Public Member Functions | Public Attributes | List of all members
o2scl::eos_crust_virial Class Reference

Virial EOS for neutrons, protons, deuterons, and alpha particles. More...

#include <eos_crust_virial.h>

Inheritance diagram for o2scl::eos_crust_virial:
o2scl::eos_had_temp_pres_base o2scl::eos_had_temp_base o2scl::eos_had_base o2scl::eos_base

Public Member Functions

virtual int calc_p (fermion &ne, fermion &pr, thermo &th)
 Equation of state as a function of the chemical potentials.
 
virtual int calc_temp_p (fermion &n, fermion &p, double T, thermo &th)
 Equation of state as a function of the chemical potentials at finite temperature. More...
 
virtual int calc_temp_p_alpha (fermion &n, fermion &p, boson &d, boson &a, double T, thermo &th)
 Equation of state as a function of the chemical potentials at finite temperature with alpha particles and deuterons.
 
void fit ()
 Fit the virial coefficients to analytical functions.
 
The virial coefficients and their temperature derivatives

These functions assume that the temperature is specified in MeV. Note that the temperature derivative functions are multiplied by the temperature after taking the derivative to make them unitless (as in Horowitz06), thus all of these functions return values without units.

virtual double bn (double T)
 
virtual double ban (double T)
 
virtual double ba (double T)
 
virtual double bpn (double T)
 
virtual double Tbn_prime (double T)
 
virtual double Tban_prime (double T)
 
virtual double Tba_prime (double T)
 
virtual double Tbpn_prime (double T)
 
- Public Member Functions inherited from o2scl::eos_had_temp_pres_base
virtual int calc_e (fermion &n, fermion &p, thermo &th)
 Equation of state as a function of density.
 
virtual int calc_temp_e (fermion &n, fermion &p, double T, thermo &th)
 Equation of state as a function of densities at finite temperature.
 
- Public Member Functions inherited from o2scl::eos_had_temp_base
virtual int calc_liqgas_dens_temp_e (fermion &n1, fermion &p1, fermion &n2, fermion &p2, double T, thermo &th1, thermo &th2)
 Compute liquid-gas phase transition densities using eos_had_temp_base::calc_temp_e() . More...
 
virtual int calc_liqgas_temp_e (fermion &n1, fermion &p1, fermion &n2, fermion &p2, double nB, double Ye, double T, thermo &th1, thermo &th2, double &chi)
 Compute the liquid-gas phase transition using eos_had_temp_base::calc_temp_e() . More...
 
virtual int calc_liqgas_beta_temp_e (fermion &n1, fermion &p1, fermion &n2, fermion &p2, double nB, double T, thermo &th1, thermo &th2, double &Ye, double &chi)
 Compute the liquid-gas phase transition in beta-equilibrium using eos_had_temp_base::calc_temp_e() . More...
 
virtual double fesym_T (double nb, double T, double delta=0.0)
 Compute the symmetry energy at finite temperature.
 
virtual double fsyment_T (double nb, double T, double delta=0.0)
 Compute the symmetry entropy at finite temperature.
 
virtual double calc_temp_mun_e (double nn, double np, double T)
 Neutron chemical potential as a function of the densities.
 
virtual double calc_temp_mup_e (double nn, double np, double T)
 Proton chemical potential as a function of the densities.
 
virtual double calc_temp_nn_p (double mun, double mup, double T)
 Neutron density as a function of the chemical potentials.
 
virtual double calc_temp_np_p (double mun, double mup, double T)
 Proton density as a function of the chemical potentials.
 
double calc_fr (double nn, double np, double T)
 Compute the free energy as a function of the temperature and the densities.
 
virtual void f_number_suscept_T (double mun, double mup, double T, double &dPdnn, double &dPdnp, double &dPdpp)
 Compute the number susceptibilities as a function of the chemical potentials, $ \partial^2 P / \partial \mu_i \mu_j $ at a fixed temperature.
 
virtual void f_inv_number_suscept_T (double mun, double mup, double T, double &dednn, double &dednp, double &dedpp)
 Compute the 'inverse' number susceptibilities as a function of the densities, $ \partial^2 \varepsilon / \partial n_i n_j $ at a fixed temperature.
 
void check_en (fermion &n, fermion &p, double T, thermo &th, double &en_deriv, double &en_err)
 Check the entropy by computing the derivative numerically.
 
void check_mu_T (fermion &n, fermion &p, double T, thermo &th, double &mun_deriv, double &mup_deriv, double &mun_err, double &mup_err)
 Check the chemical potentials at finite temperature by computing the derivative numerically.
 
virtual void set_fermion_eval_thermo (fermion_eval_thermo &f)
 Computing finite-temperature integrals. More...
 
