void reset_XYZ(void)
{
int i;
double cx=0.0,cy=0.0,cz=0.0;
//Find the center of mass for each component
for(i=0;i<N;i++)
{
cx+=x[i];
cy+=y[i];
cz+=z[i];
};
cx*=invN;
cy*=invN;
cz*=invN;
//fprintf(stderr,"%g\t%g\t%g\n",cmass(),currEtot,currnonbondE);
for(i=0;i<N;i++)
{
x[i]=x[i]-cx;
y[i]=y[i]-cy;
z[i]=z[i]-cz;
};
//Recalculate the overall energies
currEtot=Etot();
currnonbondE=nonbondEnergy();
//fprintf(stderr,"%g\t%g\t%g\n",cmass(),currEtot,currnonbondE);
}
/*Monte Carlo bond fluctuation algorithm
Similar to mcpivot, but rotates monomers betwee two randomly chosen monomers by a small amount
axis of rotation is between the two chosen monomers
NOTE this algorithm should NOT change the bond lengths, use checkbonds() to check, but should change one bond angle at a time
*/
void mccrankshaft(void)
{
int i=0,j=0,m1=0,m2=0,start=0,end=0;
double Ei=0.0,Ef=0.0; //intial and final energies (before and after diffusion)
double Ebondi=0.0,Ebondf=0.0,Enblocali=0.0,Enblocalf=0.0; //local energy variables
double rx=0.0,ry=0.0,rz=0.0;
double distr=0.0,rangle=0.0,c=0.0,s=0.0,u=0.0;
double ttx=0.0,tty=0.0,ttz=0.0;
//set temporary positions
for(j=0;j<N;++j)
{
tx[j]=x[j];
ty[j]=y[j];
tz[j]=z[j];
};
//randomly choose two monomers
m1=(int) (randd1()*N);
m2=(int) (randd1()*N);
//choose random rotation angle
rangle=DC*2.0*M_PI*(2.0*randd1()-1.0);
//below are the cases where the move wouldn't change anything
while( (m1==m2) || (abs(m1-m2)==N-1) || (abs(m1-m2)==1) )
{
m1=(int) (randd1()*N);
m2=(int) (randd1()*N);
};
//set indices for energy calculation
if( m1<m2 )
{
start=m1;
end=m2;
}
else
{
start=m2;
end=m1;
};
//Set initial energies
Ei=currEtot;
//////////Rotation
//rotation axis is the vector between m1 and m2
distr = sqrt( (x[m1]-x[m2])*(x[m1]-x[m2]) + (y[m1]-y[m2])*(y[m1]-y[m2]) + (z[m1]-z[m2])*(z[m1]-z[m2]) );
rx = (x[m1]-x[m2])/distr;
ry = (y[m1]-y[m2])/distr;
rz = (z[m1]-z[m2])/distr;
//angle constants
c=cos(rangle);
s=sin(rangle);
u=1.0-c;
//Calculate the initial local bond energy
/* for(i=start;i<end;i++)
{
distr = sqrt( (x[i]-x[i+1])*(x[i]-x[i+1]) + (y[i]-y[i+1])*(y[i]-y[i+1]) + (z[i]-z[i+1])*(z[i]-z[i+1]) );
Ebondi = Ebondi + bondpot(distr);
};
*/
//Local bond and bond angle energy - assumes the above in unecessary
Ebondi = localE(m1) + localE(m2);
/////Rotation
//now we perform the rotation
for(i=start+1;i<end;i++)
{
//calculate initial local nonbonded energy
for(j=0;j<N;j++)
if( (j<start) || (j>end) )
{
distr = sqrt( (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]) + (z[i]-z[j])*(z[i]-z[j]) );
Enblocali = Enblocali + nonbondpot(distr);
//fprintf(stderr,"%d\t%d\t%20.16f\t%20.16f\t%20.16f\n",i,j,distr,nonbondpot(distr),Enblocali);
};
//translate the rotation segment to the origin
x[i] -= x[start];
y[i] -= y[start];
z[i] -= z[start];
//store old vector for the rotation matrix below
ttx=x[i];
tty=y[i];
ttz=z[i];
//Perform the rotation on the selected segment
x[i] = (u*rx*rx + c)*ttx + (u*ry*rx - s*rz)*tty + (u*rz*rx + ry*s)*ttz;
y[i] = (u*rx*ry + rz*s)*ttx + (u*ry*ry + c)*tty + (u*rz*ry - rx*s)*ttz;
z[i] = (u*rx*rz - ry*s)*ttx + (u*ry*rz + rx*s)*tty + (u*rz*rz + c)*ttz;
//translate the rotation segment back to the original reference frame
x[i] += x[start];
y[i] += y[start];
z[i] += z[start];
//calculate final local nonbonded energy
for(j=0;j<N;j++)
if( (j<start) || (j>end) )
{
