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root/group/trunk/OOPSE/libmdtools/NPTf.cpp
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Comparing trunk/OOPSE/libmdtools/NPTf.cpp (file contents):
Revision 767 by tim, Tue Sep 16 20:02:11 2003 UTC vs.
Revision 1097 by gezelter, Mon Apr 12 20:32:20 2004 UTC

# Line 1 | Line 1
1 < #include <cmath>
1 > #include <math.h>
2 >
3 > #include "MatVec3.h"
4   #include "Atom.hpp"
5   #include "SRI.hpp"
6   #include "AbstractClasses.hpp"
# Line 7 | Line 9
9   #include "Thermo.hpp"
10   #include "ReadWrite.hpp"
11   #include "Integrator.hpp"
12 < #include "simError.h"
12 > #include "simError.h"
13  
14 + #ifdef IS_MPI
15 + #include "mpiSimulation.hpp"
16 + #endif
17  
18   // Basic non-isotropic thermostating and barostating via the Melchionna
19   // modification of the Hoover algorithm:
20   //
21   //    Melchionna, S., Ciccotti, G., and Holian, B. L., 1993,
22 < //       Molec. Phys., 78, 533.
22 > //       Molec. Phys., 78, 533.
23   //
24   //           and
25 < //
25 > //
26   //    Hoover, W. G., 1986, Phys. Rev. A, 34, 2499.
27  
28   template<typename T> NPTf<T>::NPTf ( SimInfo *theInfo, ForceFields* the_ff):
29    T( theInfo, the_ff )
30   {
31 <  int i, j;
32 <  chi = 0.0;
33 <  integralOfChidt = 0.0;
31 >  GenericData* data;
32 >  DoubleArrayData * etaValue;
33 >  vector<double> etaArray;
34 >  int i,j;
35  
36 <  for(i = 0; i < 3; i++)
37 <    for (j = 0; j < 3; j++)
36 >  for(i = 0; i < 3; i++){
37 >    for (j = 0; j < 3; j++){
38 >
39        eta[i][j] = 0.0;
40 +      oldEta[i][j] = 0.0;
41 +    }
42 +  }
43  
34  have_tau_thermostat = 0;
35  have_tau_barostat = 0;
36  have_target_temp = 0;
37  have_target_pressure = 0;
44  
45 <  have_chi_tolerance = 0;
46 <  have_eta_tolerance = 0;
47 <  have_pos_iter_tolerance = 0;
45 >  if( theInfo->useInitXSstate ){
46 >    // retrieve eta array from simInfo if it exists
47 >    data = info->getProperty(ETAVALUE_ID);
48 >    if(data){
49 >      etaValue = dynamic_cast<DoubleArrayData*>(data);
50 >      
51 >      if(etaValue){
52 >        etaArray = etaValue->getData();
53 >        
54 >        for(i = 0; i < 3; i++){
55 >          for (j = 0; j < 3; j++){
56 >            eta[i][j] = etaArray[3*i+j];
57 >            oldEta[i][j] = eta[i][j];
58 >          }
59 >        }
60 >      }
61 >    }
62 >  }
63  
43  oldPos = new double[3*nAtoms];
44  oldVel = new double[3*nAtoms];
45  oldJi = new double[3*nAtoms];
46 #ifdef IS_MPI
47  Nparticles = mpiSim->getTotAtoms();
48 #else
49  Nparticles = theInfo->n_atoms;
50 #endif
64   }
65  
66   template<typename T> NPTf<T>::~NPTf() {
67 <  delete[] oldPos;
68 <  delete[] oldVel;
56 <  delete[] oldJi;
67 >
68 >  // empty for now
69   }
70  
71 < template<typename T> void NPTf<T>::moveA() {
60 <  
61 <  int i, j, k;
62 <  DirectionalAtom* dAtom;
63 <  double Tb[3], ji[3];
64 <  double A[3][3], I[3][3];
65 <  double angle, mass;
66 <  double vel[3], pos[3], frc[3];
71 > template<typename T> void NPTf<T>::resetIntegrator() {
72  
73 <  double rj[3];
69 <  double instaTemp, instaPress, instaVol;
70 <  double tt2, tb2;
71 <  double sc[3];
72 <  double eta2ij;
73 <  double press[3][3], vScale[3][3], hm[3][3], hmnew[3][3], scaleMat[3][3];
74 <  double bigScale, smallScale, offDiagMax;
75 <  double COM[3];
73 >  int i, j;
74  
75 <  tt2 = tauThermostat * tauThermostat;
76 <  tb2 = tauBarostat * tauBarostat;
75 >  for(i = 0; i < 3; i++)
76 >    for (j = 0; j < 3; j++)