- Public Member Functions inherited from o2scl::eos_had_base
virtual double fcomp (double nb, double delta=0.0)
 Calculate the incompressibility in $ \mathrm{fm}^{-1} $ using calc_e() More...
 
virtual double fcomp_err (double nb, double delta, double &unc)
 Compute the incompressibility and its uncertainty. More...
 
virtual double feoa (double nb, double delta=0.0)
 Calculate the energy per baryon in $ \mathrm{fm}^{-1} $ using calc_e() More...
 
virtual double fesym (double nb, double delta=0.0)
 Calculate symmetry energy of matter in $ \mathrm{fm}^{-1} $ using calc_dmu_delta() . More...
 
virtual double fesym_err (double nb, double delta, double &unc)
 Calculate symmetry energy of matter and its uncertainty in $ \mathrm{fm}^{-1} $. More...
 
virtual double fesym_slope (double nb, double delta=0.0)
 The symmetry energy slope parameter in $ \mathrm{fm}^{-1} $. More...
 
virtual double fesym_curve (double nb, double delta=0.0)
 The curvature of the symmetry energy in $ \mathrm{fm}^{-1} $.
 
virtual double fesym_skew (double nb, double delta=0.0)
 The skewness of the symmetry energy in $ \mathrm{fm}^{-1} $.
 
virtual double fesym_diff (double nb)
 Calculate symmetry energy of matter as energy of neutron matter minus the energy of nuclear matter in $ \mathrm{fm}^{-1} $. More...
 
virtual double feta (double nb)
 The strength parameter for quartic terms in the symmetry energy.
 
virtual double feta_prime (double nb)
 The derivative of the strength parameter for quartic terms in the symmetry energy.
 
virtual double fkprime (double nb, double delta=0.0)
 Calculate skewness of nuclear matter in $ \mathrm{fm}^{-1} $ using calc_e() More...
 
virtual double fmsom (double nb, double delta=0.0)
 Calculate reduced neutron effective mass using calc_e() More...
 
virtual double f_effm_neut (double nb, double delta=0.0)
 Neutron (reduced) effective mass.
 
virtual double f_effm_prot (double nb, double delta=0.0)
 Proton (reduced) effective mass.
 
virtual double f_effm_scalar (double nb, double delta=0.0)
 Scalar effective mass. More...
 
virtual double f_effm_vector (double nb, double delta=1.0)
 Vector effective mass. More...
 
virtual double fn0 (double delta, double &leoa)
 Calculate saturation density using calc_e() More...
 
virtual void f_number_suscept (double mun, double mup, double &dPdnn, double &dPdnp, double &dPdpp)
 Compute the number susceptibilities as a function of the chemical potentials, $ \partial^2 P / \partial \mu_i \mu_j $.
 
virtual void f_inv_number_suscept (double mun, double mup, double &dednn, double &dednp, double &dedpp)
 Compute the 'inverse' number susceptibilities as a function of the densities, $ \partial^2 \varepsilon / \partial n_i n_j $.
 
virtual void saturation ()
 Calculates some of the EOS properties at the saturation density. More...
 
double calc_mun_e (double nn, double np)
 Compute the neutron chemical potential at fixed density. More...
 
double calc_ed (double nn, double np)
 Compute the energy density as a function of the nucleon densities.
 
double calc_pr (double nn, double np)
 Compute the pressure as a function of the nucleon chemical potentials.
 
double calc_mup_e (double nn, double np)
 Compute the proton chemical potential at fixed density. More...
 
double calc_nn_p (double mun, double mup)
 Compute the neutron density at fixed chemical potential. More...
 
double calc_np_p (double mun, double mup)
 Compute the proton density at fixed chemical potential. More...
 
double calc_dmu_delta (double delta, double nb)
 Compute the difference between neutron and proton chemical potentials as a function of the isospin asymmetry. More...
 
