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* Definition of Lorene classes Star, Star_bin and Star_bin_xcts
*
*/
/*
* Copyright (c) 2010 Michal Bejger
* Copyright (c) 2004 Francois Limousin
*
* Copyright (c) 2000-2001 Eric Gourgoulhon (for preceding class Etoile)
* Copyright (c) 2000-2001 Keisuke Taniguchi (for preceding class Etoile)
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __STAR_H_
#define __STAR_H_
/*
* $Id: star.h,v 1.32 2014/10/13 08:52:36 j_novak Exp $
* $Log: star.h,v $
* Revision 1.32 2014/10/13 08:52:36 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.31 2010/12/09 10:36:42 m_bejger
* Decouple method removed from declaration in Star_bin_xcts
*
* Revision 1.30 2010/10/26 18:47:36 m_bejger
* Modification of Star_bin_xcts::equilibrium, added table fact_resize
*
* Revision 1.29 2010/10/18 19:11:53 m_bejger
* Changes to Star::equilibrium_spher and Star_bin_xcts::equilibrium to allow for calculations with more than one domain in the star
*
* Revision 1.28 2010/06/15 08:17:43 m_bejger
* Method Star_bin_xcts::set_chi_comp() declared
*
* Revision 1.27 2010/05/04 07:53:32 m_bejger
* Class Star_bin_xcts added (initial version)
*
* Revision 1.26 2010/03/29 12:00:25 e_gourgoulhon
* Removed lnq from documentation
* (lnq has to be removed from base class Star; it is meaningfull only
* for Star_bin).
*
* Revision 1.25 2010/01/24 16:07:45 e_gourgoulhon
* New class Star_rot.
*
* Revision 1.24 2007/11/06 16:22:03 j_novak
* The data member stress_euler is now a Sym_tensor instead of a Tensor.
*
* Revision 1.23 2007/06/21 19:48:25 k_taniguchi
* Introduction of a method to compute ray_eq_3pis2.
*
* Revision 1.22 2006/05/31 09:25:47 f_limousin
* Modif. of the size of the different domains
*
* Revision 1.21 2006/04/11 14:26:12 f_limousin
* New version of the code : improvement of the computation of some
* critical sources, estimation of the dirac gauge, helical symmetry...
*
* Revision 1.20 2005/09/15 15:56:28 e_gourgoulhon
* Made the documentation compliant with Doxygen.
*
* Revision 1.19 2005/09/13 19:38:32 f_limousin
* Reintroduction of the resolution of the equations in cartesian coordinates.
*
* Revision 1.18 2005/08/13 16:14:11 m_saijo
* Corrected the document of the total shift vector
*
* Revision 1.17 2005/04/08 12:36:45 f_limousin
* Just to avoid warnings...
*
* Revision 1.16 2005/02/24 16:09:29 f_limousin
* Change the name of some variables (for instance dcov_logn --> dlogn).
* Add also member dlnq but delete dlnpsi_auto and dlogn_auto.
*
* Revision 1.15 2005/02/17 17:28:18 f_limousin
* Change the name of some quantities to be consistent with other classes
* (for instance nnn is changed to nn, shift to beta, beta to lnq...)
*
* Revision 1.14 2005/02/11 18:11:16 f_limousin
* Introduction of a member Map_af in derived class Star_bin.
*
* Revision 1.13 2004/11/11 16:29:48 j_novak
* set_der_0x0 is no longer virtual (to be coherent with Tensor/Scalar classes).
*
* Revision 1.12 2004/11/10 16:31:53 j_novak
* Star is no longer an abstract class (mass_b and mass_g are no longer
* pure virtual). Modified comments to be readable by doxygen.
*
* Revision 1.11 2004/07/21 11:48:30 f_limousin
* Remove function sprod.
*
* Revision 1.10 2004/06/22 12:47:01 f_limousin
* Change qq, qq_auto and qq_comp to beta, beta_auto and beta_comp.
*
* Revision 1.9 2004/05/25 14:48:57 f_limousin
* Add a parameter for the function equilibrium.
*
* Revision 1.8 2004/03/23 09:53:50 f_limousin
* Minor changes
*
* Revision 1.7 2004/02/27 09:41:52 f_limousin
* Scalars ssjm1_logn, ssjm1_qq ... for all metric coefficients have been
* in class Star_bin for the resolution of Poisson equations.
* The class Star is now abstract : the computational routines mass_b()
* and mass_g() = 0.
*
* Revision 1.6 2004/01/22 10:06:33 f_limousin
* Add methods set_logn_comp() and set_shift_auto().
*
* Revision 1.5 2004/01/20 15:26:00 f_limousin
* New class star and star_bin.
*
*
* $Header: /cvsroot/Lorene/C++/Include/star.h,v 1.32 2014/10/13 08:52:36 j_novak Exp $
*
*/
// Headers Lorene
#include "tensor.h"
#include "metric.h"
namespace Lorene {
class Eos ;
//---------------------------//
// base class Star //
//---------------------------//
/**
* Base class for stars. \ingroup (star)
*
* A \c Star is constructed upon (i) a mapping
* (derived class of \c Map), the center of which defines the center of the
* star, and (ii) an equation of state (derived class of \c Eos).
* It contains tensor fields (class \c Tensor) which describe the
* hydrodynamical quantities as well as the gravitational field (spacetime
* metric).
*
* According to the 3+1 formalism, the spacetime metric is written
* \f[
* ds^2 = - N^2 dt^2 + \gamma_{ij} ( dx^i + \beta^i dt )
* (dx^j + \beta^j dt )
* \f]
* where \f$\gamma_{ij}\f$ is the 3-metric, described by a Lorene object of class \c Metric.
