LORENE
et_rot_mag_global.C
1/*
2 * Methods for computing global quantities within the class Etoile_rot
3 *
4 * (see file etoile.h for documentation)
5 */
6
7/*
8 * Copyright (c) 2000-2001 Eric Gourgoulhon
9 * Copyright (c) 2002 Emmanuel Marcq
10 * Copyright (c) 2002 Jerome Novak
11 *
12 * This file is part of LORENE.
13 *
14 * LORENE is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU General Public License as published by
16 * the Free Software Foundation; either version 2 of the License, or
17 * (at your option) any later version.
18 *
19 * LORENE is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU General Public License for more details.
23 *
24 * You should have received a copy of the GNU General Public License
25 * along with LORENE; if not, write to the Free Software
26 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
27 *
28 */
29
30
31char 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 $" ;
32
33/*
34 * $Id: et_rot_mag_global.C,v 1.23 2016/11/01 09:12:59 j_novak Exp $
35 * $Log: et_rot_mag_global.C,v $
36 * Revision 1.23 2016/11/01 09:12:59 j_novak
37 * Correction of a missing '-' in mom_quad_old().
38 *
39 * Revision 1.22 2015/06/12 12:38:25 j_novak
40 * Implementation of the corrected formula for the quadrupole momentum.
41 *
42 * Revision 1.21 2014/10/13 08:52:58 j_novak
43 * Lorene classes and functions now belong to the namespace Lorene.
44 *
45 * Revision 1.20 2014/05/13 10:06:13 j_novak
46 * 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.
47 *
48 * Revision 1.19 2012/08/12 17:48:35 p_cerda
49 * Magnetstar: New classes for magnetstar. Allowing for non-equatorial symmetry in Etoile et al. Adding B_phi in Et_rot_mag.
50 *
51 * Revision 1.18 2006/01/31 15:54:57 j_novak
52 * Corrected a missing '-' sign for the theta component of the magnetic field in
53 * Et_rot_mag::Magn(). This had no influence in the calculations, only in the
54 * display of B values.
55 *
56 * Revision 1.17 2004/03/25 10:29:06 j_novak
57 * All LORENE's units are now defined in the namespace Unites (in file unites.h).
58 *
59 * Revision 1.16 2003/10/27 10:52:19 e_gourgoulhon
60 * Suppressed the global #include "unites.h"
61 * and made it local to each function.
62 *
63 * Revision 1.15 2002/10/17 11:30:54 j_novak
64 * Corrected mistake in angu_mom()
65 *
66 * Revision 1.14 2002/06/03 13:00:45 e_marcq
67 *
68 * conduc parameter read in parmag.d
69 *
70 * Revision 1.12 2002/05/22 12:20:17 j_novak
71 * *** empty log message ***
72 *
73 * Revision 1.11 2002/05/20 15:44:55 e_marcq
74 *
75 * Dimension errors corrected, parmag.d input file created and read
76 *
77 * Revision 1.10 2002/05/20 10:31:59 j_novak
78 * *** empty log message ***
79 *
80 * Revision 1.9 2002/05/20 08:27:59 j_novak
81 * *** empty log message ***
82 *
83 * Revision 1.8 2002/05/17 15:08:01 e_marcq
84 *
85 * Rotation progressive plug-in, units corrected, Q and a_j new member data
86 *
87 * Revision 1.7 2002/05/16 13:27:11 j_novak
88 * *** empty log message ***
89 *
90 * Revision 1.6 2002/05/16 10:02:09 j_novak
91 * Errors in stress energy tensor corrected
92 *
93 * Revision 1.5 2002/05/15 09:53:59 j_novak
94 * First operational version
95 *
96 * Revision 1.4 2002/05/14 13:45:30 e_marcq