double calc_musum_delta (double delta, double nb)
 Compute the sum of the neutron and proton chemical potentials as a function of the isospin asymmetry. More...
 
double calc_pressure_nb (double nb, double delta=0.0)
 Compute the pressure as a function of baryon density at fixed isospin asymmetry. More...
 
double calc_edensity_nb (double nb, double delta=0.0)
 Compute the energy density as a function of baryon density at fixed isospin asymmetry. More...
 
void const_pf_derivs (double nb, double pf, double &dednb_pf, double &dPdnb_pf)
 Compute derivatives at constant proton fraction.
 
double calc_press_over_den2 (double nb, double delta=0.0)
 Calculate pressure / baryon density squared in nuclear matter as a function of baryon density at fixed isospin asymmetry. More...
 
double calc_edensity_delta (double delta, double nb)
 Calculate energy density as a function of the isospin asymmetry at fixed baryon density. More...
 
int nuc_matter_p (size_t nv, const ubvector &x, ubvector &y, double nn0, double np0)
 Solve for the chemical potentials given the densities. More...
 
int nuc_matter_e (size_t nv, const ubvector &x, ubvector &y, double mun0, double mup0)
 Solve for the densities given the chemical potentials. More...
 
virtual void set_mroot (mroot<> &mr)
 Set class mroot object for use in calculating chemical potentials from densities. More...
 
virtual void set_sat_root (root<> &mr)
 Set class mroot object for use calculating saturation density. More...
 
virtual void set_sat_deriv (deriv_base<> &de)
 Set deriv_base object to use to find saturation properties.
 
virtual void set_sat_deriv2 (deriv_base<> &de)
 Set the second deriv_base object to use to find saturation properties. More...
 
virtual void set_n_and_p (fermion &n, fermion &p)
 Set neutron and proton.
 
void gradient_qij (fermion &n, fermion &p, thermo &th, double &qnn, double &qnp, double &qpp, double &dqnndnn, double &dqnndnp, double &dqnpdnn, double &dqnpdnp, double &dqppdnn, double &dqppdnp)
 Calculate coefficients for gradient part of Hamiltonian. More...
 
virtual const char * type ()
 Return string denoting type ("eos_had_base")
 
void check_mu (fermion &n, fermion &p, thermo &th, double &mun_deriv, double &mup_deriv, double &mun_err, double &mup_err)
 Check the chemical potentials by computing the derivatives numerically.
 
void check_den (fermion &n, fermion &p, thermo &th, double &nn_deriv, double &np_deriv, double &nn_err, double &np_err)
 Check the densities by computing the derivatives numerically.
 
- Public Member Functions inherited from o2scl::eos_base
virtual void set_thermo (thermo &th)
 Set class thermo object.
 
virtual const thermoget_thermo ()
 Get class thermo object.
 

Public Attributes

boson alpha
 Internal alpha particle.
 
boson deuteron
 Internal deuteron.
 
- Public Attributes inherited from o2scl::eos_had_temp_base
fermion_eff def_fet
 Default fermion thermodynamics object.
 
- Public Attributes inherited from o2scl::eos_had_base
double eoa
 Binding energy (without the rest mass) in $ \mathrm{fm}^{-1} $.
 
double comp
 Compression modulus in $ \mathrm{fm}^{-1} $.
 
double esym
 Symmetry energy in $ \mathrm{fm}^{-1} $.
 
double n0
 Saturation density in $ \mathrm{fm}^{-3} $.
 
double msom
 Effective mass (neutron)
 
double kprime
 Skewness in $ \mathrm{fm}^{-1} $.
 
fermion def_neutron
 The defaut neutron. More...
 
fermion def_proton
 The defaut proton. More...
 
deriv_gsl def_deriv
 The default object for derivatives. More...
 
deriv_gsl def_deriv2
 The second default object for derivatives. More...
 
mroot_hybrids def_mroot
 The default solver. More...
 
root_cern def_sat_root
 The default solver for calculating the saturation density. More...
 
- Public Attributes inherited from o2scl::eos_base
thermo def_thermo
 The default thermo object.
 