*
* The 3+1 formalism introduces two kinds of privileged observers: the
* fluid comoving observer and the Eulerian observer, whose 4-velocity
* is the unit future directed normal to the \e t = const hypersurfaces.
* The hydrodynamical quantities measured by the fluid observer correspond
* to the members \c ent, \c nbar, \c ener, and \c press.
* The hydrodynamical quantities measured by the Eulerian observer correspond
* to the members \c ener_euler, \c s_euler, \c gam_euler, and
* \c u_euler.
*
* \version $Id: star.h,v 1.32 2014/10/13 08:52:36 j_novak Exp $
*/
class Star {
// Data :
// -----
protected:
Map& mp ; ///< Mapping associated with the star
/// Number of domains of \c *mp occupied by the star
int nzet ;
const Eos& eos ; ///< Equation of state of the stellar matter
// Fluid quantities with respect to the fluid frame
// ------------------------------------------------
Scalar ent ; ///< Log-enthalpy
Scalar nbar ; ///< Baryon density in the fluid frame
Scalar ener ; ///< Total energy density in the fluid frame
Scalar press ; ///< Fluid pressure
// Fluid quantities with respect to the Eulerian frame
// ---------------------------------------------------
Scalar ener_euler ; ///< Total energy density in the Eulerian frame
/// Trace of the stress scalar in the Eulerian frame
Scalar s_euler ;
/// Lorentz factor between the fluid and Eulerian observers
Scalar gam_euler ;
/// Fluid 3-velocity with respect to the Eulerian observer
Vector u_euler ;
/** Spatial part of the stress-energy tensor with respect
* to the Eulerian observer.
*/
Sym_tensor stress_euler ;
// Metric potentials
// -----------------
/** Logarithm of the lapse \e N .
* In the Newtonian case,
* this is the Newtonian gravitational potential
* (in units of \f$c^2\f$).
*/
Scalar logn ;
/// Lapse function \e N .
Scalar nn ;
/// Shift vector.
Vector beta ;
// Scalar field \f$\ln Q = \ln(\psi^2 N)\f$
//## to be removed from base class Star
Scalar lnq ;
/// 3-metric
Metric gamma ;
// Derived data :
// ------------
protected:
/// Coordinate radius at \f$\phi=0\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq ;
/// Coordinate radius at \f$\phi=\pi/2\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq_pis2 ;
/// Coordinate radius at \f$\phi=\pi\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq_pi ;
/// Coordinate radius at \f$\phi=3\pi/2\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq_3pis2 ;
/// Coordinate radius at \f$\theta=0\f$.
mutable double* p_ray_pole ;
/** Description of the stellar surface: 2-D \c Itbl containing the
* values of the domain index \e l on the surface at the
* collocation points in \f$(\theta', \phi')\f$
*/
mutable Itbl* p_l_surf ;
/** Description of the stellar surface: 2-D \c Tbl containing the
* values of the radial coordinate \f$\xi\f$ on the surface at the
* collocation points in \f$(\theta', \phi')\f$
*/
mutable Tbl* p_xi_surf ;
mutable double* p_mass_b ; ///< Baryon mass
mutable double* p_mass_g ; ///< Gravitational mass
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the star will be defined
* @param nzet_i Number of domains occupied by the star
* @param eos_i Equation of state of the stellar matter
*
*/
Star(Map& mp_i, int nzet_i, const Eos& eos_i) ;
Star(const Star& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE* )).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve)
*/
Star(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Star() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
virtual void set_der_0x0() const ;
/** Sets to \c ETATNONDEF (undefined state) the hydrodynamical
* quantities relative to the Eulerian observer.
*/
virtual void del_hydro_euler() ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another \c Star
void operator=(const Star&) ;
/// Read/write of the mapping
Map& set_mp() {return mp; } ;
/// Assignment of the enthalpy field.
void set_enthalpy(const Scalar& ) ;
/** Computes the proper baryon and energy density, as well as
* pressure from the enthalpy.
*/
void equation_of_state() ;
/** Computes the hydrodynamical quantities relative to the Eulerian
* observer from those in the fluid frame (\c nbar, \c ener
* and \c press).
*/
virtual void hydro_euler() ;
/** Computes a spherical static configuration.
*
* @param ent_c [input] central value of the enthalpy
* @param precis [input] threshold in the relative difference between
* the enthalpy fields of two consecutive steps
* to stop the iterative procedure (default value: 1.e-14)
* @param ent_limit [input] : array of enthalpy values to be set
* at the boundaries between the domains; if set to 0x0 (default),
* the initial values will be kept.
*/
virtual void equilibrium_spher(double ent_c, double precis = 1.e-14,
const Tbl* pent_limit = 0x0 ) ;
// Accessors
// ---------
public:
/// Returns the mapping
const Map& get_mp() const {return mp; } ;
/// Returns the number of domains occupied by the star
int get_nzet() const {return nzet; } ;
/// Returns the equation of state
const Eos& get_eos() const {return eos; } ;
/// Returns the enthalpy field
const Scalar& get_ent() const {return ent;} ;
/// Returns the proper baryon density
const Scalar& get_nbar() const {return nbar;} ;
/// Returns the proper total energy density
const Scalar& get_ener() const {return ener;} ;
/// Returns the fluid pressure
const Scalar& get_press() const {return press;} ;
/// Returns the total energy density with respect to the Eulerian observer
const Scalar& get_ener_euler() const {return ener_euler;} ;
/// Returns the trace of the stress tensor in the Eulerian frame
const Scalar& get_s_euler() const {return s_euler;} ;
/// Returns the Lorentz factor between the fluid and Eulerian observers
const Scalar& get_gam_euler() const {return gam_euler;} ;
/// Returns the fluid 3-velocity with respect to the Eulerian observer
const Vector& get_u_euler() const {return u_euler;} ;
/** Returns the spatial part of the stress-energy tensor
* with respect to the Eulerian observer
*/
const Tensor& get_stress_euler() const {return stress_euler;} ;
/** Returns the logarithm of the lapse \e N.
