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root/group/branches/new-templateless/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.
branches/new-templateless/OOPSE/libmdtools/NPTf.cpp (file contents), Revision 850 by mmeineke, Mon Nov 3 22:07:17 2003 UTC

# Line 1 | Line 1
1 < #include <cmath>
1 > #include <stdlib.h>
2 > #include <math.h>
3 >
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 )
28 > NPTf::NPTf ( SimInfo *theInfo, ForceFields* the_ff):
29 >  NPT( theInfo, the_ff )
30   {
31 <  int i, j;
32 <  chi = 0.0;
33 <  integralOfChidt = 0.0;
31 >  GenericData* data;
32 >  double *etaArray;
33 >  int i,j;
34  
35 <  for(i = 0; i < 3; i++)
36 <    for (j = 0; j < 3; j++)
35 >  for(i = 0; i < 3; i++){
36 >    for (j = 0; j < 3; j++){
37 >
38        eta[i][j] = 0.0;
39 +      oldEta[i][j] = 0.0;
40 +    }
41 +  }
42  
43 <  have_tau_thermostat = 0;
44 <  have_tau_barostat = 0;
45 <  have_target_temp = 0;
46 <  have_target_pressure = 0;
43 >  // retrieve eta array from simInfo if it exists
44 >  data = info->getProperty(ETAVALUE_ID);
45 >  if(data != NULL){
46 >    
47 >    int test = data->getDarray(etaArray);
48 >    
49 >    if( test == 9 ){
50 >      
51 >      for(i = 0; i < 3; i++){
52 >        for (j = 0; j < 3; j++){
53 >          eta[i][j] = etaArray[3*i+j];
54 >          oldEta[i][j] = eta[i][j];
55 >        }
56 >      }    
57 >      delete[] etaArray;
58 >    }
59 >    else
60 >      std::cerr << "NPTf error: etaArray is not length 9 (actual = " << test
61 >                << ").\n"
62 >                << "            Simulation wil proceed with eta = 0;\n";
63 >  }
64 > }
65  
66 <  have_chi_tolerance = 0;
40 <  have_eta_tolerance = 0;
41 <  have_pos_iter_tolerance = 0;
66 > NPTf::~NPTf() {
67  
68 <  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
68 >  // empty for now
69   }
70  
71 < template<typename T> NPTf<T>::~NPTf() {
72 <  delete[] oldPos;
73 <  delete[] oldVel;
74 <  delete[] oldJi;
71 > void NPTf::resetIntegrator() {
72 >
73 >  int i, j;
74 >
75 >  for(i = 0; i < 3; i++)
76 >    for (j = 0; j < 3; j++)
77 >      eta[i][j] = 0.0;
78 >
79 >  NPT::resetIntegrator();
80   }
81  
82 < 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];
82 > void NPTf::evolveEtaA() {
83  
84 <  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];
84 >  int i, j;
85  
86 <  tt2 = tauThermostat * tauThermostat;
87 <  tb2 = tauBarostat * tauBarostat;
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 <  instaTemp = tStats->getTemperature();
97 <  tStats->getPressureTensor(press);
98 <  instaVol = tStats->getVolume();
99 <  
84 <  tStats->getCOM(COM);
96 >  for(i = 0; i < 3; i++)
97 >    for (j = 0; j < 3; j++)
98 >      oldEta[i][j] = eta[i][j];
99 > }
100  
101 <  //calculate scale factor of veloity
101 > void NPTf::evolveEtaB() {
102 >
103 >  int i,j;
104 >
105 >  for(i = 0; i < 3; i++)
106 >    for (j = 0; j < 3; j++)
107 >      prevEta[i][j] = eta[i][j];
108 >
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 > void NPTf::getVelScaleA(double sc[3], double vel[3]) {
122 >  int i,j;
123 >  double vScale[3][3];
124 >
125    for (i = 0; i < 3; i++ ) {
126      for (j = 0; j < 3; j++ ) {
127        vScale[i][j] = eta[i][j];
128 <      
128 >
129        if (i == j) {
130 <        vScale[i][j] += chi;          
131 <      }              
130 >        vScale[i][j] += chi;
131 >      }
132      }
133    }
96 –  
97 –  //evolve velocity half step
98 –  for( i=0; i<nAtoms; i++ ){
134  
135 <    atoms[i]->getVel( vel );
136 <    atoms[i]->getFrc( frc );
102 <
103 <    mass = atoms[i]->getMass();
104 <    
105 <    info->matVecMul3( vScale, vel, sc );
135 >  info->matVecMul3( vScale, vel, sc );
136 > }
137  
138 <    for (j=0; j < 3; j++) {
139 <      // velocity half step  (use chi from previous step here):
140 <      vel[j] += dt2 * ((frc[j]  / mass) * eConvert - sc[j]);
141 <  
111 <    }
138 > void NPTf::getVelScaleB(double sc[3], int index ){
139 >  int i,j;
140 >  double myVel[3];