77 >      eta[i][j] = 0.0;
78  
79 <  instaTemp = tStats->getTemperature();
80 <  tStats->getPressureTensor(press);
82 <  instaVol = tStats->getVolume();
83 <  
84 <  tStats->getCOM(COM);
79 >  T::resetIntegrator();
80 > }
81  
82 <  //calculate scale factor of veloity
87 <  for (i = 0; i < 3; i++ ) {
88 <    for (j = 0; j < 3; j++ ) {
89 <      vScale[i][j] = eta[i][j];
90 <      
91 <      if (i == j) {
92 <        vScale[i][j] += chi;          
93 <      }              
94 <    }
95 <  }
96 <  
97 <  //evolve velocity half step
98 <  for( i=0; i<nAtoms; i++ ){
82 > template<typename T> void NPTf<T>::evolveEtaA() {
83  
84 <    atoms[i]->getVel( vel );
101 <    atoms[i]->getFrc( frc );
84 >  int i, j;
85  
86 <    mass = atoms[i]->getMass();
87 <    
88 <    info->matVecMul3( vScale, vel, sc );
89 <
90 <    for (j=0; j < 3; j++) {
91 <      // velocity half step  (use chi from previous step here):
92 <      vel[j] += dt2 * ((frc[j]  / mass) * eConvert - sc[j]);
110 <  
86 >  for(i = 0; i < 3; i ++){
87 >    for(j = 0; j < 3; j++){
88 >      if( i == j)
89 >        eta[i][j] += dt2 *  instaVol *
90 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
91 >      else
92 >        eta[i][j] += dt2 * instaVol * press[i][j] / (NkBT*tb2);
93      }
94 +  }
95  
96 <    atoms[i]->setVel( vel );
97 <  
98 <    if( atoms[i]->isDirectional() ){
96 >  for(i = 0; i < 3; i++)
97 >    for (j = 0; j < 3; j++)
98 >      oldEta[i][j] = eta[i][j];
99 > }
100  
101 <      dAtom = (DirectionalAtom *)atoms[i];
101 > template<typename T> void NPTf<T>::evolveEtaB() {
102  
103 <      // get and convert the torque to body frame
120 <      
121 <      dAtom->getTrq( Tb );
122 <      dAtom->lab2Body( Tb );
123 <      
124 <      // get the angular momentum, and propagate a half step
103 >  int i,j;
104  
105 <      dAtom->getJ( ji );
106 <
107 <      for (j=0; j < 3; j++)
129 <        ji[j] += dt2 * (Tb[j] * eConvert - ji[j]*chi);
130 <      
131 <      // use the angular velocities to propagate the rotation matrix a
132 <      // full time step
133 <
134 <      dAtom->getA(A);
135 <      dAtom->getI(I);
136 <    
137 <      // rotate about the x-axis      
138 <      angle = dt2 * ji[0] / I[0][0];
139 <      this->rotate( 1, 2, angle, ji, A );
105 >  for(i = 0; i < 3; i++)
106 >    for (j = 0; j < 3; j++)
107 >      prevEta[i][j] = eta[i][j];
108  
109 <      // rotate about the y-axis
110 <      angle = dt2 * ji[1] / I[1][1];
111 <      this->rotate( 2, 0, angle, ji, A );
112 <      
113 <      // rotate about the z-axis
114 <      angle = dt * ji[2] / I[2][2];
115 <      this->rotate( 0, 1, angle, ji, A);
116 <      
117 <      // rotate about the y-axis
150 <      angle = dt2 * ji[1] / I[1][1];
151 <      this->rotate( 2, 0, angle, ji, A );
152 <      
153 <       // rotate about the x-axis
154 <      angle = dt2 * ji[0] / I[0][0];
155 <      this->rotate( 1, 2, angle, ji, A );
156 <      
157 <      dAtom->setJ( ji );
158 <      dAtom->setA( A  );    
159 <    }    
109 >  for(i = 0; i < 3; i ++){
110 >    for(j = 0; j < 3; j++){
111 >      if( i == j) {
112 >        eta[i][j] = oldEta[i][j] + dt2 *  instaVol *
113 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
114 >      } else {
115 >        eta[i][j] = oldEta[i][j] + dt2 * instaVol * press[i][j] / (NkBT*tb2);
116 >      }
117 >    }
118    }
119 + }
120  
121 <  // advance chi half step
122 <  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
121 > template<typename T> void NPTf<T>::calcVelScale(void){
