et_rot_mag_global.C
/*
* Methods for computing global quantities within the class Etoile_rot
*
* (see file etoile.h for documentation)
*/
/*
* Copyright (c) 2000-2001 Eric Gourgoulhon
* Copyright (c) 2002 Emmanuel Marcq
* Copyright (c) 2002 Jerome Novak
*
* 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
*
*/
char et_rot_mag_global_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_mag_global.C,v 1.23 2016/11/01 09:12:59 j_novak Exp $" ;
/*
* $Id: et_rot_mag_global.C,v 1.23 2016/11/01 09:12:59 j_novak Exp $
* $Log: et_rot_mag_global.C,v $
* Revision 1.23 2016/11/01 09:12:59 j_novak
* Correction of a missing '-' in mom_quad_old().
*
* Revision 1.22 2015/06/12 12:38:25 j_novak
* Implementation of the corrected formula for the quadrupole momentum.
*
* Revision 1.21 2014/10/13 08:52:58 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.20 2014/05/13 10:06:13 j_novak
* Change of magnetic units, to make the Lorene unit system coherent. Magnetic field is now expressed in Lorene units. Improvement on the comments on units.
*
* Revision 1.19 2012/08/12 17:48:35 p_cerda
* Magnetstar: New classes for magnetstar. Allowing for non-equatorial symmetry in Etoile et al. Adding B_phi in Et_rot_mag.
*
* Revision 1.18 2006/01/31 15:54:57 j_novak
* Corrected a missing '-' sign for the theta component of the magnetic field in
* Et_rot_mag::Magn(). This had no influence in the calculations, only in the
* display of B values.
*
* Revision 1.17 2004/03/25 10:29:06 j_novak
* All LORENE's units are now defined in the namespace Unites (in file unites.h).
*
* Revision 1.16 2003/10/27 10:52:19 e_gourgoulhon
* Suppressed the global #include "unites.h"
* and made it local to each function.
*
* Revision 1.15 2002/10/17 11:30:54 j_novak
* Corrected mistake in angu_mom()
*
* Revision 1.14 2002/06/03 13:00:45 e_marcq
*
* conduc parameter read in parmag.d
*
* Revision 1.12 2002/05/22 12:20:17 j_novak
* *** empty log message ***
*
* Revision 1.11 2002/05/20 15:44:55 e_marcq
*
* Dimension errors corrected, parmag.d input file created and read
*
* Revision 1.10 2002/05/20 10:31:59 j_novak
* *** empty log message ***
*
* Revision 1.9 2002/05/20 08:27:59 j_novak
* *** empty log message ***
*
* Revision 1.8 2002/05/17 15:08:01 e_marcq
*
* Rotation progressive plug-in, units corrected, Q and a_j new member data
*
* Revision 1.7 2002/05/16 13:27:11 j_novak
* *** empty log message ***
*
* Revision 1.6 2002/05/16 10:02:09 j_novak
* Errors in stress energy tensor corrected
*
* Revision 1.5 2002/05/15 09:53:59 j_novak
* First operational version
*
* Revision 1.4 2002/05/14 13:45:30 e_marcq
*
* Correction de la formule du rapport gyromagnetique
*
* Revision 1.1 2002/05/10 09:26:52 j_novak
* Added new class Et_rot_mag for magnetized rotating neutron stars (under development)
*
*
* $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_mag_global.C,v 1.23 2016/11/01 09:12:59 j_novak Exp $
*
*/
// Headers C
#include <cstdlib>
#include <cmath>
// Headers Lorene
#include "et_rot_mag.h"
#include "unites.h"
// Definition des fonctions membres differentes ou nouvelles
namespace Lorene {
void Et_rot_mag::MHD_comput() {
// Calcule les grandeurs du tenseur impulsion-energie EM a partir des champs
using namespace Unites_mag ;
Tenseur ATTENS(A_t) ;
Tenseur APTENS(A_phi) ;
Tenseur ApAp ( flat_scalar_prod_desal(APTENS.gradient_spher(),