97 *
98 * Correction de la formule du rapport gyromagnetique
99 *
100 * Revision 1.1 2002/05/10 09:26:52 j_novak
101 * Added new class Et_rot_mag for magnetized rotating neutron stars (under development)
102 *
103 *
104 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_mag_global.C,v 1.23 2016/11/01 09:12:59 j_novak Exp $
105 *
106 */
107
108// Headers C
109#include <cstdlib>
110#include <cmath>
111
112// Headers Lorene
113#include "et_rot_mag.h"
114#include "unites.h"
115
116// Definition des fonctions membres differentes ou nouvelles
117
118namespace Lorene {
120 // Calcule les grandeurs du tenseur impulsion-energie EM a partir des champs
121
122 using namespace Unites_mag ;
123
124 Tenseur ATTENS(A_t) ;
125
126 Tenseur APTENS(A_phi) ;
127
129 APTENS.gradient_spher())() );
131 ATTENS.gradient_spher())() );
133 ATTENS.gradient_spher())() );
134
135 if (ApAp.get_etat() != ETATZERO) {
136 ApAp.set().div_rsint() ;
137 ApAp.set().div_rsint() ;
138 }
139 if (ApAt.get_etat() != ETATZERO)
140 ApAt.set().div_rsint() ;
141
142 E_em = 0.5*mu0 * ( 1/(a_car*nnn*nnn) * (AtAt + 2*tnphi*ApAt)
143 + ( (tnphi*tnphi/(a_car*nnn*nnn)) + 1/(a_car*b_car) )*ApAp );
144 Jp_em = -mu0 * (ApAt + tnphi*ApAp) /(a_car*nnn) ;
145 if (Jp_em.get_etat() != ETATZERO) Jp_em.set().mult_rsint() ;
146 Srr_em = 0 ;
147 // Stt_em = -Srr_em
148 Spp_em = E_em ;
149}
150
152
153 using namespace Unites_mag ;
154
155 Cmp E_r(mp); Cmp E_t(mp);
156 E_r = 1/(sqrt(a_car())*nnn())*(A_t.dsdr()+nphi()*A_phi.dsdr()) ;
157 E_t = 1/(sqrt(a_car())*nnn())*(A_t.srdsdt()+nphi()*A_phi.srdsdt()) ;
158 E_r.va.set_base((A_t.dsdr()).va.base) ;
159 E_t.va.set_base((A_t.srdsdt()).va.base) ;
160 Tenseur Elect(mp, 1, CON, mp.get_bvect_spher()) ;
161 Elect.set_etat_qcq() ;
162 Elect.set(0) = E_r ;
163 Elect.set(1) = E_t ;
164 Elect.set(2) = 0. ;
165
166 return Elect*mu0 ;
167
168}
169
171
172 using namespace Unites_mag ;
173
174 Cmp B_r(mp); Cmp B_t(mp);
175 B_r = 1/(sqrt(a_car())*bbb())*A_phi.srdsdt();
176 B_r.va.set_base((A_phi.srdsdt()).va.base) ;
177 B_r.div_rsint();
178 B_t = 1/(sqrt(a_car())*bbb())*A_phi.dsdr();
179 B_t.va.set_base((A_phi.dsdr()).va.base) ;
180 B_t.div_rsint();
181
182 Tenseur Bmag(mp, 1, CON, mp.get_bvect_spher()) ;
183 Bmag.set_etat_qcq() ;
184 Bmag.set(0) = B_r ;
185 Bmag.set(1) = -B_t ;
186 Bmag.set(2) = B_phi ;
187
188 return Bmag*mu0 ;
189
190}
191
192double Et_rot_mag::MagMom() const {
193
194 using namespace Unites_mag ;
195
196 int Z = mp.get_mg()->get_nzone();
197 double mm ;
198
199 if(A_phi.get_etat()==ETATZERO) {
200
201 mm = 0 ;
202 }else{
203
204 Valeur** asymp = A_phi.asymptot(1) ;
205 mm = 4*M_PI*(*asymp[1])(Z-1,0,mp.get_mg()->get_nt(Z-1)-1,0) ;
206
207 delete asymp[0] ;
208 delete asymp[1] ;
209
210 delete [] asymp ;
211 }
212
213 return mm*j_unit*pow(r_unit,4) ;
214
215}
216
217double Et_rot_mag::Q_comput() const {
218
219 using namespace Unites_mag ;
220
221 int Z = mp.get_mg()->get_nzone();
222
223 if(A_t.get_etat()==ETATZERO) {
224 return 0 ;
225 }else{
226 Valeur** asymp = A_t.asymptot(1) ;
227
228 double Q_c = -4*M_PI*(*asymp[1])(Z-1,0,0,0) ;
229 delete asymp[0] ;
230 delete asymp[1] ;
231
232 delete [] asymp ;
233
234 return Q_c *(j_unit/v_unit*pow(r_unit,3)) ;}