122 >  int i,j;
123  
124 <  //calculate the integral of chidt
125 <  integralOfChidt += dt2*chi;
124 >  for (i = 0; i < 3; i++ ) {
125 >    for (j = 0; j < 3; j++ ) {
126 >      vScale[i][j] = eta[i][j];
127  
128 <  //advance eta half step
129 <  for(i = 0; i < 3; i ++)
130 <    for(j = 0; j < 3; j++){
171 <      if( i == j)
172 <        eta[i][j] += dt2 *  instaVol *
173 <          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
174 <      else
175 <        eta[i][j] += dt2 * instaVol * press[i][j] / ( NkBT*tb2);
128 >      if (i == j) {
129 >        vScale[i][j] += chi;
130 >      }
131      }
177    
178  //save the old positions
179  for(i = 0; i < nAtoms; i++){
180    atoms[i]->getPos(pos);
181    for(j = 0; j < 3; j++)
182      oldPos[i*3 + j] = pos[j];
132    }
133 <  
185 <  //the first estimation of r(t+dt) is equal to  r(t)
186 <    
187 <  for(k = 0; k < 4; k ++){
133 > }
134  
135 <    for(i =0 ; i < nAtoms; i++){
135 > template<typename T> void NPTf<T>::getVelScaleA(double sc[3], double vel[3]) {
136 >
137 >  matVecMul3( vScale, vel, sc );
138 > }
139  
140 <      atoms[i]->getVel(vel);
141 <      atoms[i]->getPos(pos);
140 > template<typename T> void NPTf<T>::getVelScaleB(double sc[3], int index ){
141 >  int j;
142 >  double myVel[3];
143 >  double vScale[3][3];
144  
145 <      for(j = 0; j < 3; j++)
146 <        rj[j] = (oldPos[i*3 + j] + pos[j])/2 - COM[j];
196 <      
197 <      info->matVecMul3( eta, rj, sc );
198 <      
199 <      for(j = 0; j < 3; j++)
200 <        pos[j] = oldPos[i*3 + j] + dt*(vel[j] + sc[j]);
145 >  for (j = 0; j < 3; j++)
146 >    myVel[j] = oldVel[3*index + j];
147  
148 <      atoms[i]->setPos( pos );
148 >  matVecMul3( vScale, myVel, sc );
149 > }
150  
151 <    }
151 > template<typename T> void NPTf<T>::getPosScale(double pos[3], double COM[3],
152 >                                               int index, double sc[3]){
153 >  int j;
154 >  double rj[3];
155  
156 <  }  
156 >  for(j=0; j<3; j++)
157 >    rj[j] = ( oldPos[index*3+j] + pos[j]) / 2.0 - COM[j];
158  
159 <
159 >  matVecMul3( eta, rj, sc );
160 > }
161 >
162 > template<typename T> void NPTf<T>::scaleSimBox( void ){
163 >
164 >  int i,j,k;
165 >  double scaleMat[3][3];
166 >  double eta2ij;
167 >  double bigScale, smallScale, offDiagMax;
168 >  double hm[3][3], hmnew[3][3];
169 >
170 >
171 >
172    // Scale the box after all the positions have been moved:
173 <  
173 >
174    // Use a taylor expansion for eta products:  Hmat = Hmat . exp(dt * etaMat)
175    //  Hmat = Hmat . ( Ident + dt * etaMat  + dt^2 * etaMat*etaMat / 2)
176 <  
176 >
177    bigScale = 1.0;
178    smallScale = 1.0;
179    offDiagMax = 0.0;
180 <  
180 >
181    for(i=0; i<3; i++){
182      for(j=0; j<3; j++){
183 <      
183 >
184        // Calculate the matrix Product of the eta array (we only need
185        // the ij element right now):
186 <      
186 >
187        eta2ij = 0.0;
188        for(k=0; k<3; k++){
189          eta2ij += eta[i][k] * eta[k][j];
190        }
191 <      
191 >
192        scaleMat[i][j] = 0.0;
193        // identity matrix (see above):
194        if (i == j) scaleMat[i][j] = 1.0;
# Line 233 | Line 196 | template<typename T> void NPTf<T>::moveA() {
196        scaleMat[i][j] += dt*eta[i][j]  + 0.5*dt*dt*eta2ij;
197  
198        if (i != j)
199 <        if (fabs(scaleMat[i][j]) > offDiagMax)
199 >        if (fabs(scaleMat[i][j]) > offDiagMax)
200            offDiagMax = fabs(scaleMat[i][j]);