distr = sqrt( (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]) + (z[i]-z[j])*(z[i]-z[j]) );
Enblocalf = Enblocalf + nonbondpot(distr);
//fprintf(stderr,"%d\t%d\t%20.16f\t%20.16f\t%20.16f\n",i,j,distr,nonbondpot(distr),Enblocalf);
};
};
//Calculate the initial local bond energy
/* for(i=start;i<end;i++)
{
distr = sqrt( (x[i]-x[i+1])*(x[i]-x[i+1]) + (y[i]-y[i+1])*(y[i]-y[i+1]) + (z[i]-z[i+1])*(z[i]-z[i+1]) );
Ebondf = Ebondf + bondpot(distr);
};
*/
//Local bond and bond angle energy - assumes the above in unecessary
Ebondf = localE(m1) + localE(m2);
//Bond-angles should be unaffected by this move
Ef = Ei + (Ebondf - Ebondi) + (Enblocalf - Enblocali);
attemptside+=1;
if(Metropolis(Ei,Ef)==1)
{
acceptside+=1;
if( (acceptside%1000) == 0 )
{
currEtot = Etot();
};
}
else
{
//reject
for(j=0;j<N;++j)
{
x[j]=tx[j];
y[j]=ty[j];
z[j]=tz[j];
};
};
}
/*
Monte Carlo pivot around a random direction
Random direction generated using the Marsaglia method
NOTE this algorithm should NOT change the bond lengths, use checkbonds() to check, but should change one bond angle at a time
*/
void mcrandpivot(void)
{
int m=0,i=0,j=0,direction=0,start=0,end1=0,end2=0;
double Ei=0.0,Ef=0.0; //intial and final energies (before and after diffusion)
double Ebondi=0.0,Ebondf=0.0,Enblocali=0.0,Enblocalf=0.0; //local energy variables
double eta1=0.0,eta2=0.0,etasq=0.0,rx=0.0,ry=0.0,rz=0.0;
double distr=0.0,rangle=0.0,c=0.0,s=0.0,u=0.0;
double ttx=0.0,tty=0.0,ttz=0.0;
//set temperorary variables
for(j=0;j<N;++j)
{
tx[j]=x[j];
ty[j]=y[j];
tz[j]=z[j];
};
//choose random monomer
m=(int) (randd1()*(N-2)+1.0); //note, never choses monomers on the ends, as this would do nothing to the internal degrees of freedom
//choose random rotation angle
rangle=DC*2.0*M_PI*(2.0*randd1()-1.0);
//select the shortest portion of the chain to the left or right of the random monomer
if(m < N/2.0)
{
direction = -1;
start=m;
end1=0;
end2=N-1;
}
else
{
direction = 1;
start=m;
end1=N-1;
end2=0;
};
//choose a random direction using the Marsaglia method
etasq = 2.0; //simply set to a value greater than 1.0 (the while condition below)
while( etasq > 1.0 )
{
eta1 = 1.0 - 2.0*randd1();
eta2 = 1.0 - 2.0*randd1();
etasq = eta1*eta1 + eta2*eta2;
};
//these are the new unit vectors
rx = 2.0*eta1*sqrt(1.0-etasq);
ry = 2.0*eta2*sqrt(1.0-etasq);
rz = 1.0 - 2.0*etasq;
//angle constants
c=cos(rangle);
s=sin(rangle);
u=1.0-c;
//set energies
Ei=currEtot;
//Calculate the initial local bond energy (NOTE: this cannot go in the rotation loop)
/* i=start;
while( i != end1 )
{
i=i+direction;
j=i-direction;
distr = sqrt( (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]) + (z[i]-z[j])*(z[i]-z[j]) );
Ebondi = Ebondi + bondpot(distr);
//fprintf(stderr,"%d\t%d\t%d\t%f\t%f\n",m,i,i-direction,distr,bondpot(distr));
};
*/
//Local bond and bond angle energy - assumes bond lengths don't change (unlike above commented out section)
Ebondi = Ebondi + localE(m);
/////Rotation
//now we perform the rotation
i=start;
while( i != end1 )
{
i=i+direction;
//Calculate the initial local nonbond energy
for(j=end2;j!=start;j+=direction)
{
distr = sqrt( (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]) + (z[i]-z[j])*(z[i]-z[j]) );
Enblocali = Enblocali + nonbondpot(distr);
//fprintf(stderr,"%d\t%d\n",i,j);
};
//translate the rotation segment to the origin
x[i] -= x[start];