235 }
236
237
238double Et_rot_mag::Q_int() const {
239
240 using namespace Unites_mag ;
241
242 double Qi = 0. ;
243
244 if (relativistic) {
245
246 Cmp dens = a_car() * bbb() * nnn() * j_t ;
247
248 dens.std_base_scal() ;
249
250 Qi = dens.integrale() ;
251
252
253 }
254 else{ // Newtonian case
255 assert(nbar.get_etat() == ETATQCQ) ;
256
257 Qi = ( j_t.integrale() ) ;
258
259 }
260
261
262
263 return Qi * (j_unit/v_unit*pow(r_unit,3)) ;
264
265}
266
267
268double Et_rot_mag::GyroMag() const {
269
270 using namespace Unites_mag ;
271
272 return 2*MagMom()*mass_g()/(Q_comput()*angu_mom()*v_unit*r_unit);
273
274}
275 //----------------------------//
276 // Gravitational mass //
277 //----------------------------//
278
279double Et_rot_mag::mass_g() const {
280
281 if (p_mass_g == 0x0) { // a new computation is required
282
283 if (relativistic) {
284
285 Tenseur source = nnn * (ener_euler + E_em + s_euler + Spp_em) +
286 nphi * Jp_em + 2 * bbb * (ener_euler + press) * tnphi * uuu ;
287
288 source = a_car * bbb * source ;
289
290 source.set_std_base() ;
291
292 p_mass_g = new double( source().integrale() ) ;
293
294
295 }
296 else{ // Newtonian case
297 p_mass_g = new double( mass_b() ) ; // in the Newtonian case
298 // M_g = M_b
299 }
300 }
301
302 return *p_mass_g ;
303
304}
305
306 //----------------------------//
307 // Angular momentum //
308 //----------------------------//
309
310double Et_rot_mag::angu_mom() const {
311
312 if (p_angu_mom == 0x0) { // a new computation is required
313
314 Cmp dens = uuu() ;
315
316 dens.mult_r() ; // Multiplication by
317 dens.va = (dens.va).mult_st() ; // r sin(theta)
318
319 if (relativistic) {
320 dens = a_car() * (b_car() * (ener_euler() + press())
321 * dens + bbb() * Jp_em()) ;
322 }
323 else { // Newtonian case
324 dens = nbar() * dens ;
325 }
326
327 dens.std_base_scal() ;
328
329 p_angu_mom = new double( dens.integrale() ) ;
330
331 }
332
333 return *p_angu_mom ;
334
335}
336
337
338 //----------------------------//
339 // T/W //
340 //----------------------------//
341
342// Redefini en virtual dans le .h : A CHANGER
343
344double Et_rot_mag::tsw() const {
345
346 if (p_tsw == 0x0) { // a new computation is required
347
348 double tcin = 0.5 * omega * angu_mom() ;
349
350 if (relativistic) {
351
352 Cmp dens = a_car() * bbb() * gam_euler() * ener() ;
353 dens.std_base_scal() ;
354 double mass_p = dens.integrale() ;
355
356 p_tsw = new double( tcin / ( mass_p + tcin - mass_g() ) ) ;
357
358 }
359 else { // Newtonian case
360 Cmp dens = 0.5 * nbar() * logn() ;
361 dens.std_base_scal() ;
362 double wgrav = dens.integrale() ;
363 p_tsw = new double( tcin / fabs(wgrav) ) ;
364 }
365
366
367 }
368
369 return *p_tsw ;
370
371}
372
373
374 //----------------------------//
375 // GRV2 //
376 //----------------------------//
377
378double Et_rot_mag::grv2() const {
379
380 if (p_grv2 == 0x0) { // a new computation is required
381
382 // To get qpig:
383 using namespace Unites ;
384
385 Tenseur sou_m = 2 * qpig * a_car * (press + (ener_euler+press)
386 * uuu*uuu ) ;
387
388 Tenseur sou_q = 2 * qpig * a_car * Spp_em + 1.5 * ak_car
390
391 p_grv2 = new double( double(1) - lambda_grv2(sou_m(), sou_q()) ) ;
392
393 }