201      }
202  
203      if (scaleMat[i][i] > bigScale) bigScale = scaleMat[i][i];
204      if (scaleMat[i][i] < smallScale) smallScale = scaleMat[i][i];
205    }
206 <  
207 <  if ((bigScale > 1.1) || (smallScale < 0.9)) {
206 >
207 >  if ((bigScale > 1.01) || (smallScale < 0.99)) {
208      sprintf( painCave.errMsg,
209 <             "NPTf error: Attempting a Box scaling of more than 10 percent.\n"
209 >             "NPTf error: Attempting a Box scaling of more than 1 percent.\n"
210               " Check your tauBarostat, as it is probably too small!\n\n"
211               " scaleMat = [%lf\t%lf\t%lf]\n"
212               "            [%lf\t%lf\t%lf]\n"
# Line 253 | Line 216 | template<typename T> void NPTf<T>::moveA() {
216               scaleMat[2][0],scaleMat[2][1],scaleMat[2][2]);
217      painCave.isFatal = 1;
218      simError();
219 <  } else if (offDiagMax > 0.1) {
219 >  } else if (offDiagMax > 0.01) {
220      sprintf( painCave.errMsg,
221 <             "NPTf error: Attempting an off-diagonal Box scaling of more than 10 percent.\n"
221 >             "NPTf error: Attempting an off-diagonal Box scaling of more than 1 percent.\n"
222               " Check your tauBarostat, as it is probably too small!\n\n"
223               " scaleMat = [%lf\t%lf\t%lf]\n"
224               "            [%lf\t%lf\t%lf]\n"
# Line 267 | Line 230 | template<typename T> void NPTf<T>::moveA() {
230      simError();
231    } else {
232      info->getBoxM(hm);
233 <    info->matMul3(hm, scaleMat, hmnew);
233 >    matMul3(hm, scaleMat, hmnew);
234      info->setBoxM(hmnew);
235    }
273  
236   }
237  
238 < template<typename T> void NPTf<T>::moveB( void ){
238 > template<typename T> bool NPTf<T>::etaConverged() {
239 >  int i;
240 >  double diffEta, sumEta;
241  
242 <  int i, j, k;
279 <  DirectionalAtom* dAtom;
280 <  double Tb[3], ji[3];
281 <  double vel[3], frc[3];
282 <  double mass;
283 <
284 <  double instaTemp, instaPress, instaVol;
285 <  double tt2, tb2;
286 <  double sc[3];
287 <  double press[3][3], vScale[3][3];
288 <  double oldChi, prevChi;
289 <  double oldEta[3][3], preEta[3][3], diffEta;
290 <  
291 <  tt2 = tauThermostat * tauThermostat;
292 <  tb2 = tauBarostat * tauBarostat;
293 <
294 <
295 <  // Set things up for the iteration:
296 <
297 <  oldChi = chi;
298 <  
242 >  sumEta = 0;
243    for(i = 0; i < 3; i++)
244 <    for(j = 0; j < 3; j++)
301 <      oldEta[i][j] = eta[i][j];
244 >    sumEta += pow(prevEta[i][i] - eta[i][i], 2);
245  
246 <  for( i=0; i<nAtoms; i++ ){
246 >  diffEta = sqrt( sumEta / 3.0 );
247  
248 <    atoms[i]->getVel( vel );
248 >  return ( diffEta <= etaTolerance );
249 > }
250  
251 <    for (j=0; j < 3; j++)
308 <      oldVel[3*i + j]  = vel[j];
251 > template<typename T> double NPTf<T>::getConservedQuantity(void){
252  
253 <    if( atoms[i]->isDirectional() ){
253 >  double conservedQuantity;
254 >  double totalEnergy;
255 >  double thermostat_kinetic;
256 >  double thermostat_potential;
257 >  double barostat_kinetic;
258 >  double barostat_potential;
259 >  double trEta;
260 >  double a[3][3], b[3][3];
261  
262 <      dAtom = (DirectionalAtom *)atoms[i];
262 >  totalEnergy = tStats->getTotalE();
263  
264 <      dAtom->getJ( ji );
264 >  thermostat_kinetic = fkBT * tt2 * chi * chi /
265 >    (2.0 * eConvert);
266  
267 <      for (j=0; j < 3; j++)
317 <        oldJi[3*i + j] = ji[j];
267 >  thermostat_potential = fkBT* integralOfChidt / eConvert;
268  
