# Re: Fixing Langevin piston to allow off-diagonal stress (and why does the source say "FIX THIS"?)

From: FX (fxcoudert_at_gmail.com)
Date: Wed Mar 06 2013 - 16:36:04 CST

Hi all,

I just wanted to send an updated version of my patch, in case someone who knows the Langevin piston code can give it a look. I have now been able to test this code, and it seems to give good results. I have actually been able to use it to calculate stiffness constants (aka elastic constants) of a material from unit cell fluctuations, although I do not have a reference run with another software to compare it with.

FX

PS: I realize my email subject is wrong, as it's not about "fixing" the barostat but about extending it, really…

@@ -704,14 +704,14 @@ void Controller::langevinPiston1(int ste
BigReal f2 = sqrt( ( 1. - f1*f1 ) * kT / mass );
strainRate *= f1;
if ( simParams->useFlexibleCell ) {
- // We only use on-diagonal terms (for now)
if ( simParams->useConstantRatio ) {
BigReal r = f2 * random->gaussian();
strainRate.xx += r;
strainRate.yy += r;
strainRate.zz += f2 * random->gaussian();
} else {
- strainRate += f2 * Tensor::diagonal(random->gaussian_vector());
+ // FXC
+ strainRate += f2 * Tensor::symmetric(random->gaussian_vector(), random->gaussian_vector());
}
} else {
strainRate += f2 * Tensor::identity(random->gaussian());
@@ -746,17 +746,28 @@ void Controller::langevinPiston1(int ste

if ( ! ( (step-1-slowFreq/2) % slowFreq ) )
{
- // We only use on-diagonal terms (for now)
Tensor factor;
- if ( !simParams->useConstantArea ) {
- factor.xx = exp( dt_long * strainRate.xx );
- factor.yy = exp( dt_long * strainRate.yy );
- } else {
+ if ( simParams->useConstantArea ) {
factor.xx = factor.yy = 1;
+ factor.zz = exp( dt_long * strainRate.zz );
+ } else {
+ // FXC
+ // Matrix exponential... we approximate to second order
+ Tensor t2;
+ t2.xx = strainRate.xx*strainRate.xx + strainRate.xy*strainRate.xy + strainRate.xz*strainRate.xz;
+ t2.yy = strainRate.xy*strainRate.xy + strainRate.yy*strainRate.yy + strainRate.yz*strainRate.yz;
+ t2.zz = strainRate.xz*strainRate.xz + strainRate.yz*strainRate.yz + strainRate.zz*strainRate.zz;
+ t2.xy = strainRate.xx*strainRate.xy + strainRate.xy*strainRate.yy + strainRate.xz*strainRate.yz;
+ t2.xz = strainRate.xx*strainRate.xz + strainRate.xy*strainRate.yz + strainRate.xz*strainRate.zz;
+ t2.yz = strainRate.xy*strainRate.xz + strainRate.yy*strainRate.yz + strainRate.yz*strainRate.zz;
+ t2.yx = t2.xy;
+ t2.zx = t2.xz;
+ t2.zy = t2.yz;
+ factor = Tensor::identity() + dt_long * strainRate + 0.5 * dt_long * dt_long * t2;
}
- factor.zz = exp( dt_long * strainRate.zz );
state->lattice.rescale(factor);
+
#ifdef DEBUG_PRESSURE
iout << iINFO << "rescaling by: " << factor << "\n";
#endif
@@ -841,7 +852,6 @@ void Controller::langevinPiston2(int ste

strainRate += ( 0.5 * dt * cellDims * state->lattice.volume() / mass ) *
( controlPressure - ptarget );
-

#ifdef DEBUG_PRESSURE
iout << iINFO << "integrating half step, strain rate: " << strainRate << "\n";
@@ -854,14 +864,14 @@ void Controller::langevinPiston2(int ste
BigReal f2 = sqrt( ( 1. - f1*f1 ) * kT / mass );
strainRate *= f1;
if ( simParams->useFlexibleCell ) {
- // We only use on-diagonal terms (for now)
if ( simParams->useConstantRatio ) {
BigReal r = f2 * random->gaussian();
strainRate.xx += r;
strainRate.yy += r;
strainRate.zz += f2 * random->gaussian();
} else {
- strainRate += f2 * Tensor::diagonal(random->gaussian_vector());
+ // FXC
+ strainRate += f2 * Tensor::symmetric(random->gaussian_vector(), random->gaussian_vector());
}
} else {
strainRate += f2 * Tensor::identity(random->gaussian());
@@ -1211,16 +1221,17 @@ void Controller::receivePressure(int ste
}

if ( simParameters->useFlexibleCell ) {
+ // FXC
// use symmetric pressure to control rotation
- // controlPressure_normal = symmetric(controlPressure_normal);
- // controlPressure_nbond = symmetric(controlPressure_nbond);
- // controlPressure_slow = symmetric(controlPressure_slow);
- // controlPressure = symmetric(controlPressure);
+ controlPressure_normal = symmetric(controlPressure_normal);
+ controlPressure_nbond = symmetric(controlPressure_nbond);
+ controlPressure_slow = symmetric(controlPressure_slow);
+ controlPressure = symmetric(controlPressure);
// only use on-diagonal components for now
- controlPressure_normal = Tensor::diagonal(diagonal(controlPressure_normal));
- controlPressure_nbond = Tensor::diagonal(diagonal(controlPressure_nbond));
- controlPressure_slow = Tensor::diagonal(diagonal(controlPressure_slow));
- controlPressure = Tensor::diagonal(diagonal(controlPressure));
+ // controlPressure_normal = Tensor::diagonal(diagonal(controlPressure_normal));
+ // controlPressure_nbond = Tensor::diagonal(diagonal(controlPressure_nbond));
+ // controlPressure_slow = Tensor::diagonal(diagonal(controlPressure_slow));
+ // controlPressure = Tensor::diagonal(diagonal(controlPressure));
if ( simParameters->useConstantRatio ) {
#define AVGXY(T) T.xy = T.yx = 0; T.xx = T.yy = 0.5 * ( T.xx + T.yy );\
T.xz = T.zx = T.yz = T.zy = 0.5 * ( T.xz + T.yz );

Le 6 mars 2013 à 11:43, FX <fxcoudert_at_gmail.com> a écrit :

> Hi all,
>
> I am currently trying to modify the NAMD sources related to the Langevin piston barostat method, in order to allow off-diagonal stress fluctuations (shearing). I think I have gotten the parts in Controller.C okay (my "first attempt" patch is attached, but I have not yet tested it), but I do not understand well what is done in Sequencer::langevinPiston:
>
>> void Sequencer::langevinPiston(int step)
>> {
>> if ( simParams->langevinPistonOn && ! ( (step-1-slowFreq/2) % slowFreq ) )
>> {
>> FullAtom *a = patch->atom.begin();
>> int numAtoms = patch->numAtoms;
>> // JCP FIX THIS!!!
>> Vector velFactor(1/factor.xx,1/factor.yy,1/factor.zz);
>> patch->lattice.rescale(factor);
>
> It seems to me that the position rescaling code will work fine, even with my modifications to the calculation of the rescale factor. However, I have the following questions:
>
> 1. Why is the velocity scaled by the inverse of the position scaling factor? I cannot get that from the Langevin piston equations…
> 2. Who is JCP? (James C. Phillips?) Does he read this list?
> 3. How much should I be scared of the "FIX THIS" comment?
>