y[i] -= y[start];
z[i] -= z[start];
//store old vector for the rotation matrix below
ttx=x[i];
tty=y[i];
ttz=z[i];
//Perform the rotation on the selected segment
x[i] = (u*rx*rx + c)*ttx + (u*ry*rx - s*rz)*tty + (u*rz*rx + ry*s)*ttz;
y[i] = (u*rx*ry + rz*s)*ttx + (u*ry*ry + c)*tty + (u*rz*ry - rx*s)*ttz;
z[i] = (u*rx*rz - ry*s)*ttx + (u*ry*rz + rx*s)*tty + (u*rz*rz + c)*ttz;
//translate the rotation segment back to the original reference frame
x[i] += x[start];
y[i] += y[start];
z[i] += z[start];
//Final local nonbond energy
for(j=end2;j!=start;j+=direction)
{
distr = sqrt( (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]) + (z[i]-z[j])*(z[i]-z[j]) );
Enblocalf = Enblocalf + nonbondpot(distr);
//fprintf(stderr,"%d\t%d\n",i,j);
};
};
//Calculate the final local bond energy (NOTE: this cannot go in the rotation loop)
/* i=start;
while( i != end1 )
{
i=i+direction;
j=i-direction;
distr = sqrt( (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]) + (z[i]-z[j])*(z[i]-z[j]) );
Ebondf = Ebondf + bondpot(distr);
//fprintf(stderr,"%d\t%d\t%d\t%f\t%f\n",m,i,i-direction,distr,bondpot(distr));
};
*/
//Local bond and bond angle energy - assumes bond lengths don't change (unlike above commented out section)
Ebondf = Ebondf + localE(m);
Ef = Ei + (Ebondf - Ebondi) + (Enblocalf - Enblocali);
//Ef=Etot();
attemptpivot+=1;
if(Metropolis(Ei,Ef)==1)
{
acceptpivot+=1;
if( (acceptpivot%1000) == 0 ) //this insures that errors do not accumulate over time
{
currEtot = Etot();
};
}
else
{
//reject
for(j=0;j<N;++j)
{
x[j]=tx[j];
y[j]=ty[j];
z[j]=tz[j];
};
};
}
double Planet::Etotal(int i){
return Etot(i);
}
//initialize the polymer chain with one end at the origin
//and all nn bonds at the ground state, in the x-y plane
void initialize(void)
{
int i;
double a=1.0;
//for relatively big jumps
D=0.05; DC=1.0; DD=0.1;
//precalculations for chain length
invN=1.0/(1.0*N);
rootinvN = 1.0/sqrt(1.0*N);
//term used to set the FENE+LJ potential's minimum at 1.0
sigmaFENE = pow((0.5+sqrt(23.0/44.0)),(1.0/6.0));
//precalculation for the LJ potential
sigmaLJ=pow(0.5,1.0/6.0);
//term used to shift the LJ potential such that it is zero at r=1.0
shiftLJ = pow((1.0/Rcutnonbond),12.0) - 2.0*pow((1.0/Rcutnonbond),6.0);
//precalculations for the nn bond angle potentials
PI=2.0*acos(0.0);
ANG=PI;
COSANG=cos(ANG);
T=5.0;
//Dynamic Memory Allocation - this has to be done because an input file is used.
//x,y,z coordinates
x = malloc( N * sizeof(double) );
y = malloc( N * sizeof(double) );
z = malloc( N * sizeof(double) );
if ( (x == NULL) || (y == NULL) || (z == NULL) )
{
fprintf(stderr,"\nFailure to allocate memory for 'x,y, or z'. See 'initialize()'.\n");
exit(1);
};
//tx,ty,tz - used as temporary coordinates in many of the "move" functions
tx = malloc( N * sizeof(double) );
ty = malloc( N * sizeof(double) );
tz = malloc( N * sizeof(double) );
if ( (tx == NULL) || (ty == NULL) || (tz == NULL) )
{
fprintf(stderr,"\nFailure to allocate memory for 'tx,ty, or tz'. See 'initialize()'.\n");
exit(1);
};
//Initialize the tmp coordinates
for(i=0;i++;i<N)
{
tx[i]=0.0;
ty[i]=0.0;
tz[i]=0.0;
};
//Initializing the chain
//One end starts at the origin
x[0]=0.0;
y[0]=0.0;
z[0]=0.0;
//Initialize the rest of the chain
for(i=1;i<N;++i)
{
x[i]=x[i-1]+1.0;
y[i]=0.0;
z[i]=0.0;
};
currEtot=Etot();
currnonbondE=nonbondEnergy();
}