269 <    }
270 <  }
269 >  transposeMat3(eta, a);
270 >  matMul3(a, eta, b);
271 >  trEta = matTrace3(b);
272  
273 <  // do the iteration:
273 >  barostat_kinetic = NkBT * tb2 * trEta /
274 >    (2.0 * eConvert);
275  
276 <  instaVol = tStats->getVolume();
277 <  
326 <  for (k=0; k < 4; k++) {
327 <    
328 <    instaTemp = tStats->getTemperature();
329 <    tStats->getPressureTensor(press);
276 >  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
277 >    eConvert;
278  
279 <    // evolve chi another half step using the temperature at t + dt/2
279 >  conservedQuantity = totalEnergy + thermostat_kinetic + thermostat_potential +
280 >    barostat_kinetic + barostat_potential;
281  
282 <    prevChi = chi;
334 <    chi = oldChi + dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
335 <    
336 <    for(i = 0; i < 3; i++)
337 <      for(j = 0; j < 3; j++)
338 <        preEta[i][j] = eta[i][j];
282 >  return conservedQuantity;
283  
340    //advance eta half step and calculate scale factor for velocity
341    for(i = 0; i < 3; i ++)
342      for(j = 0; j < 3; j++){
343        if( i == j){
344          eta[i][j] = oldEta[i][j] + dt2 *  instaVol *
345            (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
346          vScale[i][j] = eta[i][j] + chi;
347        }
348        else
349        {
350          eta[i][j] = oldEta[i][j] + dt2 * instaVol * press[i][j] / (NkBT*tb2);
351          vScale[i][j] = eta[i][j];
352        }
353    }      
354
355    //advance velocity half step
356    for( i=0; i<nAtoms; i++ ){
357
358      atoms[i]->getFrc( frc );
359      atoms[i]->getVel(vel);
360      
361      mass = atoms[i]->getMass();
362      
363      info->matVecMul3( vScale, vel, sc );
364
365      for (j=0; j < 3; j++) {
366        // velocity half step  (use chi from previous step here):
367        vel[j] = oldVel[3*i+j] + dt2 * ((frc[j]  / mass) * eConvert - sc[j]);
368      }
369      
370      atoms[i]->setVel( vel );
371      
372      if( atoms[i]->isDirectional() ){
373
374        dAtom = (DirectionalAtom *)atoms[i];
375  
376        // get and convert the torque to body frame      
377  
378        dAtom->getTrq( Tb );
379        dAtom->lab2Body( Tb );      
380            
381        for (j=0; j < 3; j++)
382          ji[j] = oldJi[3*i + j] + dt2 * (Tb[j] * eConvert - oldJi[3*i+j]*chi);
383      
384          dAtom->setJ( ji );
385      }
386    }
387
388    
389    diffEta = 0;
390    for(i = 0; i < 3; i++)
391      diffEta += pow(preEta[i][i] - eta[i][i], 2);    
392    
393    if (fabs(prevChi - chi) <= chiTolerance && sqrt(diffEta / 3) <= etaTolerance)
394      break;
395  }
396
397  //calculate integral of chida
398  integralOfChidt += dt2*chi;
399
400  
284   }
285  
286 < template<typename T> void NPTf<T>::resetIntegrator() {
287 <  int i,j;
288 <  
289 <  chi = 0.0;
286 > template<typename T> string NPTf<T>::getAdditionalParameters(void){
287 >  string parameters;
288 >  const int BUFFERSIZE = 2000; // size of the read buffer
289 >  char buffer[BUFFERSIZE];
290  
291 <  for(i = 0; i < 3; i++)
292 <    for (j = 0; j < 3; j++)
410 <      eta[i][j] = 0.0;
291 >  sprintf(buffer,"\t%G\t%G;", chi, integralOfChidt);
292 >  parameters += buffer;
293  
294 < }
295 <
296 < template<typename T> int NPTf<T>::readyCheck() {
415 <
416 <  //check parent's readyCheck() first
417 <  if (T::readyCheck() == -1)
418 <    return -1;
419 <
420 <  // First check to see if we have a target temperature.