* In the Newtonian case, this is the Newtonian
* gravitational potential (in units of \f$c^2\f$).
*/
const Scalar& get_logn() const {return logn;} ;
/// Returns the lapse function \e N
const Scalar& get_nn() const {return nn;} ;
/// Returns the shift vector \f$\beta^i\f$.
const Vector& get_beta() const {return beta;} ;
// Returns the scalar field \f$\ln Q\f$.
//## to be removed from base class Star
const Scalar& get_lnq() const {return lnq;} ;
/// Returns the 3-metric \f$\gamma\f$.
const Metric& get_gamma() const {return gamma;} ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
/// Display
friend ostream& operator<<(ostream& , const Star& ) ;
protected:
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Coordinate radius at \f$\phi=0\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq() const ;
/// Coordinate radius at \f$\phi=\pi/2\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq_pis2() const ;
/// Coordinate radius at \f$\phi=\pi\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq_pi() const ;
/// Coordinate radius at \f$\phi=3\pi/2\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq_3pis2() const ;
/// Coordinate radius at \f$\theta=0\f$ [r_unit].
double ray_pole() const ;
/** Description of the stellar surface: returns a 2-D \c Itbl
* containing the
* values of the domain index \e l on the surface at the
* collocation points in \f$(\theta', \phi')\f$.
* The stellar surface is defined as the location where
* the enthalpy (member \c ent) vanishes.
*/
virtual const Itbl& l_surf() const ;
/** Description of the stellar surface: returns a 2-D \c Tbl
* containing the values of the radial coordinate \f$\xi\f$
* on the surface at the
* collocation points in \f$(\theta', \phi')\f$.
* The stellar surface is defined as the location where
* the enthalpy (member \c ent) vanishes.
*/
const Tbl& xi_surf() const ;
/// Baryon mass
virtual double mass_b() const = 0 ;
/// Gravitational mass
virtual double mass_g() const = 0 ;
};
ostream& operator<<(ostream& , const Star& ) ;
//---------------------------//
// class Star_bin //
//---------------------------//
/**
* Class for stars in binary system. *** UNDER DEEVELOPMENT *** \ingroup (star)
*
* A \c Star_bin can be construted in two states, represented by
* the \c bool member \c irrotational: (i) irrotational
* (i.e. the fluid motion is irrotational) or (ii) rigidly corotating
* with respect to the orbital motion (synchronized binary).
*
* @version #$Id: star.h,v 1.32 2014/10/13 08:52:36 j_novak Exp $#
*/
class Star_bin : public Star {
// Data :
// -----
protected:
/** \c true for an irrotational star, \c false for a
* corotating one
*/
bool irrotational ;
/** Scalar potential \f$\Psi_0\f$ of the non-translational part of
* fluid 4-velocity (in the irrotational case)
*/
Scalar psi0 ;
/** Gradient of \f$\Psi\f$ (in the irrotational case)
* (Spherical components with respect to the mapping of the star)
*/
Vector d_psi ;
/** Spatial projection of the fluid 3-velocity with respect to
* the co-orbiting observer.
* (Spherical components with respect to the mapping of the star)
*/
Vector wit_w ;
/** Logarithm of the Lorentz factor between the fluid and
* the co-orbiting observer.
*/
Scalar loggam ;
/** 3-vector shift, divided by \e N, of the rotating coordinates,
* \f$\beta^i/N\f$.
* (Spherical components with respect to the mapping of the star)
*/
Vector bsn ;
/// Centrifugal potential
Scalar pot_centri ;
/** Part of the lapse logarithm (gravitational potential at the
* Newtonian limit) generated principally by the star.
*/
Scalar logn_auto ;
/** Part of the lapse logarithm (gravitational potential at the
* Newtonian limit) generated principally by the companion star.
*/
Scalar logn_comp ;
/// Covariant derivative of the total logarithm of the lapse.
Vector dcov_logn ;
/// Contravariant derivative of the total logarithm of the lapse.
Vector dcon_logn ;
/** Scalar field \f$ Q = \psi^2 N \f$ generated principally by the
* star.
*/
Scalar lnq_auto ;
/** Scalar field \f$ Q = \psi^2 N \f$ generated principally by the
* companion star.
*/
Scalar lnq_comp ;
/// Conformal factor \f$\psi^4\f$
Scalar psi4 ;
/// Covariant derivative of the logarithm of the conformal factor
Vector dcov_phi ;
/// Contravariant derivative of the logarithm of the conformal factor
Vector dcon_phi ;
/** Flat metric defined on the mapping (Spherical components
* with respect to the mapping of the star) .
*/
Metric_flat flat ;
/// Conformal metric \f$\tilde \gamma_{ij}\f$
Metric gtilde ;
/** Part of the shift vector generated principally by the star
* (Spherical components with respect to the mapping of the star)
*/
Vector beta_auto ;
/** Part of the shift vector generated principally by the star
* (Spherical components with respect to the mapping of the star)
*/
Vector beta_comp ;
/** Total deviation of the inverse conformal metric
* \f$\tilde \gamma^{ij}\f$ from the inverse flat metric.