APTENS.gradient_spher())() );
Tenseur ApAt ( flat_scalar_prod_desal(APTENS.gradient_spher(),
ATTENS.gradient_spher())() );
Tenseur AtAt ( flat_scalar_prod_desal(ATTENS.gradient_spher(),
ATTENS.gradient_spher())() );
if (ApAp.get_etat() != ETATZERO) {
ApAp.set().div_rsint() ;
ApAp.set().div_rsint() ;
}
if (ApAt.get_etat() != ETATZERO)
ApAt.set().div_rsint() ;
E_em = 0.5*mu0 * ( 1/(a_car*nnn*nnn) * (AtAt + 2*tnphi*ApAt)
+ ( (tnphi*tnphi/(a_car*nnn*nnn)) + 1/(a_car*b_car) )*ApAp );
Jp_em = -mu0 * (ApAt + tnphi*ApAp) /(a_car*nnn) ;
if (Jp_em.get_etat() != ETATZERO) Jp_em.set().mult_rsint() ;
Srr_em = 0 ;
// Stt_em = -Srr_em
Spp_em = E_em ;
}
Tenseur Et_rot_mag::Elec() const {
using namespace Unites_mag ;
Cmp E_r(mp); Cmp E_t(mp);
E_r = 1/(sqrt(a_car())*nnn())*(A_t.dsdr()+nphi()*A_phi.dsdr()) ;
E_t = 1/(sqrt(a_car())*nnn())*(A_t.srdsdt()+nphi()*A_phi.srdsdt()) ;
E_r.va.set_base((A_t.dsdr()).va.base) ;
E_t.va.set_base((A_t.srdsdt()).va.base) ;
Tenseur Elect(mp, 1, CON, mp.get_bvect_spher()) ;
Elect.set_etat_qcq() ;
Elect.set(0) = E_r ;
Elect.set(1) = E_t ;
Elect.set(2) = 0. ;
return Elect*mu0 ;
}
Tenseur Et_rot_mag::Magn() const {
using namespace Unites_mag ;
Cmp B_r(mp); Cmp B_t(mp);
B_r = 1/(sqrt(a_car())*bbb())*A_phi.srdsdt();
B_r.va.set_base((A_phi.srdsdt()).va.base) ;
B_r.div_rsint();
B_t = 1/(sqrt(a_car())*bbb())*A_phi.dsdr();
B_t.va.set_base((A_phi.dsdr()).va.base) ;
B_t.div_rsint();
Tenseur Bmag(mp, 1, CON, mp.get_bvect_spher()) ;
Bmag.set_etat_qcq() ;
Bmag.set(0) = B_r ;
Bmag.set(1) = -B_t ;
Bmag.set(2) = B_phi ;
return Bmag*mu0 ;
}
double Et_rot_mag::MagMom() const {
using namespace Unites_mag ;
int Z = mp.get_mg()->get_nzone();
double mm ;
if(A_phi.get_etat()==ETATZERO) {
mm = 0 ;
}else{
Valeur** asymp = A_phi.asymptot(1) ;
mm = 4*M_PI*(*asymp[1])(Z-1,0,mp.get_mg()->get_nt(Z-1)-1,0) ;
delete asymp[0] ;
delete asymp[1] ;
delete [] asymp ;
}
return mm*j_unit*pow(r_unit,4) ;
}
double Et_rot_mag::Q_comput() const {
using namespace Unites_mag ;
int Z = mp.get_mg()->get_nzone();
if(A_t.get_etat()==ETATZERO) {
return 0 ;
}else{
Valeur** asymp = A_t.asymptot(1) ;
double Q_c = -4*M_PI*(*asymp[1])(Z-1,0,0,0) ;
delete asymp[0] ;
delete asymp[1] ;
delete [] asymp ;
return Q_c *(j_unit/v_unit*pow(r_unit,3)) ;}
}
double Et_rot_mag::Q_int() const {
using namespace Unites_mag ;
double Qi = 0. ;
if (relativistic) {
Cmp dens = a_car() * bbb() * nnn() * j_t ;
dens.std_base_scal() ;
Qi = dens.integrale() ;
}
else{ // Newtonian case
assert(nbar.get_etat() == ETATQCQ) ;
Qi = ( j_t.integrale() ) ;
}
return Qi * (j_unit/v_unit*pow(r_unit,3)) ;
}
double Et_rot_mag::GyroMag() const {
using namespace Unites_mag ;
return 2*MagMom()*mass_g()/(Q_comput()*angu_mom()*v_unit*r_unit);
}
//----------------------------//
// Gravitational mass //
//----------------------------//
double Et_rot_mag::mass_g() const {
if (p_mass_g == 0x0) { // a new computation is required
if (relativistic) {
Tenseur source = nnn * (ener_euler + E_em + s_euler + Spp_em) +
nphi * Jp_em + 2 * bbb * (ener_euler + press) * tnphi * uuu ;
source = a_car * bbb * source ;
source.set_std_base() ;
p_mass_g = new double( source().integrale() ) ;
}
else{ // Newtonian case
p_mass_g = new double( mass_b() ) ; // in the Newtonian case
// M_g = M_b
}
}
return *p_mass_g ;
}
//----------------------------//
// Angular momentum //
//----------------------------//