141 >  double vScale[3][3];
142  
143 <    atoms[i]->setVel( vel );
144 <  
145 <    if( atoms[i]->isDirectional() ){
143 >  for (i = 0; i < 3; i++ ) {
144 >    for (j = 0; j < 3; j++ ) {
145 >      vScale[i][j] = eta[i][j];
146  
147 <      dAtom = (DirectionalAtom *)atoms[i];
148 <
149 <      // get and convert the torque to body frame
150 <      
121 <      dAtom->getTrq( Tb );
122 <      dAtom->lab2Body( Tb );
123 <      
124 <      // get the angular momentum, and propagate a half step
125 <
126 <      dAtom->getJ( ji );
127 <
128 <      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 );
140 <
141 <      // rotate about the y-axis
142 <      angle = dt2 * ji[1] / I[1][1];
143 <      this->rotate( 2, 0, angle, ji, A );
144 <      
145 <      // rotate about the z-axis
146 <      angle = dt * ji[2] / I[2][2];
147 <      this->rotate( 0, 1, angle, ji, A);
148 <      
149 <      // 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 <    }    
147 >      if (i == j) {
148 >        vScale[i][j] += chi;
149 >      }
150 >    }
151    }
152  
153 <  // advance chi half step
154 <  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
153 >  for (j = 0; j < 3; j++)
154 >    myVel[j] = oldVel[3*index + j];
155  
156 <  //calculate the integral of chidt
157 <  integralOfChidt += dt2*chi;
156 >  info->matVecMul3( vScale, myVel, sc );
157 > }
158  
159 <  //advance eta half step
160 <  for(i = 0; i < 3; i ++)
161 <    for(j = 0; j < 3; j++){
162 <      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);
176 <    }
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];
183 <  }
184 <  
185 <  //the first estimation of r(t+dt) is equal to  r(t)
186 <    
187 <  for(k = 0; k < 4; k ++){
159 > void NPTf::getPosScale(double pos[3], double COM[3],
160 >                                               int index, double sc[3]){
161 >  int j;
162 >  double rj[3];
163  
164 <    for(i =0 ; i < nAtoms; i++){
164 >  for(j=0; j<3; j++)
165 >    rj[j] = ( oldPos[index*3+j] + pos[j]) / 2.0 - COM[j];
166  
167 <      atoms[i]->getVel(vel);
168 <      atoms[i]->getPos(pos);
167 >  info->matVecMul3( eta, rj, sc );
168 > }
169  
170 <      for(j = 0; j < 3; j++)
195 <        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]);
170 > void NPTf::scaleSimBox( void ){
171  
172 <      atoms[i]->setPos( pos );
172 >  int i,j,k;
173 >  double scaleMat[3][3];
174 >  double eta2ij;
175 >  double bigScale, smallScale, offDiagMax;
176 >  double hm[3][3], hmnew[3][3];
177  
204 –    }
178  
206 –  }  
179  
208 –
180    // Scale the box after all the positions have been moved:
181 <  
181 >
182    // Use a taylor expansion for eta products:  Hmat = Hmat . exp(dt * etaMat)
183    //  Hmat = Hmat . ( Ident + dt * etaMat  + dt^2 * etaMat*etaMat / 2)
184 <  
184 >
185    bigScale = 1.0;
186    smallScale = 1.0;
187    offDiagMax = 0.0;
188 <  
188 >
189    for(i=0; i<3; i++){
190      for(j=0; j<3; j++){
191 <      
191 >
192        // Calculate the matrix Product of the eta array (we only need
193        // the ij element right now):
194 <      
194 >
195        eta2ij = 0.0;
196        for(k=0; k<3; k++){
197          eta2ij += eta[i][k] * eta[k][j];
198        }
199 <      
199 >
200        scaleMat[i][j] = 0.0;
201        // identity matrix (see above):
202        if (i == j) scaleMat[i][j] = 1.0;
# Line 233 | Line 204 | template<typename T> void NPTf<T>::moveA() {
204        scaleMat[i][j] += dt*eta[i][j]  + 0.5*dt*dt*eta2ij;
205  
206        if (i != j)
207 <        if (fabs(scaleMat[i][j]) > offDiagMax)
207 >        if (fabs(scaleMat[i][j]) > offDiagMax)
208            offDiagMax = fabs(scaleMat[i][j]);
209      }
210  
211      if (scaleMat[i][i] > bigScale) bigScale = scaleMat[i][i];
212      if (scaleMat[i][i] < smallScale) smallScale = scaleMat[i][i];
213    }
214 <  
214 >
215    if ((bigScale > 1.1) || (smallScale < 0.9)) {
216      sprintf( painCave.errMsg,
217               "NPTf error: Attempting a Box scaling of more than 10 percent.\n"