394
395 return *p_grv2 ;
396
397}
398
399
400 //----------------------------//
401 // GRV3 //
402 //----------------------------//
403
404double Et_rot_mag::grv3(ostream* ost) const {
405
406 if (p_grv3 == 0x0) { // a new computation is required
407
408 // To get qpig:
409 using namespace Unites ;
410
411 Tenseur source(mp) ;
412
413 // Gravitational term [cf. Eq. (43) of Gourgoulhon & Bonazzola
414 // ------------------ Class. Quantum Grav. 11, 443 (1994)]
415
416 if (relativistic) {
417 Tenseur alpha = dzeta - logn ;
418 Tenseur beta = log( bbb ) ;
419 beta.set_std_base() ;
420
421 source = 0.75 * ak_car
424 + 0.5 * flat_scalar_prod(alpha.gradient_spher(),
425 beta.gradient_spher() ) ;
426
427 Cmp aa = alpha() - 0.5 * beta() ;
428 Cmp daadt = aa.srdsdt() ; // 1/r d/dth
429
430 // What follows is valid only for a mapping of class Map_radial :
431 const Map_radial* mpr = dynamic_cast<const Map_radial*>(&mp) ;
432 if (mpr == 0x0) {
433 cout << "Etoile_rot::grv3: the mapping does not belong"
434 << " to the class Map_radial !" << endl ;
435 abort() ;
436 }
437
438 // Computation of 1/tan(theta) * 1/r daa/dtheta
439 if (daadt.get_etat() == ETATQCQ) {
440 Valeur& vdaadt = daadt.va ;
441 vdaadt = vdaadt.ssint() ; // division by sin(theta)
442 vdaadt = vdaadt.mult_ct() ; // multiplication by cos(theta)
443 }
444
445 Cmp temp = aa.dsdr() + daadt ;
446 temp = ( bbb() - a_car()/bbb() ) * temp ;
447 temp.std_base_scal() ;
448
449 // Division by r
450 Valeur& vtemp = temp.va ;
451 vtemp = vtemp.sx() ; // division by xi in the nucleus
452 // Id in the shells
453 // division by xi-1 in the ZEC
454 vtemp = (mpr->xsr) * vtemp ; // multiplication by xi/r in the nucleus
455 // by 1/r in the shells
456 // by r(xi-1) in the ZEC
457
458 // In the ZEC, a multiplication by r has been performed instead
459 // of the division:
460 temp.set_dzpuis( temp.get_dzpuis() + 2 ) ;
461
462 source = bbb() * source() + 0.5 * temp ;
463
464 }
465 else{
466 source = - 0.5 * flat_scalar_prod(logn.gradient_spher(),
467 logn.gradient_spher() ) ;
468 }
469
470 source.set_std_base() ;
471
472 double int_grav = source().integrale() ;
473
474 // Matter term
475 // -----------
476
477 if (relativistic) {
478 source = qpig * a_car * bbb * ( s_euler + Spp_em ) ;
479 }
480 else{
481 source = qpig * ( 3 * press + nbar * uuu * uuu ) ;
482 }
483
484 source.set_std_base() ;
485
486 double int_mat = source().integrale() ;
487
488 // Virial error
489 // ------------
490 if (ost != 0x0) {
491 *ost << "Etoile_rot::grv3 : gravitational term : " << int_grav
492 << endl ;
493 *ost << "Etoile_rot::grv3 : matter term : " << int_mat
494 << endl ;
495 }
496
497 p_grv3 = new double( (int_grav + int_mat) / int_mat ) ;
498
499 }
500
501 return *p_grv3 ;
502
503}
504
505 //----------------------------//
506 // Quadrupole moment //
507 //----------------------------//
508
510
511 if (p_mom_quad_old == 0x0) { // a new computation is required
512
513 // To get qpig:
514 using namespace Unites ;
515
516 // Source for of the Poisson equation for nu
517 // -----------------------------------------
518
519 Tenseur source(mp) ;
520
521 if (relativistic) {
522 Tenseur beta = log(bbb) ;
523 beta.set_std_base() ;