*/
Sym_tensor hij ;
/** Deviation of the inverse conformal metric
* \f$\tilde \gamma^{ij}\f$ from the inverse flat metric generated
* principally by the star.
*/
Sym_tensor hij_auto ;
/** Deviation of the inverse conformal metric
* \f$\tilde \gamma^{ij}\f$ from the inverse flat metric generated
* principally by the companion star.
*/
Sym_tensor hij_comp ;
/** Part of the extrinsic curvature tensor \f$\tilde K^{ij}\f$
* generated by \c beta_auto.
* (Spherical components with respect to the mapping of the star)
*/
Sym_tensor tkij_auto ;
/** Part of the extrinsic curvature tensor \f$\tilde K^{ij}\f$
* generated by \c beta_comp.
* (Spherical components with respect to the mapping of the star)
*/
Sym_tensor tkij_comp ;
/** Part of the scalar \f$K_{ij} K^{ij}\f$
* generated by \c beta_auto, i.e.
* \f$K_{ij}^{\rm auto} K^{ij}_{\rm auto}\f$
*/
Scalar kcar_auto ;
/** Part of the scalar \f$K_{ij} K^{ij}\f$
* generated by \c beta_auto and \c beta_comp, i.e.
* \f$K_{ij}^{\rm auto} K^{ij}_{\rm comp}\f$
*/
Scalar kcar_comp ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c logn_auto.
*/
Scalar ssjm1_logn ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c lnq_auto.
*/
Scalar ssjm1_lnq ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c khi. (second scalar equation
* for the resolution of the vectorial poisson equation for the shift)
*/
Scalar ssjm1_khi ;
Vector ssjm1_wbeta ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c h00_auto.
*/
Scalar ssjm1_h11 ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c h10_auto.
*/
Scalar ssjm1_h21 ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c h20_auto.
*/
Scalar ssjm1_h31 ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c h11_auto.
*/
Scalar ssjm1_h22 ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c h21_auto.
*/
Scalar ssjm1_h32 ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c h22_auto.
*/
Scalar ssjm1_h33 ;
/**
* Function used to construct the part \f$lnq_auto\f$ generated by
* the star from the total \f$lnq\f$.
* Mainly this \c Scalar is 1 around the star and 0 around
* the companion
* and the sum of \c decouple for the star and his companion is 1
* everywhere.
*/
Scalar decouple ;
/** \c true if the 3-metric is conformally flat, \c false
* for a more general metric.
*/
bool conf_flat ;
// Derived data :
// ------------
protected:
/// Absolute coordinate X of the barycenter of the baryon density
mutable double* p_xa_barycenter ;
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the star will be defined
* @param nzet_i Number of domains occupied by the star
* @param eos_i Equation of state of the stellar matter
* @param irrot should be \c true for an irrotational star,
* \c false for a corotating one
* @param conf_flat should be \c true for a conformally flat metric
* \c false for a general one
*/
Star_bin(Map& mp_i, int nzet_i, const Eos& eos_i,
bool irrot, bool conf_flat) ;
Star_bin(const Star_bin& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE* )).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve)
*/
Star_bin(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Star_bin() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
virtual void set_der_0x0() const ;
/** Sets to \c ETATNONDEF (undefined state) the hydrodynamical
* quantities relative to the Eulerian observer.
*/
virtual void del_hydro_euler() ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another \c Star_bin
void operator=(const Star_bin& ) ;
/// Read/write the centrifugal potential
Scalar& set_pot_centri() ;
/** Read/write of the logarithm of the lapse generated
* principally by the companion.
*/
Scalar& set_logn_comp() ;
/// Assignment of a new logn_auto
void set_logn_auto(const Scalar& logn_auto_new) {logn_auto = logn_auto_new ;
return ;}
/// Assignment of a new lnq_auto
void set_lnq_auto(const Scalar& lnq_auto_new) {lnq_auto = lnq_auto_new ;
return ;}
/// Read/write of \f$beta_auto\f$
Vector& set_beta_auto() ;
/// Read/write of \f$beta\f$
Vector& set_beta() ;
/// Write if conformally flat
void set_conf_flat(bool confflat) {conf_flat = confflat ; return ;}
// Accessors
// ---------
public:
/** Returns \c true for an irrotational motion, \c false for
* a corotating one.
*/
bool is_irrotational() const {return irrotational; } ;
/// Returns the non-translational part of the velocity potential
const Scalar& get_psi0() const {return psi0;} ;
/** Returns the covariant derivative of the velocity potential
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_d_psi() const {return d_psi;} ;
/** Returns the spatial projection of the fluid 3-velocity with
* respect to the co-orbiting observer.
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_wit_w() const {return wit_w;} ;
/** Returns the logarithm of the Lorentz factor between the fluid and
* the co-orbiting observer.
*/
const Scalar& get_loggam() const {return loggam;} ;
/** Returns the shift vector, divided by \e N, of the rotating
* coordinates, \f$\beta^i/N\f$.
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_bsn() const {return bsn;} ;
/// Returns the centrifugal potential
const Scalar& get_pot_centri() const {return pot_centri;} ;
/** Returns the part of the lapse logarithm (gravitational potential
* at the Newtonian limit) generated principally by the star.
*/
const Scalar& get_logn_auto() const {return logn_auto;} ;
/** Returns the part of the lapse logarithm (gravitational potential
* at the Newtonian limit) generated principally by the companion star.
*/
const Scalar& get_logn_comp() const {return logn_comp;} ;
/** Returns the part of the shift vector \f$\beta^i\f$ generated
* principally by the star.
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_beta_auto() const {return beta_auto;} ;
/** Returns the part of the shift vector \f$\beta^i\f$ generated
* principally by the star.