double Et_rot_mag::angu_mom() const {
if (p_angu_mom == 0x0) { // a new computation is required
Cmp dens = uuu() ;
dens.mult_r() ; // Multiplication by
dens.va = (dens.va).mult_st() ; // r sin(theta)
if (relativistic) {
dens = a_car() * (b_car() * (ener_euler() + press())
* dens + bbb() * Jp_em()) ;
}
else { // Newtonian case
dens = nbar() * dens ;
}
dens.std_base_scal() ;
p_angu_mom = new double( dens.integrale() ) ;
}
return *p_angu_mom ;
}
//----------------------------//
// T/W //
//----------------------------//
// Redefini en virtual dans le .h : A CHANGER
double Et_rot_mag::tsw() const {
if (p_tsw == 0x0) { // a new computation is required
double tcin = 0.5 * omega * angu_mom() ;
if (relativistic) {
Cmp dens = a_car() * bbb() * gam_euler() * ener() ;
dens.std_base_scal() ;
double mass_p = dens.integrale() ;
p_tsw = new double( tcin / ( mass_p + tcin - mass_g() ) ) ;
}
else { // Newtonian case
Cmp dens = 0.5 * nbar() * logn() ;
dens.std_base_scal() ;
double wgrav = dens.integrale() ;
p_tsw = new double( tcin / fabs(wgrav) ) ;
}
}
return *p_tsw ;
}
//----------------------------//
// GRV2 //
//----------------------------//
double Et_rot_mag::grv2() const {
if (p_grv2 == 0x0) { // a new computation is required
// To get qpig:
using namespace Unites ;
Tenseur sou_m = 2 * qpig * a_car * (press + (ener_euler+press)
* uuu*uuu ) ;
Tenseur sou_q = 2 * qpig * a_car * Spp_em + 1.5 * ak_car
- flat_scalar_prod(logn.gradient_spher(), logn.gradient_spher() ) ;
p_grv2 = new double( double(1) - lambda_grv2(sou_m(), sou_q()) ) ;
}
return *p_grv2 ;
}
//----------------------------//
// GRV3 //
//----------------------------//
double Et_rot_mag::grv3(ostream* ost) const {
if (p_grv3 == 0x0) { // a new computation is required
// To get qpig:
using namespace Unites ;
Tenseur source(mp) ;
// Gravitational term [cf. Eq. (43) of Gourgoulhon & Bonazzola
// ------------------ Class. Quantum Grav. 11, 443 (1994)]
if (relativistic) {
Tenseur alpha = dzeta - logn ;
Tenseur beta = log( bbb ) ;
beta.set_std_base() ;
source = 0.75 * ak_car
- flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() )
+ 0.5 * flat_scalar_prod(alpha.gradient_spher(),
beta.gradient_spher() ) ;
Cmp aa = alpha() - 0.5 * beta() ;
Cmp daadt = aa.srdsdt() ; // 1/r d/dth
// What follows is valid only for a mapping of class Map_radial :
const Map_radial* mpr = dynamic_cast<const Map_radial*>(&mp) ;
if (mpr == 0x0) {
cout << "Etoile_rot::grv3: the mapping does not belong"
<< " to the class Map_radial !" << endl ;
abort() ;
}
// Computation of 1/tan(theta) * 1/r daa/dtheta
if (daadt.get_etat() == ETATQCQ) {
Valeur& vdaadt = daadt.va ;
vdaadt = vdaadt.ssint() ; // division by sin(theta)
vdaadt = vdaadt.mult_ct() ; // multiplication by cos(theta)
}
Cmp temp = aa.dsdr() + daadt ;
temp = ( bbb() - a_car()/bbb() ) * temp ;
temp.std_base_scal() ;
// Division by r
Valeur& vtemp = temp.va ;
vtemp = vtemp.sx() ; // division by xi in the nucleus
// Id in the shells
// division by xi-1 in the ZEC
vtemp = (mpr->xsr) * vtemp ; // multiplication by xi/r in the nucleus
// by 1/r in the shells
// by r(xi-1) in the ZEC
// In the ZEC, a multiplication by r has been performed instead
// of the division:
temp.set_dzpuis( temp.get_dzpuis() + 2 ) ;
source = bbb() * source() + 0.5 * temp ;
}
else{
source = - 0.5 * flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() ) ;
