f$ are defined such that @f$ C^a_k = a_k = X_k @f$. @f$ C^s_k @f$, + * @f$ C^a_k @f$ are defined such that @f$ C^a_k = a_k = X_k @f$. @f$ C^s_k @f$, * the standard concentration, is defined to be equal to one. @f$ a_k @f$ are * activities used in the thermodynamic functions. These activity (or * generalized) concentrations are used by kinetics manager classes to compute @@ -308,8 +308,8 @@ class LatticePhase : public ThermoPhase * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the pure species molar volumes. We @@ -321,9 +321,9 @@ class LatticePhase : public ThermoPhase //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T,P)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity, //! which depends only on temperature and the pressure. Activity is assumed //! to be molality-based here. //! @{ diff --git a/include/cantera/thermo/MargulesVPSSTP.h b/include/cantera/thermo/MargulesVPSSTP.h index e6ecbf1220..c43620699c 100644 --- a/include/cantera/thermo/MargulesVPSSTP.h +++ b/include/cantera/thermo/MargulesVPSSTP.h @@ -115,7 +115,7 @@ namespace Cantera * * ## Application within Kinetics Managers * - * @f$ C^a_k@f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where + * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where * @f$ C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are * activities used in the thermodynamic functions. These activity (or * generalized) concentrations are used by kinetics manager classes to compute @@ -207,7 +207,7 @@ namespace Cantera * k^{-1} = k^1 K^1_c * @f] * - * @f$k^{-1} @f$ has units of s-1. + * @f$ k^{-1} @f$ has units of s-1. * * @ingroup thermoprops */ @@ -239,9 +239,9 @@ class MargulesVPSSTP : public GibbsExcessVPSSTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T,P)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity, //! which depends only on temperature and pressure. //! @{ diff --git a/include/cantera/thermo/MolalityVPSSTP.h b/include/cantera/thermo/MolalityVPSSTP.h index d61ba69609..9df7005b7d 100644 --- a/include/cantera/thermo/MolalityVPSSTP.h +++ b/include/cantera/thermo/MolalityVPSSTP.h @@ -130,7 +130,7 @@ const int PHSCALE_NBS = 1; * @f] * * where @f$ \gamma_k^{\triangle} @f$ is the molality based activity coefficient - * for species @f$k@f$. + * for species @f$ k @f$. * * The chemical potential of the solvent is thus expressed in a different format * than the chemical potential of the solutes. Additionally, the activity of the @@ -329,11 +329,11 @@ class MolalityVPSSTP : public VPStandardStateTP * m_i = \frac{X_i}{M_o/1000 * X_{o,p}} * @f] * where - * - @f$M_o@f$ is the molecular weight of the solvent - * - @f$X_o@f$ is the mole fraction of the solvent - * - @f$X_i@f$ is the mole fraction of the solute. - * - @f$X_{o,p} = \max(X_o^{min}, X_o)@f$ - * - @f$X_o^{min}@f$ = minimum mole fraction of solvent allowed + * - @f$ M_o @f$ is the molecular weight of the solvent + * - @f$ X_o @f$ is the mole fraction of the solvent + * - @f$ X_i @f$ is the mole fraction of the solute. + * - @f$ X_{o,p} = \max(X_o^{min}, X_o) @f$ + * - @f$ X_o^{min} @f$ = minimum mole fraction of solvent allowed * in the denominator. * * The formulas for calculating mole fractions are @@ -375,9 +375,9 @@ class MolalityVPSSTP : public VPStandardStateTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The - //! quantity @f$\mu_k^0(T,P)@f$ is the chemical potential at unit activity, + //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity, //! which depends only on temperature and pressure. //! @{ diff --git a/include/cantera/thermo/Mu0Poly.h b/include/cantera/thermo/Mu0Poly.h index 4fac37e606..71529106d3 100644 --- a/include/cantera/thermo/Mu0Poly.h +++ b/include/cantera/thermo/Mu0Poly.h @@ -24,7 +24,7 @@ namespace Cantera * The Mu0Poly class implements a piecewise constant heat capacity * approximation. of the standard state chemical potential of one species at a * single reference pressure. The chemical potential is input as a series of - * (@f$T@f$, @f$ \mu^o(T)@f$) values. The first temperature is assumed to be + * (@f$ T @f$, @f$ \mu^o(T) @f$) values. The first temperature is assumed to be * equal to 298.15 K; however, this may be relaxed in the future. This * information, and an assumption of a constant heat capacity within each * interval is enough to calculate all thermodynamic functions. diff --git a/include/cantera/thermo/Nasa9Poly1.h b/include/cantera/thermo/Nasa9Poly1.h index 2e2d1df4ed..eb0ec52c2b 100644 --- a/include/cantera/thermo/Nasa9Poly1.h +++ b/include/cantera/thermo/Nasa9Poly1.h @@ -29,8 +29,8 @@ namespace Cantera * Individual Species," B. J. McBride, M. J. Zehe, S. Gordon * NASA/TP-2002-211556, Sept. 2002 * - * Nine coefficients @f$(a_0,\dots,a_8)@f$ are used to represent - * @f$ C_p^0(T)@f$, @f$ H^0(T)@f$, and @f$ S^0(T) @f$ as + * Nine coefficients @f$ (a_0,\dots,a_8) @f$ are used to represent + * @f$ C_p^0(T) @f$, @f$ H^0(T) @f$, and @f$ S^0(T) @f$ as * polynomials in @f$ T @f$ : * @f[ * \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T diff --git a/include/cantera/thermo/NasaPoly1.h b/include/cantera/thermo/NasaPoly1.h index 7fd3b71c7f..cb9902bbed 100644 --- a/include/cantera/thermo/NasaPoly1.h +++ b/include/cantera/thermo/NasaPoly1.h @@ -27,8 +27,8 @@ namespace Cantera * the Chemkin software package, but differs from the form used in the more * recent NASA equilibrium program. * - * Seven coefficients @f$(a_0,\dots,a_6)@f$ are used to represent - * @f$ c_p^0(T)@f$, @f$ h^0(T)@f$, and @f$ s^0(T) @f$ as + * Seven coefficients @f$ (a_0,\dots,a_6) @f$ are used to represent + * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as * polynomials in @f$ T @f$ : * @f[ * \frac{c_p(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4 diff --git a/include/cantera/thermo/NasaPoly2.h b/include/cantera/thermo/NasaPoly2.h index 5a16615735..9df7e2062d 100644 --- a/include/cantera/thermo/NasaPoly2.h +++ b/include/cantera/thermo/NasaPoly2.h @@ -26,8 +26,8 @@ namespace Cantera * the Chemkin software package, but differs from the form used in the more * recent NASA equilibrium program. * - * Seven coefficients @f$(a_0,\dots,a_6)@f$ are used to represent - * @f$ c_p^0(T)@f$, @f$ h^0(T)@f$, and @f$ s^0(T) @f$ as + * Seven coefficients @f$ (a_0,\dots,a_6) @f$ are used to represent + * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as * polynomials in @f$ T @f$ : * @f[ * \frac{c_p(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4 diff --git a/include/cantera/thermo/PengRobinson.h b/include/cantera/thermo/PengRobinson.h index 1f1aa606bf..3a129d7fab 100644 --- a/include/cantera/thermo/PengRobinson.h +++ b/include/cantera/thermo/PengRobinson.h @@ -72,7 +72,7 @@ class PengRobinson : public MixtureFugacityTP * \qquad \text{For } \omega > 0.491 * @f] * - * Coefficients @f$ a_{mix}, b_{mix} @f$ and @f$(a \alpha)_{mix}@f$ are calculated as + * Coefficients @f$ a_{mix}, b_{mix} @f$ and @f$ (a \alpha)_{mix} @f$ are calculated as * * @f[ * a_{mix} = \sum_i \sum_j X_i X_j a_{i, j} = \sum_i \sum_j X_i X_j \sqrt{a_i a_j} @@ -160,8 +160,8 @@ class PengRobinson : public MixtureFugacityTP //! Set the pure fluid interaction parameters for a species /*! * @param species Name of the species - * @param a @f$a@f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2] - * @param