Protected Attributes

Interpolation objects for virial coefficients
std::vector< double > Tv
 
std::vector< double > bnv
 
std::vector< double > Tbnpv
 
std::vector< double > bpnv
 
std::vector< double > Tbpnpv
 
std::vector< double > banv
 
std::vector< double > Tbanpv
 
std::vector< double > bav
 
std::vector< double > Tbapv
 
interp_vec< std::vector< double > > ibn
 
interp_vec< std::vector< double > > iTbnp
 
interp_vec< std::vector< double > > ibpn
 
interp_vec< std::vector< double > > iTbpnp
 
interp_vec< std::vector< double > > iban
 
interp_vec< std::vector< double > > iTbanp
 
interp_vec< std::vector< double > > iba
 
interp_vec< std::vector< double > > iTbap
 
- Protected Attributes inherited from o2scl::eos_had_temp_base
fermion_eval_thermofet
 Fermion thermodynamics (default is def_fet)
 
- Protected Attributes inherited from o2scl::eos_had_base
mrooteos_mroot
 The EOS solver.
 
rootsat_root
 The solver to compute saturation properties.
 
deriv_basesat_deriv
 The derivative object for saturation properties.
 
deriv_basesat_deriv2
 The second derivative object for saturation properties.
 
fermionneutron
 The neutron object.
 
fermionproton
 The proton object.
 
- Protected Attributes inherited from o2scl::eos_base
thermoeos_thermo
 A pointer to the thermo object.
 

Additional Inherited Members

- Public Types inherited from o2scl::eos_had_base
typedef boost::numeric::ublas::vector< double > ubvector
 
- Protected Member Functions inherited from o2scl::eos_had_temp_base
int nuc_matter_temp_e (size_t nv, const ubvector &x, ubvector &y, double nn0, double np0, double T)
 Solve for nuclear matter at finite temperature given density.
 
int nuc_matter_temp_p (size_t nv, const ubvector &x, ubvector &y, double mun0, double mup0, double T)
 Solve for nuclear matter at finite temperature given mu.
 
int liqgas_dens_solve (size_t nv, const ubvector &x, ubvector &y, fermion &n1, fermion &p1, fermion &n2, fermion &p2, double T, thermo &th1, thermo &th2)
 Solve for the liquid gas phase transition as a function of the densities.
 
int liqgas_solve (size_t nv, const ubvector &x, ubvector &y, fermion &n1, fermion &p1, fermion &n2, fermion &p2, double nB0, double Ye0, double T, thermo &th1, thermo &th2)
 Solve for the liquid-gas phase transition at fixed baryon density and electron fraction.
 
int liqgas_beta_solve (size_t nv, const ubvector &x, ubvector &y, fermion &n1, fermion &p1, fermion &n2, fermion &p2, double nB0, double T, thermo &th1, thermo &th2, fermion &e)
 Solve for the liquid-gas phase transition in beta-equilibrium.
 
double calc_entropy_delta (double delta, double nb, double T)
 Compute the entropy.
 
double calc_dmu_delta_T (double delta, double nb, double T)
 Compute the difference between the neutron and proton chemical potentials.
 
- Protected Member Functions inherited from o2scl::eos_had_base
double t1_fun (double barn)
 Compute t1 for gradient_qij().
 
double t2_fun (double barn)
 Compute t2 for gradient_qij().
 

Detailed Description

Virial EOS from Horowitz06 and Horowitz06b .

Note
This class likely fails for temperatures smaller than 1 MeV and larger than 20 MeV.
Warning
This class is implemented as a o2scl::eos_had_temp_pres_base object because it might be helpful to be able to use o2scl::eos_had_temp_pres_base::calc_temp_e(), but because of the alpha particles and deuterons, some of the other o2scl::eos_had_base methods don't have the correct interpretation.

Definition at line 56 of file eos_crust_virial.h.

Member Function Documentation

◆ calc_temp_p()

virtual int o2scl::eos_crust_virial::calc_temp_p ( fermion n,
fermion p,
double  T,
thermo th 
)
virtual

As in o2scl::eos_had_temp_base::calc_temp_p() the temperature argument should be in $ \mathrm{fm}^{-1} $, even though the virial coefficient functions take their temperature arguments in MeV.

Implements o2scl::eos_had_temp_pres_base.


The documentation for this class was generated from the following file:

Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).