}
source.set_std_base() ;
double int_grav = source().integrale() ;
// Matter term
// -----------
if (relativistic) {
source = qpig * a_car * bbb * ( s_euler + Spp_em ) ;
}
else{
source = qpig * ( 3 * press + nbar * uuu * uuu ) ;
}
source.set_std_base() ;
double int_mat = source().integrale() ;
// Virial error
// ------------
if (ost != 0x0) {
*ost << "Etoile_rot::grv3 : gravitational term : " << int_grav
<< endl ;
*ost << "Etoile_rot::grv3 : matter term : " << int_mat
<< endl ;
}
p_grv3 = new double( (int_grav + int_mat) / int_mat ) ;
}
return *p_grv3 ;
}
//----------------------------//
// Quadrupole moment //
//----------------------------//
double Et_rot_mag::mom_quad_old() const {
if (p_mom_quad_old == 0x0) { // a new computation is required
// To get qpig:
using namespace Unites ;
// Source for of the Poisson equation for nu
// -----------------------------------------
Tenseur source(mp) ;
if (relativistic) {
Tenseur beta = log(bbb) ;
beta.set_std_base() ;
source = qpig * a_car *( ener_euler + s_euler + Spp_em )
+ ak_car - flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() + beta.gradient_spher()) ;
}
else {
source = qpig * nbar ;
}
source.set_std_base() ;
// Multiplication by -r^2 P_2(cos(theta))
// [cf Eq.(7) of Salgado et al. Astron. Astrophys. 291, 155 (1994) ]
// ------------------------------------------------------------------
// Multiplication by r^2 :
// ----------------------
Cmp& csource = source.set() ;
csource.mult_r() ;
csource.mult_r() ;
if (csource.check_dzpuis(2)) {
csource.inc2_dzpuis() ;
}
// Muliplication by cos^2(theta) :
// -----------------------------
Cmp temp = csource ;
// What follows is valid only for a mapping of class Map_radial :
assert( dynamic_cast<const Map_radial*>(&mp) != 0x0 ) ;
if (temp.get_etat() == ETATQCQ) {
Valeur& vtemp = temp.va ;
vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
}
// Muliplication by -P_2(cos(theta)) :
// ----------------------------------
source = 0.5 * source() - 1.5 * temp ;
// Final result
// ------------
p_mom_quad_old = new double( - source().integrale() / qpig ) ;
}
return *p_mom_quad_old ;
}
}
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
Lorene::Cmp::get_etat
int get_etat() const
Returns the logical state.
Definition cmp.h:899
Lorene::Cmp::va
Valeur va
The numerical value of the Cmp.
Definition cmp.h:464
Lorene::Cmp::std_base_scal
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition cmp.C:644
Lorene::Cmp::get_dzpuis
int get_dzpuis() const
Returns dzpuis.
Definition cmp.h:903
Lorene::Cmp::mult_r
void mult_r()
Multiplication by r everywhere.
Definition cmp_r_manip.C:91
Lorene::Cmp::inc2_dzpuis
void inc2_dzpuis()
Increases by 2 the value of dzpuis and changes accordingly the values of the Cmp in the external comp...
Definition cmp_r_manip.C:192
Lorene::Cmp::set_dzpuis
void set_dzpuis(int)
Set a value to dzpuis.
Definition cmp.C:654
Lorene::Cmp::integrale
double integrale() const
Computes the integral over all space of *this .
Definition cmp_integ.C:55
Lorene::Cmp::srdsdt
const Cmp & srdsdt() const
Returns of *this .
Definition cmp_deriv.C:105
Lorene::Cmp::check_dzpuis
bool check_dzpuis(int dzi) const
Returns false if the last domain is compactified and *this is not zero in this domain and dzpuis is n...
Definition cmp.C:715
Lorene::Cmp::div_rsint
void div_rsint()
Division by .