b @f$a@f$ parameter in the Peng-Robinson model [m^3/kmol] + * @param a @f$ a @f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2] + * @param b @f$ a @f$ parameter in the Peng-Robinson model [m^3/kmol] * @param w acentric factor */ void setSpeciesCoeffs(const std::string& species, double a, double b, @@ -171,7 +171,7 @@ class PengRobinson : public MixtureFugacityTP /*! * @param species_i Name of one species * @param species_j Name of the other species - * @param a @f$a@f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2] + * @param a @f$ a @f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2] */ void setBinaryCoeffs(const std::string& species_i, const std::string& species_j, double a); @@ -191,13 +191,13 @@ class PengRobinson : public MixtureFugacityTP // Special functions not inherited from MixtureFugacityTP - //! Calculate temperature derivative @f$d(a \alpha)/dT@f$ + //! Calculate temperature derivative @f$ d(a \alpha)/dT @f$ /*! * These are stored internally. */ double daAlpha_dT() const; - //! Calculate second derivative @f$d^2(a \alpha)/dT^2@f$ + //! Calculate second derivative @f$ d^2(a \alpha)/dT^2 @f$ /*! * These are stored internally. */ @@ -209,21 +209,21 @@ class PengRobinson : public MixtureFugacityTP virtual double thermalExpansionCoeff() const; virtual double soundSpeed() const; - //! Calculate @f$dp/dV@f$ and @f$dp/dT@f$ at the current conditions + //! Calculate @f$ dp/dV @f$ and @f$ dp/dT @f$ at the current conditions /*! * These are stored internally. */ void calculatePressureDerivatives() const; - //! Update the @f$a@f$, @f$b@f$, and @f$\alpha@f$ parameters + //! Update the @f$ a @f$, @f$ b @f$, and @f$ \alpha @f$ parameters /*! - * The @f$a@f$ and the @f$b@f$ parameters depend on the mole fraction and the - * parameter @f$\alpha@f$ depends on the temperature. This function updates + * The @f$ a @f$ and the @f$ b @f$ parameters depend on the mole fraction and the + * parameter @f$ \alpha @f$ depends on the temperature. This function updates * the internal numbers based on the state of the object. */ virtual void updateMixingExpressions(); - //! Calculate the @f$a@f$, @f$b@f$, and @f$\alpha@f$ parameters given the temperature + //! Calculate the @f$ a @f$, @f$ b @f$, and @f$ \alpha @f$ parameters given the temperature /*! * This function doesn't change the internal state of the object, so it is a * const function. It does use the stored mole fractions in the object. @@ -240,19 +240,19 @@ class PengRobinson : public MixtureFugacityTP int solveCubic(double T, double pres, double a, double b, double aAlpha, double Vroot[3]) const; protected: - //! Value of @f$b@f$ in the equation of state + //! Value of @f$ b @f$ in the equation of state /*! * `m_b` is a function of the mole fractions and species-specific b values. */ double m_b = 0.0; - //! Value of @f$a@f$ in the equation of state + //! Value of @f$ a @f$ in the equation of state /*! * `m_a` depends only on the mole fractions. */ double m_a = 0.0; - //! Value of @f$a \alpha@f$ in the equation of state + //! Value of @f$ a \alpha @f$ in the equation of state /*! * `m_aAlpha_mix` is a function of the temperature and the mole fractions. */ diff --git a/include/cantera/thermo/Phase.h b/include/cantera/thermo/Phase.h index eb3a28500c..e688198404 100644 --- a/include/cantera/thermo/Phase.h +++ b/include/cantera/thermo/Phase.h @@ -599,15 +599,15 @@ class Phase //! Elemental mass fraction of element m /*! - * The elemental mass fraction @f$Z_{\mathrm{mass},m}@f$ of element @f$m@f$ + * The elemental mass fraction @f$ Z_{\mathrm{mass},m} @f$ of element @f$ m @f$ * is defined as * @f[ * Z_{\mathrm{mass},m} = \sum_k \frac{a_{m,k} M_m}{M_k} Y_k * @f] - * with @f$a_{m,k}@f$ being the number of atoms of element @f$m@f$ in - * species @f$k@f$, @f$M_m@f$ the atomic weight of element @f$m@f$, - * @f$M_k@f$ the molecular weight of species @f$k@f$, and @f$Y_k@f$ - * the mass fraction of species @f$k@f$. + * with @f$ a_{m,k} @f$ being the number of atoms of element @f$ m @f$ in + * species @f$ k @f$, @f$ M_m @f$ the atomic weight of element @f$ m @f$, + * @f$ M_k @f$ the molecular weight of species @f$ k @f$, and @f$ Y_k @f$ + * the mass fraction of species @f$ k @f$. * * @param[in] m Index of the element within the phase. If m is outside * the valid range, an exception will be thrown. @@ -618,7 +618,7 @@ class Phase //! Elemental mole fraction of element m /*! - * The elemental mole fraction @f$Z_{\mathrm{mole},m}@f$ of element @f$m@f$ + * The elemental mole fraction @f$ Z_{\mathrm{mole},m} @f$ of element @f$ m @f$ * is the number of atoms of element *m* divided by the total number of * atoms. It is defined as: * @@ -626,9 +626,9 @@ class Phase * Z_{\mathrm{mole},m} = \frac{\sum_k a_{m,k} X_k} * {\sum_k \sum_j a_{j,k} X_k} * @f] - * with @f$a_{m,k}@f$ being the number of atoms of element @f$m@f$ in - * species @f$k@f$, @f$\sum_j@f$ being a sum over all elements, and - * @f$X_k@f$ being the mole fraction of species @f$k@f$. + * with @f$ a_{m,k} @f$ being the number of atoms of element @f$ m @f$ in + * species @f$ k @f$, @f$ \sum_j @f$ being a sum over all elements, and + * @f$ X_k @f$ being the mole fraction of species @f$ k @f$. * * @param[in] m Index of the element within the phase. If m is outside the * valid range, an exception will be thrown. diff --git a/include/cantera/thermo/PlasmaPhase.h b/include/cantera/thermo/PlasmaPhase.h index 06dfd7b494..6903a3b114 100644 --- a/include/cantera/thermo/PlasmaPhase.h +++ b/include/cantera/thermo/PlasmaPhase.h @@ -180,7 +180,7 @@ class PlasmaPhase: public IdealGasPhase /** * Electron pressure. Units: Pa. - * @f[P = n_{k_e} R T_e@f] + * @f[P = n_{k_e} R T_e @f] */ virtual double electronPressure() const { return GasConstant * concentration(m_electronSpeciesIndex) * diff --git a/include/cantera/thermo/RedlichKisterVPSSTP.h b/include/cantera/thermo/RedlichKisterVPSSTP.h index f33437c9ac..ab52a61d1e 100644 --- a/include/cantera/thermo/RedlichKisterVPSSTP.h +++ b/include/cantera/thermo/RedlichKisterVPSSTP.h @@ -133,7 +133,7 @@ namespace Cantera * * ## Application within Kinetics Managers * - * @f$ C^a_k@f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where + * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where * @f$ C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are * activities used in the thermodynamic functions. These activity (or * generalized) concentrations are used by kinetics manager classes to compute @@ -225,7 +225,7 @@ namespace Cantera * k^{-1} = k^1 K^1_c * @f] * - * @f$k^{-1} @f$ has units of s-1. + * @f$ k^{-1} @f$ has units of s-1. * * @ingroup thermoprops */ @@ -257,9 +257,9 @@ class RedlichKisterVPSSTP : public GibbsExcessVPSSTP //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is + //! The activity @f$ a_k @f$ of a species in solution is //! related to the chemical potential by @f[ \mu_k = \mu_k^0(T) - //! + \hat R T \log a_k. @f] The quantity @f$\mu_k^0(T,P)@f$ is + //! + \hat R T \log a_k. @f] The quantity @f$ \mu_k^0(T,P) @f$ is //! the chemical potential at unit activity, which depends only //! on temperature and pressure. //! @{ diff --git a/include/cantera/thermo/ShomatePoly.h b/include/cantera/thermo/ShomatePoly.h index b5d2abaa3b..e7755da815 100644 --- a/include/cantera/thermo/ShomatePoly.h +++ b/include/cantera/thermo/ShomatePoly.h @@ -22,8 +22,8 @@ namespace Cantera //! The Shomate polynomial parameterization for one temperature range for one //! species /*! - * Seven coefficients @f$(A,\dots,G)@f$ are used to represent - * @f$ c_p^0(T)@f$, @f$ h^0(T)@f$, and @f$ s^0(T) @f$ as + * Seven coefficients @f$ (A,\dots,G) @f$ are used to represent + * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as * polynomials in the temperature, @f$ T @f$ : * * @f[ @@ -42,7 +42,7 @@ namespace Cantera * dimensional units, but the temperature,@f$ t @f$, is divided by 1000. The * following dimensions are assumed in the above expressions: * - * - @f$ \tilde{c}_p^0(T)@f$ = Heat Capacity (J/gmol*K) + * - @f$ \tilde{c}_p^0(T) @f$ = Heat Capacity (J/gmol*K) * - @f$ \tilde{h}^0(T) @f$ = standard Enthalpy (kJ/gmol) * - @f$ \tilde{s}^0(T) @f$= standard Entropy (J/gmol*K) * - @f$ t @f$= temperature (K) / 1000. @@ -195,8 +195,8 @@ class ShomatePoly : public SpeciesThermoInterpType //! The Shomate polynomial parameterization for two temperature ranges for one //! species /*! - * Seven coefficients @f$(A,\dots,G)@f$ are used to represent - * @f$ c_p^0(T)@f$, @f$ h^0(T)@f$, and @f$ s^0(T) @f$ as + * Seven coefficients @f$ (A,\dots,G) @f$ are used to represent + * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as * polynomials in the temperature, @f$ T @f$, in one temperature region: * * @f[ @@ -215,7 +215,7 @@ class ShomatePoly : public SpeciesThermoInterpType * in dimensional units, but the temperature,@f$ t @f$, is divided by 1000. The * following dimensions are assumed in the above expressions: * - * - @f$ \tilde{c}_p^0(T)@f$ = Heat Capacity (J/gmol*K) + * - @f$ \tilde{c}_p^0(T) @f$ = Heat Capacity (J/gmol*K) * - @f$ \tilde{h}^0(T) @f$ = standard Enthalpy (kJ/gmol) * - @f$ \tilde{s}^0(T) @f$= standard Entropy (J/gmol*K) * - @f$ t @f$= temperature (K) / 1000. diff --git a/include/cantera/thermo/SingleSpeciesTP.h b/include/cantera/thermo/SingleSpeciesTP.h index f698152d97..5e124cce4d 100644 --- a/include/cantera/thermo/SingleSpeciesTP.h +++ b/include/cantera/thermo/SingleSpeciesTP.h @@ -84,9 +84,9 @@ class SingleSpeciesTP : public ThermoPhase //! @} //! @name Activities, Standard State, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_k @f$ of a species in solution is related to the //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] - //! The quantity @f$\mu_k^0(T)@f$ is the chemical potential at unit activity, + //! The quantity @f$ \mu_k^0(T) @f$ is the chemical potential at unit activity, //! which depends only on temperature. //! @{ diff --git a/include/cantera/thermo/StoichSubstance.h b/include/cantera/thermo/StoichSubstance.h index e6b0b38f68..b902ad0edf 100644 --- a/include/cantera/thermo/StoichSubstance.h +++ b/include/cantera/thermo/StoichSubstance.h @@ -33,7 +33,7 @@ namespace Cantera * * For an incompressible, stoichiometric substance, the molar internal energy is * independent of pressure. Since the thermodynamic properties are specified by - * giving the standard-state enthalpy, the term @f$ P_0 \hat v@f$ is subtracted + * giving the standard-state enthalpy, the term @f$ P_0 \hat v @f$ is subtracted * from the specified molar enthalpy to compute the molar internal energy. The * entropy is assumed to be independent of the pressure. * @@ -46,7 +46,7 @@ namespace Cantera * * For an incompressible, stoichiometric substance, the molar internal energy is * independent of pressure. Since the thermodynamic properties are specified by - * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v@f$ is + * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v @f$ is * subtracted from the specified reference molar enthalpy to compute the molar * internal energy. * @@ -141,7 +141,7 @@ class StoichSubstance : public SingleSpeciesTP //! This method returns an array of generalized concentrations /*! - * @f$ C^a_k@f$ are defined such that @f$ a_k = C^a_k / C^0_k, @f$ where + * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^0_k, @f$ where * @f$ C^0_k @f$ is a standard concentration defined below and @f$ a_k @f$ * are activities used in the thermodynamic functions. These activity (or * generalized) concentrations are used by kinetics manager classes to @@ -202,7 +202,7 @@ class StoichSubstance : public SingleSpeciesTP * For an incompressible, stoichiometric substance, the molar internal * energy is independent of pressure. Since the thermodynamic properties * are specified by giving the standard-state enthalpy, the term - * @f$ P_{ref} \hat v@f$ is subtracted from the specified reference molar + * @f$ P_{ref} \hat v @f$ is subtracted from the specified reference molar * enthalpy to compute the standard state molar internal energy. * * @param urt output vector of nondimensional standard state diff --git a/include/cantera/thermo/SurfPhase.h b/include/cantera/thermo/SurfPhase.h index 3c43f2dc1f..8940e56cef 100644 --- a/include/cantera/thermo/SurfPhase.h +++ b/include/cantera/thermo/SurfPhase.h @@ -167,7 +167,7 @@ class SurfPhase : public ThermoPhase * @f$ n_0 @f$ is the surface site density for the phase, and * @f$ s_k @f$ is the surface size of species k. * - * @f$ C^a_k@f$ that are defined such that @f$ a_k = C^a_k / C^0_k, @f$ + * @f$ C^a_k @f$ that are defined such that @f$ a_k = C^a_k / C^0_k, @f$ * where @f$ C^0_k @f$ is a standard concentration defined below and @f$ a_k * @f$ are activities used in the thermodynamic functions. These activity * concentrations are used by kinetics manager classes to compute the diff --git a/include/cantera/thermo/ThermoPhase.h b/include/cantera/thermo/ThermoPhase.h index 6dabdf9a37..2f344fb3e1 100644 --- a/include/cantera/thermo/ThermoPhase.h +++ b/include/cantera/thermo/ThermoPhase.h @@ -336,9 +336,9 @@ class ThermoPhase : public Phase //! @} //! @name Activities, Standard States, and Activity Concentrations //! - //! The activity @f$a_k@f$ of a species in solution is related to the + //! The activity @f$ a_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. @f] - //! The quantity @f$\mu_k^0(T,P)@f$ is the standard chemical potential at + //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard chemical potential at //! unit activity, which depends on temperature and pressure, but not on //! composition. The activity is dimensionless. //! @{ @@ -393,7 +393,7 @@ class ThermoPhase : public Phase //! This method returns an array of generalized concentrations /*! - * @f$ C^a_k@f$ are defined such that @f$ a_k = C^a_k / C^0_k, @f$ where + * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^0_k, @f$ where * @f$ C^0_k @f$ is a standard concentration defined below and @f$ a_k @f$ * are activities used in the thermodynamic functions. These activity (or * generalized) concentrations are used by kinetics manager classes to diff --git a/include/cantera/thermo/VPStandardStateTP.h b/include/cantera/thermo/VPStandardStateTP.h index 8798f561dc..e1691b55dd 100644 --- a/include/cantera/thermo/VPStandardStateTP.h +++ b/include/cantera/thermo/VPStandardStateTP.h @@ -172,8 +172,8 @@ class VPStandardStateTP : public ThermoPhase * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} * @f] * - * where @f$X_k@f$ are the mole fractions, @f$W_k@f$ are the molecular - * weights, and @f$V_k@f$ are the pure species molar volumes. + * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular + * weights, and @f$ V_k @f$ are the pure species molar volumes. * * Note, the basis behind this formula is that in an ideal solution the * partial molar volumes are equal to the pure species molar volumes. We diff --git a/include/cantera/thermo/WaterProps.h b/include/cantera/thermo/WaterProps.h index 11890b2d4d..aaeffb4b66 100644 --- a/include/cantera/thermo/WaterProps.h +++ b/include/cantera/thermo/WaterProps.h @@ -26,15 +26,15 @@ class PDSS_Water; * * ### Treatment of the phase potential and the electrochemical potential of a species * - * The electrochemical potential of species @f$k@f$ in a phase @f$p@f$, @f$ \zeta_k @f$, + * The electrochemical potential of species @f$ k @f$ in a phase @f$ p @f$, @f$ \zeta_k @f$, * is related to the chemical potential via the following equation, * * @f[ * \zeta_{k}(T,P) = \mu_{k}(T,P) + z_k \phi_p * @f] * - * where @f$ \nu_k @f$ is the charge of species @f$k@f$, and @f$ \phi_p @f$ is - * the electric potential of phase @f$p@f$. + * where @f$ \nu_k @f$ is the charge of species @f$ k @f$, and @f$ \phi_p @f$ is + * the electric potential of phase @f$ p @f$. * * The potential @f$ \phi_p @f$ is tracked and internally stored within the * base ThermoPhase object. It constitutes a specification of the internal state diff --git a/include/cantera/thermo/WaterPropsIAPWS.h b/include/cantera/thermo/WaterPropsIAPWS.h index e4b54d9851..8d0bd6a15d 100644 --- a/include/cantera/thermo/WaterPropsIAPWS.h +++ b/include/cantera/thermo/WaterPropsIAPWS.h @@ -110,12 +110,12 @@ namespace Cantera * * This class is not a ThermoPhase. However, it does maintain an internal * state of the object that is dependent on temperature and density. The - * internal state is characterized by an internally stored @f$ \tau@f$ and a + * internal state is characterized by an internally stored @f$ \tau @f$ and a * @f$ \delta @f$ value, and an iState value, which indicates whether the * point is a liquid, a gas, or a supercritical fluid. Along with that the - * @f$ \tau@f$ and a @f$ \delta @f$ values are polynomials of @f$ \tau@f$ and + * @f$ \tau @f$ and a @f$ \delta @f$ values are polynomials of @f$ \tau @f$ and * a @f$ \delta @f$ that are kept by the WaterPropsIAPWSphi class. Therefore, - * whenever @f$ \tau@f$ or @f$ \delta @f$ is changed, the function setState() + * whenever @f$ \tau @f$ or @f$ \delta @f$ is changed, the function setState() * must be called in order for the internal state to be kept up to date. * * The class is pretty straightforward. However, one function deserves diff --git a/src/oneD/MultiNewton.cpp b/src/oneD/MultiNewton.cpp index 4baec5df07..683273326f 100644 --- a/src/oneD/MultiNewton.cpp +++ b/src/oneD/MultiNewton.cpp @@ -90,13 +90,13 @@ doublereal bound_step(const doublereal* x, const doublereal* step, * @f[ * \sum_{n,j} \left(\frac{s_{n,j}}{w_n}\right)^2 * @f] - * where the error weight for solution component @f$n@f$ is given by + * where the error weight for solution component @f$ n @f$ is given by * @f[ * w_n = \epsilon_{r,n} \frac{\sum_j |x_{n,j}|}{J} + \epsilon_{a,n}. * @f] - * Here @f$\epsilon_{r,n} @f$ is the relative error tolerance for component n, + * Here @f$ \epsilon_{r,n} @f$ is the relative error tolerance for component n, * and multiplies the average magnitude of solution component n in the domain. - * The second term, @f$\epsilon_{a,n}@f$, is the absolute error tolerance for + * The second term, @f$ \epsilon_{a,n} @f$, is the absolute error tolerance for * component n. */ doublereal norm_square(const doublereal* x,