# Line 270 | Line 241 | template<typename T> void NPTf<T>::moveA() {
241      info->matMul3(hm, scaleMat, hmnew);
242      info->setBoxM(hmnew);
243    }
273 –  
244   }
245  
246 < template<typename T> void NPTf<T>::moveB( void ){
246 > bool NPTf::etaConverged() {
247 >  int i;
248 >  double diffEta, sumEta;
249  
250 <  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 <  
250 >  sumEta = 0;
251    for(i = 0; i < 3; i++)
252 <    for(j = 0; j < 3; j++)
301 <      oldEta[i][j] = eta[i][j];
252 >    sumEta += pow(prevEta[i][i] - eta[i][i], 2);
253  
254 <  for( i=0; i<nAtoms; i++ ){
254 >  diffEta = sqrt( sumEta / 3.0 );
255  
256 <    atoms[i]->getVel( vel );
256 >  return ( diffEta <= etaTolerance );
257 > }
258  
259 <    for (j=0; j < 3; j++)
308 <      oldVel[3*i + j]  = vel[j];
259 > double NPTf::getConservedQuantity(void){
260  
261 <    if( atoms[i]->isDirectional() ){
261 >  double conservedQuantity;
262 >  double totalEnergy;
263 >  double thermostat_kinetic;
264 >  double thermostat_potential;
265 >  double barostat_kinetic;
266 >  double barostat_potential;
267 >  double trEta;
268 >  double a[3][3], b[3][3];
269  
270 <      dAtom = (DirectionalAtom *)atoms[i];
270 >  totalEnergy = tStats->getTotalE();
271  
272 <      dAtom->getJ( ji );
272 >  thermostat_kinetic = fkBT * tt2 * chi * chi /
273 >    (2.0 * eConvert);
274  
275 <      for (j=0; j < 3; j++)
317 <        oldJi[3*i + j] = ji[j];
275 >  thermostat_potential = fkBT* integralOfChidt / eConvert;
276  
277 <    }
278 <  }
277 >  info->transposeMat3(eta, a);
278 >  info->matMul3(a, eta, b);
279 >  trEta = info->matTrace3(b);
280  
281 <  // do the iteration:
281 >  barostat_kinetic = NkBT * tb2 * trEta /
282 >    (2.0 * eConvert);
283  
284 <  instaVol = tStats->getVolume();
285 <  
326 <  for (k=0; k < 4; k++) {
327 <    
328 <    instaTemp = tStats->getTemperature();
329 <    tStats->getPressureTensor(press);
284 >  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
285 >    eConvert;
286  
287 <    // evolve chi another half step using the temperature at t + dt/2
287 >  conservedQuantity = totalEnergy + thermostat_kinetic + thermostat_potential +
288 >    barostat_kinetic + barostat_potential;
289  
290 <    prevChi = chi;
291 <    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];
290 > //   cout.width(8);
291 > //   cout.precision(8);
292  
293 <    //advance eta half step and calculate scale factor for velocity
294 <    for(i = 0; i < 3; i ++)
295 <      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 <    }      
293 > //   cerr << info->getTime() << "\t" << Energy << "\t" << thermostat_kinetic <<
294 > //       "\t" << thermostat_potential << "\t" << barostat_kinetic <<
295 > //       "\t" << barostat_potential << "\t" << conservedQuantity << endl;
296  
297 <    //advance velocity half step
356 <    for( i=0; i<nAtoms; i++ ){
297 >  return conservedQuantity;
298  
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 –  
299   }
300  
301 < template<typename T> void NPTf<T>::resetIntegrator() {
302 <  int i,j;
303 <  
304 <  chi = 0.0;
301 > string NPTf::getAdditionalParameters(void){
302 >  string parameters;
303 >  const int BUFFERSIZE = 2000; // size of the read buffer
304 >  char buffer[BUFFERSIZE];
305  
306 <  for(i = 0; i < 3; i++)
307 <    for (j = 0; j < 3; j++)
410 <      eta[i][j] = 0.0;
306 >  sprintf(buffer,"\t%lf\t%lf;", chi, integralOfChidt);
307 >  parameters += buffer;
308  
309 < }
310 <
311 < 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;
309 >  for(int i = 0; i < 3; i++){
310 >    sprintf(buffer,"\t%lf\t%lf\t%lf;", eta[3*i], eta[3*i+1], eta[3*i+2]);
311 >    parameters += buffer;
312    }
313  
314 <  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 <  }    
314 >  return parameters;
315  
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;
316   }
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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