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_beta_comp() const {return beta_comp;} ;
/** Returns the part of the vector field \f$Q\f$ generated principally
* by the star.
*/
const Scalar& get_lnq_auto() const {return lnq_auto;} ;
/** Returns the part of the vector field \f$Q\f$ generated principally
* by the companion star.
*/
const Scalar& get_lnq_comp() const {return lnq_comp;} ;
/** Returns the covariant derivative of \f$logn\f$.
*/
const Vector& get_dcov_logn() const {return dcov_logn;} ;
/** Returns the contravariant derivative of \f$logn\f$.
*/
const Vector& get_dcon_logn() const {return dcon_logn;} ;
/** Returns the covariant derivative of \f$\Phi\f$
* (logarithm of the conformal factor).
*/
const Vector& get_dcov_phi() const {return dcov_phi;} ;
/** Returns the contravariant derivative of \f$\Phi\f$
* (logarithm of the conformal factor).
*/
const Vector& get_dcon_phi() const {return dcon_phi;} ;
/// Return the conformal factor \f$\psi^4\f$
const Scalar& get_psi4() const {return psi4;} ;
/** Return the flat metric defined on the mapping (Spherical
* components with respect to the mapping of the star)
*/
const Metric& get_flat() const {return flat;} ;
/// Return the conformal 3-metric \f$\tilde \gamma\f$
const Metric& get_gtilde() const {return gtilde;} ;
/** Return the total deviation of the inverse conformal metric
* \f$\tilde \gamma^{ij}\f$ from the inverse flat metric.
*/
const Sym_tensor& get_hij() const {return hij;} ;
/** Return the deviation of the inverse conformal metric
* \f$\tilde \gamma^{ij}\f$ from the inverse flat metric principally
* generated by the star.
*/
const Sym_tensor& get_hij_auto() const {return hij_auto;} ;
/** Return the deviation of the inverse conformal metric
* \f$\tilde \gamma^{ij}\f$ from the inverse flat metric generated
* principally by the companion star.
*/
const Sym_tensor& get_hij_comp() const {return hij_comp;} ;
/** Returns the part of the extrinsic curvature tensor
* \f$\tilde K^{ij}\f$ generated by \c beta_auto.
* (Spherical components with respect to the mapping of the star)
*/
const Sym_tensor& get_tkij_auto() const {return tkij_auto;} ;
/** Returns the part of the extrinsic curvature tensor
* \f$\tilde K^{ij}\f$ generated by \c beta_comp.
* (Spherical components with respect to the mapping of the star)
*/
const Sym_tensor& get_tkij_comp() const {return tkij_comp;} ;
/** Returns the part of
* \f$\tilde K^{ij} \tilde K_{ij}\f$ generated by \c beta_auto.
*/
const Scalar& get_kcar_auto() const {return kcar_auto;} ;
/** Returns the part of
* \f$\tilde K^{ij} \tilde K_{ij}\f$ generated by \c beta_comp.
*/
const Scalar& get_kcar_comp() const {return kcar_comp;} ;
/**
* Returns the function used to construct \c beta_auto
from \c beta.
*/
const Scalar get_decouple() const {return decouple ;}
bool is_conf_flat() const {return conf_flat; } ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
protected:
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Baryon mass
virtual double mass_b() const ;
/// Gravitational mass
virtual double mass_g() const ;
/// Absolute coordinate X of the barycenter of the baryon density,
virtual double xa_barycenter() const ;
// Computational routines
// ----------------------
public:
/** Computes the hydrodynamical quantities relative to the Eulerian
* observer from those in the fluid frame, as well as
* \c wit_w and \c loggam.
*
* The calculation is performed starting from the quantities
* \c ent, \c ener, \c press and \c bsn,
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c gam_euler, \c u_euler, \c ener_euler,
* \c s_euler, \c stress_euler,
* \c wit_w and \c loggam.
*
*/
virtual void hydro_euler() ;
/** Computes metric coefficients from known potentials,
* when the companion is another star.
*
* The calculation is performed starting from the quantities
* \c logn_auto, \c lnq_auto, \c beta_auto,
* \c hij_auto, \c comp.logn_auto, \c comp.lnq_auto,
* \c comp.beta_auto, \c comp.hij_auto
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c logn_comp, \c lnq_comp, \c beta_comp,
* \c hij_comp, \c nn, \c psi4, \c beta,
*
* @param comp companion star.
* @param omega angular velocity with respect to an asymptotically
* inertial observer
*/
void update_metric(const Star_bin& comp, double omega) ;
/** Same as \c update_metric(const Star_bin\& ) but with
* relaxation.
*
* @param comp companion star.
* @param star_prev previous value of the star.
* @param relax relaxation parameter.
* @param omega angular velocity with respect to an asymptotically
* inertial observer
*/
void update_metric(const Star_bin& comp, const Star_bin& star_prev,
double relax, double omega) ;
/** Computes the derivative of metric functions related to the
* companion star.
* @param omega angular velocity with respect to an asymptotically
* inertial observer
*/
void update_metric_der_comp(const Star_bin& comp, double omega) ;
/** Computes the quantities \c bsn and \c pot_centri.
*
* The calculation is performed starting from the quantities
* \c nn, \c beta, \c Q,
* which are supposed to be up to date.
*
* @param omega angular velocity with respect to an asymptotically
* inertial observer
* @param x_axe absolute X coordinate of the rotation axis
*/
void kinematics(double omega, double x_axe) ;
/** Computes the gradient of the total velocity potential \f$\psi\f$.
*
*/
void fait_d_psi() ;
/** Computes \c tkij_auto and \c akcar_auto from
* \c beta_auto, \c nn and \c Q.