524 source = qpig * a_car *( ener_euler + s_euler + Spp_em )
526 logn.gradient_spher() + beta.gradient_spher()) ;
527 }
528 else {
529 source = qpig * nbar ;
530 }
531 source.set_std_base() ;
532
533 // Multiplication by -r^2 P_2(cos(theta))
534 // [cf Eq.(7) of Salgado et al. Astron. Astrophys. 291, 155 (1994) ]
535 // ------------------------------------------------------------------
536
537 // Multiplication by r^2 :
538 // ----------------------
539 Cmp& csource = source.set() ;
540 csource.mult_r() ;
541 csource.mult_r() ;
542 if (csource.check_dzpuis(2)) {
543 csource.inc2_dzpuis() ;
544 }
545
546 // Muliplication by cos^2(theta) :
547 // -----------------------------
548 Cmp temp = csource ;
549
550 // What follows is valid only for a mapping of class Map_radial :
551 assert( dynamic_cast<const Map_radial*>(&mp) != 0x0 ) ;
552
553 if (temp.get_etat() == ETATQCQ) {
554 Valeur& vtemp = temp.va ;
555 vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
556 vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
557 }
558
559 // Muliplication by -P_2(cos(theta)) :
560 // ----------------------------------
561 source = 0.5 * source() - 1.5 * temp ;
562
563 // Final result
564 // ------------
565
566 p_mom_quad_old = new double( - source().integrale() / qpig ) ;
567
568 }
569
570 return *p_mom_quad_old ;
571
572 }
573
574}
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
void mult_rsint()
Multiplication by .
int get_etat() const
Returns the logical state.
Definition cmp.h:899
Valeur va
The numerical value of the Cmp
Definition cmp.h:464
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition cmp.C:644
int get_dzpuis() const
Returns dzpuis.
Definition cmp.h:903
void mult_r()
Multiplication by r everywhere.
Definition cmp_r_manip.C:91
void inc2_dzpuis()
Increases by 2 the value of dzpuis and changes accordingly the values of the Cmp in the external comp...
void set_dzpuis(int)
Set a value to dzpuis.
Definition cmp.C:654
double integrale() const
Computes the integral over all space of *this .
Definition cmp_integ.C:55
const Cmp & srdsdt() const
Returns of *this .
Definition cmp_deriv.C:105
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
Valeur ** asymptot(int n, const int flag=0) const
Asymptotic expansion at r = infinity.
const Cmp & dsdr() const
Returns of *this .
Definition cmp_deriv.C:84
virtual double mom_quad_old() const
Part of the quadrupole moment.
double Q_int() const
Computed charge from the integration of charge density over the star (i.e.
Tenseur Srr_em
rr component of the electromagnetic stress 3-tensor, as measured in the Eulerian frame....
Definition et_rot_mag.h:170
double Q_comput() const
Computed charge deduced from the asymptotic behaviour of At [SI units].
virtual void MHD_comput()
Computes the electromagnetic part of the stress-energy tensor.
Cmp A_phi
-component of the electromagnetic potential 1-form divided by .
Definition et_rot_mag.h:155
Tenseur Spp_em
component of the electromagnetic stress 3-tensor, as measured in the Eulerian frame.
Definition et_rot_mag.h:173
double MagMom() const
Magnetic Momentum in SI units.
virtual double grv3(ostream *ost=0x0) const
Error on the virial identity GRV3.
virtual double tsw() const
Ratio T/W.