Definition cmp_r_manip.C:141
Lorene::Cmp::dsdr
const Cmp & dsdr() const
Returns of *this .
Definition cmp_deriv.C:84
Lorene::Et_rot_mag::mom_quad_old
virtual double mom_quad_old() const
Part of the quadrupole moment.
Definition et_rot_mag_global.C:509
Lorene::Et_rot_mag::Q_int
double Q_int() const
Computed charge from the integration of charge density over the star (i.e.
Definition et_rot_mag_global.C:238
Lorene::Et_rot_mag::Srr_em
Tenseur Srr_em
rr component of the electromagnetic stress 3-tensor, as measured in the Eulerian frame....
Definition et_rot_mag.h:170
Lorene::Et_rot_mag::Q_comput
double Q_comput() const
Computed charge deduced from the asymptotic behaviour of At [SI units].
Definition et_rot_mag_global.C:217
Lorene::Et_rot_mag::MHD_comput
virtual void MHD_comput()
Computes the electromagnetic part of the stress-energy tensor.
Definition et_rot_mag_global.C:119
Lorene::Et_rot_mag::A_phi
Cmp A_phi
-component of the electromagnetic potential 1-form divided by .
Definition et_rot_mag.h:155
Lorene::Et_rot_mag::Spp_em
Tenseur Spp_em
component of the electromagnetic stress 3-tensor, as measured in the Eulerian frame.
Definition et_rot_mag.h:173
Lorene::Et_rot_mag::MagMom
double MagMom() const
Magnetic Momentum in SI units.
Definition et_rot_mag_global.C:192
Lorene::Et_rot_mag::grv3
virtual double grv3(ostream *ost=0x0) const
Error on the virial identity GRV3.
Definition et_rot_mag_global.C:404
Lorene::Et_rot_mag::tsw
virtual double tsw() const
Ratio T/W.
Definition et_rot_mag_global.C:344
Lorene::Et_rot_mag::A_t
Cmp A_t
t-component of the elecctromagnetic potential 1-form, divided by .
Definition et_rot_mag.h:150
Lorene::Et_rot_mag::GyroMag
double GyroMag() const
Gyromagnetic ratio .
Definition et_rot_mag_global.C:268
Lorene::Et_rot_mag::mass_g
virtual double mass_g() const
Gravitational mass.
Definition et_rot_mag_global.C:279
Lorene::Et_rot_mag::j_t
Cmp j_t
t-component of the current 4-vector
Definition et_rot_mag.h:158
Lorene::Et_rot_mag::grv2
virtual double grv2() const
Error on the virial identity GRV2.
Definition et_rot_mag_global.C:378
Lorene::Et_rot_mag::E_em
Tenseur E_em
electromagnetic energy density in the Eulerian frame
Definition et_rot_mag.h:161
Lorene::Et_rot_mag::Jp_em
Tenseur Jp_em
component of the electromagnetic momentum density 3-vector, as measured in the Eulerian frame.
Definition et_rot_mag.h:167
Lorene::Et_rot_mag::Elec
Tenseur Elec() const
Computes the electric field spherical components in Lorene's units.
Definition et_rot_mag_global.C:151
Lorene::Et_rot_mag::B_phi
Cmp B_phi
-component of the magnetic field
Definition et_rot_mag.h:157
Lorene::Et_rot_mag::Magn
Tenseur Magn() const
Computes the magnetic field spherical components in Lorene's units.
Definition et_rot_mag_global.C:170
Lorene::Et_rot_mag::angu_mom
virtual double angu_mom() const
Angular momentum.
Definition et_rot_mag_global.C:310
Lorene::Etoile_rot::uuu
Tenseur uuu
Norm of u_euler.
Definition etoile.h:1518
Lorene::Etoile_rot::omega
double omega
Rotation angular velocity ([f_unit] ).
Definition etoile.h:1501
Lorene::Etoile_rot::logn
Tenseur & logn
Metric potential = logn_auto.
Definition etoile.h:1521
Lorene::Etoile_rot::p_mom_quad_old
double * p_mom_quad_old
Part of the quadrupole moment.
Definition etoile.h:1642
Lorene::Etoile_rot::nphi
Tenseur nphi
Metric coefficient .
Definition etoile.h:1510
Lorene::Etoile_rot::mass_b
virtual double mass_b() const
Baryon mass.