* @param omega angular velocity with respect to an asymptotically
* inertial observer
*/
void extrinsic_curvature(double omega) ;
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy
* @param mermax [input] Maximum number of steps
* @param mermax_poisson [input] Maximum number of steps in
* poisson scalar
* @param relax_poisson [input] Relaxation factor in poisson scalar
* @param mermax_potvit [input] Maximum number of steps in
* Map_radial::poisson_compact
* @param relax_potvit [input] Relaxation factor in
* Map_radial::poisson_compact
* @param thres_adapt [input] Threshold on dH/dr for the adaptation
* of the mapping
* @param diff [output] 1-D \c Tbl for the storage of some
* error indicators
*/
void equilibrium(double ent_c, int mermax, int mermax_potvit,
int mermax_poisson, double relax_poisson,
double relax_potvit, double thres_adapt, Tbl& diff,
double om) ;
/** Computes the non-translational part of the velocity scalar potential
* \f$\psi0\f$ by solving the continuity equation.
*
* @param mermax [input] Maximum number of steps in the iteration
* @param precis [input] Required precision: the iteration will
* be stopped when the relative difference
* on \f$\psi0\f$ between two successive steps
* is lower than \c precis.
* @param relax [input] Relaxation factor.
*
* @return Relative error of the resolution obtained by comparing
* the operator acting on the solution with the source.
*/
double velocity_potential(int mermax, double precis, double relax) ;
/** Performs a relaxation on \c ent, \c logn_auto,
* \c lnq_auto, \c beta_auto and \c hij_auto.
*
* @param star_prev [input] star at the previous step.
* @param relax_ent [input] Relaxation factor for \c ent
* @param relax_met [input] Relaxation factor for \c logn_auto,
* \c lnq_auto, \c beta_auto,
* only if \c (mer \% fmer_met == 0).
* @param mer [input] Step number
* @param fmer_met [input] Step interval between metric updates
*/
void relaxation(const Star_bin& star_prev, double relax_ent,
double relax_met, int mer, int fmer_met) ;
/// Test if the gauge conditions we impose are well satisfied
void test_K_Hi() const ;
/// Test of the helical symmetry
void helical(double omega) const ;
friend class Binary ;
};
//---------------------------//
// class Star_bin_xcts //
//---------------------------//
/**
* Class for stars in binary system in eXtended Conformal Thin Sandwich
* formulation. *** UNDER DEEVELOPMENT *** \ingroup (star)
*
* A \c Star_bin_xcts can be construted in two states, represented by
* the \c bool member \c irrotational: (i) irrotational
* (i.e. the fluid motion is irrotational) or (ii) rigidly corotating
* with respect to the orbital motion (synchronized binary).
*
*/
class Star_bin_xcts : public Star {
// Data :
// -----
protected:
/** \c true for an irrotational star, \c false for a
* corotating one
*/
bool irrotational ;
/** Scalar potential \f$\Psi_0\f$ of the non-translational part of
* fluid 4-velocity (in the irrotational case)
*/
Scalar psi0 ;
/** Gradient of \f$\Psi\f$ (in the irrotational case)
* (Spherical components with respect to the mapping of the star)
*/
Vector d_psi ;
/** Spatial projection of the fluid 3-velocity with respect to
* the co-orbiting observer.
* (Spherical components with respect to the mapping of the star)
*/
Vector wit_w ;
/** Logarithm of the Lorentz factor between the fluid and
* the co-orbiting observer.
*/
Scalar loggam ;
/** 3-vector shift, divided by \e N, of the rotating coordinates,
* \f$\beta^i/N\f$.
* (Spherical components with respect to the mapping of the star)
*/
Vector bsn ;
/// Centrifugal potential
Scalar pot_centri ;
/** Scalar field \f$ \chi_{auto} = (N\Psi)_{auto} \f$ generated
* principally by the star.
*/
Scalar chi_auto ;
/** Scalar field \f$ \chi_{comp} = (N\Psi)_{comp} \f$ generated
* principally by the companion star.
*/
Scalar chi_comp ;
/** Scalar field \f$\Psi_{auto}\f$ generated principally by the
* star.
*/
Scalar Psi_auto ;
/** Scalar field \f$\Psi_{comp}\f$ generated principally by the
* companion star.
*/
Scalar Psi_comp ;
/// Total conformal factor \f$\Psi\f$
Scalar Psi ;
/// Total function \f$\chi\f$
Scalar chi ;
/// Conformal factor \f$\psi^4\f$
Scalar psi4 ;
/** Solution for the vector part of the vector Poisson equation
* for \f$\beta^i\f$
*/
Vector w_beta ;
/** Solution for the scalar part of the vector Poisson equation
* for \f$\beta^i\f$
*/
Scalar khi ;
/// Covariant derivative of the conformal factor \f$\Psi\f$
Vector dcov_Psi ;
/// Covariant derivative of the function \f$\chi\f$
Vector dcov_chi ;
///Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) .
Metric_flat flat ;
/** Part of the shift vector generated principally by the star
* (Spherical components with respect to the mapping of the star)
*/
Vector beta_auto ;
/** Part of the shift vector generated principally by the star
* (Spherical components with respect to the mapping of the star)
*/
Vector beta_comp ;
/** Part of the extrinsic curvature tensor \f$\hat{A}^{ij}\f$
* generated by \c beta_auto.
* (Spherical components with respect to the mapping of the star)
*/
Sym_tensor haij_auto ;
/** Part of the extrinsic curvature tensor \f$\hat{A}^{ij}\f$
* generated by \c beta_comp.