421 <  // Not having one is fatal.
422 <  
423 <  if (!have_target_temp) {
424 <    sprintf( painCave.errMsg,
425 <             "NPTf error: You can't use the NPTf integrator\n"
426 <             "   without a targetTemp!\n"
427 <             );
428 <    painCave.isFatal = 1;
429 <    simError();
430 <    return -1;
294 >  for(int i = 0; i < 3; i++){
295 >    sprintf(buffer,"\t%G\t%G\t%G;", eta[i][0], eta[i][1], eta[i][2]);
296 >    parameters += buffer;
297    }
298  
299 <  if (!have_target_pressure) {
434 <    sprintf( painCave.errMsg,
435 <             "NPTf error: You can't use the NPTf integrator\n"
436 <             "   without a targetPressure!\n"
437 <             );
438 <    painCave.isFatal = 1;
439 <    simError();
440 <    return -1;
441 <  }
442 <  
443 <  // We must set tauThermostat.
444 <  
445 <  if (!have_tau_thermostat) {
446 <    sprintf( painCave.errMsg,
447 <             "NPTf error: If you use the NPTf\n"
448 <             "   integrator, you must set tauThermostat.\n");
449 <    painCave.isFatal = 1;
450 <    simError();
451 <    return -1;
452 <  }    
299 >  return parameters;
300  
454  // We must set tauBarostat.
455  
456  if (!have_tau_barostat) {
457    sprintf( painCave.errMsg,
458             "NPTf error: If you use the NPTf\n"
459             "   integrator, you must set tauBarostat.\n");
460    painCave.isFatal = 1;
461    simError();
462    return -1;
463  }    
464
465  // We need NkBT a lot, so just set it here:
466
467  NkBT = (double)Nparticles * kB * targetTemp;
468  fkBT = (double)info->ndf * kB * targetTemp;
469
470  return 1;
301   }
472
473 template<typename T> double NPTf<T>::getConservedQuantity(void){
474
475  double conservedQuantity;
476  double tb2;
477  double trEta;  
478  double U;
479  double thermo;
480  double integral;
481  double baro;
482  double PV;
483
484  U = tStats->getTotalE();
485  thermo = (fkBT * tauThermostat * tauThermostat * chi * chi / 2.0) / eConvert;
486
487  tb2 = tauBarostat * tauBarostat;
488  trEta = info->matTrace3(eta);
489  baro = ((double)info->ndfTrans * kB * targetTemp * tb2 * trEta * trEta / 2.0) / eConvert;
490
491  integral = ((double)(info->ndf + 1) * kB * targetTemp * integralOfChidt) /eConvert;
492
493  PV = (targetPressure * tStats->getVolume() / p_convert) / eConvert;
494
495
496  cout.width(8);
497  cout.precision(8);
498  
499  cout << info->getTime() << "\t"
500       << chi << "\t"
501       << trEta << "\t"
502       << U << "\t"
503       << thermo << "\t"
504       << baro << "\t"
505       << integral << "\t"
506       << PV << "\t"
507       << U+thermo+integral+PV+baro << endl;
508
509  conservedQuantity = U+thermo+integral+PV+baro;
510  return conservedQuantity;
511  
512 }

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