Definition et_rot_global.C:125
Lorene::Etoile_rot::lambda_grv2
static double lambda_grv2(const Cmp &sou_m, const Cmp &sou_q)
Computes the coefficient which ensures that the GRV2 virial identity is satisfied.
Definition et_rot_lambda_grv2.C:79
Lorene::Etoile_rot::bbb
Tenseur bbb
Metric factor B.
Definition etoile.h:1504
Lorene::Etoile_rot::ak_car
Tenseur ak_car
Scalar .
Definition etoile.h:1586
Lorene::Etoile_rot::dzeta
Tenseur & dzeta
Metric potential = beta_auto.
Definition etoile.h:1534
Lorene::Etoile_rot::p_grv3
double * p_grv3
Error on the virial identity GRV3.
Definition etoile.h:1634
Lorene::Etoile_rot::p_grv2
double * p_grv2
Error on the virial identity GRV2.
Definition etoile.h:1633
Lorene::Etoile_rot::p_angu_mom
double * p_angu_mom
Angular momentum.
Definition etoile.h:1631
Lorene::Etoile_rot::p_tsw
double * p_tsw
Ratio T/W.
Definition etoile.h:1632
Lorene::Etoile_rot::b_car
Tenseur b_car
Square of the metric factor B.
Definition etoile.h:1507
Lorene::Etoile_rot::tnphi
Tenseur tnphi
Component of the shift vector.
Definition etoile.h:1515
Lorene::Etoile::p_mass_g
double * p_mass_g
Gravitational mass.
Definition etoile.h:548
Lorene::Etoile::nnn
Tenseur nnn
Total lapse function.
Definition etoile.h:509
Lorene::Etoile::nbar
Tenseur nbar
Baryon density in the fluid frame.
Definition etoile.h:459
Lorene::Etoile::gam_euler
Tenseur gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition etoile.h:471
Lorene::Etoile::mp
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Lorene::Etoile::ener
Tenseur ener
Total energy density in the fluid frame.
Definition etoile.h:460
Lorene::Etoile::press
Tenseur press
Fluid pressure.
Definition etoile.h:461
Lorene::Etoile::relativistic
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition etoile.h:437
Lorene::Etoile::ener_euler
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition etoile.h:465
Lorene::Etoile::s_euler
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition etoile.h:468
Lorene::Etoile::a_car
Tenseur a_car
Total conformal factor .
Definition etoile.h:515
Lorene::Map_radial
Base class for pure radial mappings.
Definition map.h:1536
Lorene::Map_radial::xsr
Coord xsr
in the nucleus; \ 1/R in the non-compactified shells; \ in the compactified outer domain.
Definition map.h:1549
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
Lorene::Tenseur::set_std_base
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition tenseur.C:1170
Lorene::Tenseur::gradient_spher
const Tenseur & gradient_spher() const
Returns the gradient of *this (Spherical coordinates) (scalar field only).
Definition tenseur.C:1548
Lorene::Tenseur::get_etat
int get_etat() const
Returns the logical state.
Definition tenseur.h:707
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition valeur.h:287
Lorene::Valeur::mult_ct
const Valeur & mult_ct() const
Returns applied to *this.
Definition valeur_mult_ct.C:98
Lorene::Valeur::sx
const Valeur & sx() const
Returns (r -sampling = RARE ) \ Id (r sampling = FIN ) \ (r -sampling = UNSURR ).
Definition valeur_sx.C:110
Lorene::Valeur::set_base
void set_base(const Base_val &)
Sets the bases for spectral expansions (member base ).
Definition valeur.C:810
Lorene::Valeur::ssint
const Valeur & ssint() const
Returns of *this.
Definition valeur_ssint.C:112
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Lorene::flat_scalar_prod
Tenseur flat_scalar_prod(const Tenseur &t1, const Tenseur &t2)
Scalar product of two Tenseur when the metric is : performs the contraction of the last index of t1 w...
Definition tenseur_operateur.C:653
Lorene::flat_scalar_prod_desal
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Definition tenseur_operateur.C:735
Lorene
Lorene prototypes.
Definition app_hor.h:64
Lorene::integrale
virtual Tbl * integrale(const Cmp &) const =0
Computes the integral over all space of a Cmp .
Unites_mag
Standard electro-magnetic units.
Unites
Standard units of space, time and mass.