* (Spherical components with respect to the mapping of the star)
*/
Sym_tensor haij_comp ;
/** Part of the scalar \f$\hat{A}_{ij}\hat{A}^{ij}\f$
* generated by \c beta_auto, i.e.
* \f$\hat{A}_{ij}^{\rm auto}\hat{A}^{ij}_{\rm auto}\f$
*/
Scalar hacar_auto ;
/** Part of the scalar \f$\hat{A}_{ij}\hat{A}^{ij}\f$
* generated by \c beta_auto and \c beta_comp, i.e.
* \f$\hat{A}_{ij}^{\rm auto}\hat{A}^{ij}_{\rm comp}\f$
*/
Scalar hacar_comp ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c \chi_auto.
*/
Scalar ssjm1_chi ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c \Psi_auto.
*/
Scalar ssjm1_psi ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c khi. (second scalar equation
* for the resolution of the vectorial poisson equation for the shift)
*/
Scalar ssjm1_khi ;
/** Effective source at the previous step for wbeta of
* the vector Poisson equation for \c wbeta (needed for the
* solution of the vector Poisson equation for the shift
* \f$\beta^i\f$)
*/
Vector ssjm1_wbeta ;
// Derived data :
// ------------
protected:
/// Absolute coordinate X of the barycenter of the baryon density
mutable double* p_xa_barycenter ;
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the star will be defined
* @param nzet_i Number of domains occupied by the star
* @param eos_i Equation of state of the stellar matter
* @param irrot should be \c true for an irrotational star,
* \c false for a corotating one
*/
Star_bin_xcts(Map& mp_i, int nzet_i, const Eos& eos_i, bool irrot) ;
Star_bin_xcts(const Star_bin_xcts& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE* )).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve)
*/
Star_bin_xcts(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Star_bin_xcts() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
virtual void set_der_0x0() const ;
/** Sets to \c ETATNONDEF (undefined state) the hydrodynamical
* quantities relative to the Eulerian observer.
*/
virtual void del_hydro_euler() ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another \c Star_bin_xcts
void operator=(const Star_bin_xcts& ) ;
/// Read/write the centrifugal potential
Scalar& set_pot_centri() ;
/// Read/write the conformal factor \f$\Psi_{auto}\f$
Scalar& set_Psi_auto() ;
/// Read/write the conformal factor \f$\Psi_{comp}\f$
Scalar& set_Psi_comp() ;
/// Read/write the conformal factor \f$\chi_{auto}\f$
Scalar& set_chi_auto() ;
/// Read/write the conformal factor \f$\chi_{comp}\f$
Scalar& set_chi_comp() ;
/// Read/write of \f$\beta_{auto}\f$
Vector& set_beta_auto() ;
/// Read/write of \f$\beta\f$
Vector& set_beta() ;
// Accessors
// ---------
public:
/** Returns \c true for an irrotational motion, \c false for
* a corotating one.
*/
bool is_irrotational() const { return irrotational; } ;
/// Returns the non-translational part of the velocity potential
const Scalar& get_psi0() const {return psi0 ; } ;
/** Returns the covariant derivative of the velocity potential
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_d_psi() const {return d_psi ; } ;
/** Returns the spatial projection of the fluid 3-velocity with
* respect to the co-orbiting observer.
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_wit_w() const {return wit_w ; } ;
/** Returns the logarithm of the Lorentz factor between the fluid and
* the co-orbiting observer.
*/
const Scalar& get_loggam() const {return loggam ; } ;
/** Returns the shift vector, divided by \e N, of the rotating
* coordinates, \f$\beta^i/N\f$.
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_bsn() const {return bsn ; } ;
/// Returns the centrifugal potential
const Scalar& get_pot_centri() const {return pot_centri ; } ;
/** Returns the part of the shift vector \f$\beta^i\f$ generated
* principally by the star (\f$\beta^i_{auto}\f$).
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_beta_auto() const {return beta_auto ; } ;
/** Returns the part of the shift vector \f$\beta^i\f$ generated
* principally by the companion (\f$\beta^i_{comp}\f$).
* (Spherical components with respect to the mapping of the star)
*/
const Vector& get_beta_comp() const {return beta_comp ; } ;
/** Returns the scalar field \f$\Psi_{auto}\f$ generated principally
* by the star.
*/
const Scalar& get_Psi_auto() const {return Psi_auto ; } ;
/** Returns the scalar field \f$\Psi_{comp}\f$ generated principally
* by the companion star.
*/
const Scalar& get_Psi_comp() const {return Psi_comp ; } ;
/** Returns the scalar field \f$\chi_{auto} = (N\Psi)_{auto}\f$
* generated principally by the star.
*/
const Scalar& get_chi_auto() const {return chi_auto ; } ;
/** Returns the scalar field \f$\chi_{comp} = (N\Psi)_{comp}\f$
* generated principally by the companion star.
*/
const Scalar& get_chi_comp() const {return chi_comp ; } ;
/** Returns the covariant derivative of \f$\chi\f$.
*/
const Vector& get_dcov_chi() const {return dcov_chi ; } ;
/** Returns the covariant derivative of
* the conformal factor \f$\Psi\f$
*/
const Vector& get_dcov_Psi() const {return dcov_Psi ; } ;
/// Return the conformal factor \f$\Psi\f$
const Scalar& get_Psi() const {return Psi ; } ;
/// Return the function \f$\chi\f$
const Scalar& get_chi() const {return chi ; } ;
/// Return the conformal factor \f$\Psi^4\f$
const Scalar& get_psi4() const {return psi4 ; } ;
/** Return the flat metric defined on the mapping (Spherical
* components with respect to the mapping of the star)
*/
const Metric& get_flat() const {return flat ; } ;
/** Returns the part of the extrinsic curvature tensor
* \f$\hat{A}^{ij}\f$ generated by \c beta_auto.