Cmp A_t
t-component of the elecctromagnetic potential 1-form, divided by .
Definition et_rot_mag.h:150
double GyroMag() const
Gyromagnetic ratio .
virtual double mass_g() const
Gravitational mass.
Cmp j_t
t-component of the current 4-vector
Definition et_rot_mag.h:158
virtual double grv2() const
Error on the virial identity GRV2.
Tenseur E_em
electromagnetic energy density in the Eulerian frame
Definition et_rot_mag.h:161
Tenseur Jp_em
component of the electromagnetic momentum density 3-vector, as measured in the Eulerian frame.
Definition et_rot_mag.h:167
Tenseur Elec() const
Computes the electric field spherical components in Lorene's units.
Cmp B_phi
-component of the magnetic field
Definition et_rot_mag.h:157
Tenseur Magn() const
Computes the magnetic field spherical components in Lorene's units.
virtual double angu_mom() const
Angular momentum.
Tenseur uuu
Norm of u_euler.
Definition etoile.h:1518
double omega
Rotation angular velocity ([f_unit] )
Definition etoile.h:1501
Tenseur & logn
Metric potential = logn_auto.
Definition etoile.h:1521
double * p_mom_quad_old
Part of the quadrupole moment.
Definition etoile.h:1642
Tenseur nphi
Metric coefficient .
Definition etoile.h:1510
virtual double mass_b() const
Baryon mass.
static double lambda_grv2(const Cmp &sou_m, const Cmp &sou_q)
Computes the coefficient which ensures that the GRV2 virial identity is satisfied.
Tenseur bbb
Metric factor B.
Definition etoile.h:1504
Tenseur ak_car
Scalar .
Definition etoile.h:1586
Tenseur & dzeta
Metric potential = beta_auto.
Definition etoile.h:1534
double * p_grv3
Error on the virial identity GRV3.
Definition etoile.h:1634
double * p_grv2
Error on the virial identity GRV2.
Definition etoile.h:1633
double * p_angu_mom
Angular momentum.
Definition etoile.h:1631
double * p_tsw
Ratio T/W.
Definition etoile.h:1632
Tenseur b_car
Square of the metric factor B.
Definition etoile.h:1507
Tenseur tnphi
Component of the shift vector.
Definition etoile.h:1515
double * p_mass_g
Gravitational mass.
Definition etoile.h:548
Tenseur nnn
Total lapse function.
Definition etoile.h:509
Tenseur nbar
Baryon density in the fluid frame.
Definition etoile.h:459
Tenseur gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition etoile.h:471
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Tenseur ener
Total energy density in the fluid frame.
Definition etoile.h:460
Tenseur press
Fluid pressure.
Definition etoile.h:461
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition etoile.h:437
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition etoile.h:465
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition etoile.h:468
Tenseur a_car
Total conformal factor .
Definition etoile.h:515
Base class for pure radial mappings.
Definition map.h:1536
Coord xsr
in the nucleus; \ 1/R in the non-compactified shells; \ in the compactified outer domain.
Definition map.h:1549
const Base_vect_spher & get_bvect_spher() const
Returns the orthonormal vectorial basis associated with the coordinates of the mapping.
Definition map.h:783
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition map.h:765
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition tenseur.C:1170
const Tenseur & gradient_spher() const
Returns the gradient of *this (Spherical coordinates) (scalar field only).
Definition tenseur.C:1548
int get_etat() const
Returns the logical state.
Definition tenseur.h:707
Values and coefficients of a (real-value) function.
Definition valeur.h:287
const Valeur & mult_ct() const
Returns applied to *this.
const Valeur & sx() const
Returns (r -sampling = RARE ) \ Id (r sampling = FIN ) \ (r -sampling = UNSURR )
Definition valeur_sx.C:110
void set_base(const Base_val &)
Sets the bases for spectral expansions (member base )
Definition valeur.C:810
const Valeur & ssint() const
Returns of *this.
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
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...
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Lorene prototypes.
Definition app_hor.h:64
Standard electro-magnetic units.
Standard units of space, time and mass.