* (Spherical components with respect to the mapping of the star)
*/
const Sym_tensor& get_haij_auto() const {return haij_auto ; } ;
/** Returns the part of the extrinsic curvature tensor
* \f$\hat{A}^{ij}\f$ generated by \c beta_comp.
* (Spherical components with respect to the mapping of the star)
*/
const Sym_tensor& get_haij_comp() const {return haij_comp ; } ;
/** Returns the part of
* \f$\hat{A}^{ij}\hat{A}_{ij}\f$ generated by \c beta_auto.
*/
const Scalar& get_hacar_auto() const {return hacar_auto ; } ;
/** Returns the part of
* \f$\hat{A}^{ij}\hat{A}_{ij}\f$ generated by \c beta_comp.
*/
const Scalar& get_hacar_comp() const {return hacar_comp ; } ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
protected:
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Baryon mass
virtual double mass_b() const ;
/// Gravitational mass
virtual double mass_g() const ;
/// Absolute coordinate X of the barycenter of the baryon density,
virtual double xa_barycenter() const ;
// Computational routines
// ----------------------
public:
/** Computes the hydrodynamical quantities relative to the Eulerian
* observer from those in the fluid frame, as well as
* \c wit_w and \c loggam.
*
* The calculation is performed starting from the quantities
* \c ent, \c ener, \c press and \c bsn,
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c gam_euler, \c u_euler, \c ener_euler,
* \c s_euler, \c stress_euler,
* \c wit_w and \c loggam.
*
*/
virtual void hydro_euler() ;
/** Computes metric coefficients from known potentials,
* when the companion is another star.
*
* The calculation is performed starting from the quantities
* \c Psi_auto, \c chi_auto, \c beta_auto,
* \c comp.Psi_auto, \c comp.chi_auto,
* \c comp.beta_auto
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c Psi_comp, \c chi_comp, \c beta_comp,
* \c nn, \c psi4, \c beta.
*
* @param comp companion star.
* @param omega angular velocity with respect to an asymptotically
* inertial observer
*/
void update_metric(const Star_bin_xcts& comp) ;
/** Same as \c update_metric(const Star_bin_xcts\& ) but with
* relaxation.
*
* @param comp companion star.
* @param star_prev previous value of the star.
* @param relax relaxation parameter.
* @param omega angular velocity with respect to an asymptotically
* inertial observer
*/
void update_metric(const Star_bin_xcts& comp,
const Star_bin_xcts& star_prev,
double relax) ;
/** Computes the derivative of metric functions related to the
* companion star
*/
void update_metric_der_comp(const Star_bin_xcts& comp) ;
/** Computes the quantities \c bsn and \c pot_centri.
*
* The calculation is performed starting from the quantities
* \c nn, \c beta, \c Psi,
* which are supposed to be up to date.
*
* @param omega angular velocity with respect to an asymptotically
* inertial observer
* @param x_axe absolute X coordinate of the rotation axis
*/
void kinematics(double omega, double x_axe) ;
/** Computes the gradient of the total velocity potential \f$\psi\f$.
*
*/
void fait_d_psi() ;
/** Computes \c haij_auto and \c hacar_auto from
* \c beta_auto, \c nn and \c Psi .
*/
void extrinsic_curvature() ;
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy
* @param mermax [input] Maximum number of steps
* @param mermax_poisson [input] Maximum number of steps in
* poisson scalar
* @param relax_poisson [input] Relaxation factor in poisson scalar
* @param mermax_potvit [input] Maximum number of steps in
* Map_radial::poisson_compact
* @param relax_potvit [input] Relaxation factor in
* Map_radial::poisson_compact
* @param thres_adapt [input] Threshold on dH/dr for the adaptation
* of the mapping
* @param fact [input] 1-D \c Tbl for the input of some factors:
* \li \c fact(0) : A resizing factor for the first shell
* @param ent_limit [input] array of enthalpy values to be set at
* the boundaries between the domains; if set to 0x0 (default),
* the initial values will be kept.
* @param diff [output] 1-D \c Tbl for the storage of some
* error indicators
*/
void equilibrium(double ent_c, int mermax, int mermax_potvit,
int mermax_poisson, double relax_poisson,
double relax_potvit, double thres_adapt,
const Tbl& fact, const Tbl* pent_limit,
Tbl& diff) ;
/** Computes the non-translational part of the velocity scalar potential
* \f$\psi0\f$ by solving the continuity equation.
*
* @param mermax [input] Maximum number of steps in the iteration
* @param precis [input] Required precision: the iteration will
* be stopped when the relative difference
* on \f$\psi0\f$ between two successive steps
* is lower than \c precis.
* @param relax [input] Relaxation factor.
*
* @return Relative error of the resolution obtained by comparing
* the operator acting on the solution with the source.
*/
double velocity_potential(int mermax, double precis, double relax) ;
/** Performs a relaxation on \c ent, \c Psi_auto,
* \c chi_auto and \c beta_auto.
*
* @param star_prev [input] star at the previous step.
* @param relax_ent [input] Relaxation factor for \c ent
* @param relax_met [input] Relaxation factor for \c logn_auto,
* \c lnq_auto, \c beta_auto,
* only if \c (mer \% fmer_met == 0).
* @param mer [input] Step number
* @param fmer_met [input] Step interval between metric updates
*/
void relaxation(const Star_bin_xcts& star_prev, double relax_ent,
double relax_met, int mer, int fmer_met) ;
friend class Binary_xcts ;
};
}
#endif
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