double N_from_mu(Minimizer *min, Grid *potential, const Grid &constraint, double mu) {
Functional f = constrain(constraint, OfEffectivePotential(HS + IdealGas()
+ ChemicalPotential(mu)));
double Nnow = 0;
min->minimize(f, potential->description());
for (int i=0;i<numiters && min->improve_energy(false);i++) {
Grid density(potential->description(), EffectivePotentialToDensity()(1, potential->description(), *potential));
Nnow = density.sum()*potential->description().dvolume;
printf("Nnow is %g vs %g\n", Nnow, N);
fflush(stdout);
density.epsNativeSlice("papers/contact/figs/box.eps",
Cartesian(0,ymax+2,0), Cartesian(0,0,zmax+2),
Cartesian(0,-ymax/2-1,-zmax/2-1));
density.epsNativeSlice("papers/contact/figs/box-diagonal.eps",
Cartesian(xmax+2,0,zmax+2), Cartesian(0,ymax+2,0),
Cartesian(-xmax/2-1,-ymax/2-1,-zmax/2-1));
//sleep(3);
}
return Nnow;
}
void run_with_eta(double eta, const char *name, Functional fhs) {
// Generates a data file for the pair distribution function, for filling fraction eta
// and distance of first sphere from wall of z0. Data saved in a table such that the
// columns are x values and rows are z1 values.
printf("Now starting run_with_eta with eta = %g name = %s\n",
eta, name);
Functional f = OfEffectivePotential(fhs + IdealGas());
double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
f = OfEffectivePotential(fhs + IdealGas()
+ ChemicalPotential(mu));
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width));
GridDescription gd(lat, dx);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinsphere);
f = constrain(constraint, f);
potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
potential = -potential.cwise().log();
const double approx_energy = (fhs + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*uipow(width,3);
const double precision = fabs(approx_energy*1e-10);
//printf("Minimizing to %g absolute precision...\n", precision);
{ // Put mimizer in block so as to free it when we finish minimizing to save memory.
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, 1,
&potential,
QuadraticLineMinimizer));
for (int i=0;min.improve_energy(true) && i<100;i++) {
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
took("Doing the minimization");
}
Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
Grid gsigma(gd, gSigmaA(1.0)(1, gd, density));
Grid nA(gd, ShellConvolve(2)(1, density)/(4*M_PI*4));
Grid n3(gd, StepConvolve(1)(1, density));
Grid nbar_sokolowski(gd, StepConvolve(1.6)(1, density));
nbar_sokolowski /= (4.0/3.0*M_PI*ipow(1.6, 3));
// Create the walls directory if it doesn't exist.
if (mkdir("papers/pair-correlation/figs/walls", 0777) != 0 && errno != EEXIST) {
// We failed to create the directory, and it doesn't exist.
printf("Failed to create papers/pair-correlation/figs/walls: %s",
strerror(errno));
exit(1); // fail immediately with error code
}
// here you choose the values of z0 to use
// dx is the resolution at which we compute the density.
char *plotname = new char[4096];
for (double z0 = 2.1; z0 < 4.5; z0 += 2.1) {
// For each z0, we now pick one of our methods for computing the
// pair distribution function:
for (int version = 0; version < numplots; version++) {
sprintf(plotname,
"papers/pair-correlation/figs/triplet%s-%s-%04.2f-%1.2f.dat",
name, fun[version], eta, z0);
FILE *out = fopen(plotname,"w");
FILE *xfile = fopen("papers/pair-correlation/figs/triplet-x.dat","w");
FILE *zfile = fopen("papers/pair-correlation/figs/triplet-z.dat","w");
// the +1 for z0 and z1 are to shift the plot over, so that a sphere touching the wall
// is at z = 0, to match with the monte carlo data
const Cartesian r0(0,0,z0);
for (double x = 0; x < 4; x += dx) {
for (double z1 = -4; z1 <= 9; z1 += dx) {
const Cartesian r1(x,0,z1);
double g2 = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out, "%g\t", g3);
fprintf(xfile, "%g\t", x);
fprintf(zfile, "%g\t", z1);
}
fprintf(out, "\n");
fprintf(xfile, "\n");
fprintf(zfile, "\n");
}
fclose(out);
fclose(xfile);
fclose(zfile);
}
}
delete[] plotname;
took("Dumping the triplet dist plots");
const double ds = 0.01; // step size to use in path plots, FIXME increase for publication!
const double delta = .1; //this is the value of radius of the
//particle as it moves around the contact
//sphere on its path
char *plotname_path = new char[4096];
for (int version = 0; version < numplots; version++) {
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet%s-path-%s-%04.2f.dat",
name, fun[version], eta);
FILE *out_path = fopen(plotname_path, "w");
if (!out_path) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-back-contact-%s-%04.2f.dat",
fun[version], eta);
FILE *out_back = fopen(plotname_path, "w");
if (!out_back) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
fprintf(out_path, "# unused\tg3\tz\tx\n");
fprintf(out_back, "# unused\tg3\tz\tx\n");
const Cartesian r0(0,0, 2.0+delta);
const double max_theta = M_PI*2.0/3;
for (double z = 7; z >= 2*(2.0 + delta); z-=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double z = -7; z <= -(2.0 + delta); z+=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
const double dtheta = ds/2;
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, (2.0+delta)*(1+cos(theta)));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0,-(2.0+delta)*cos(theta));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double x = (2.0+delta)*sqrt(3)/2; x<=6; x+=ds){
const Cartesian r1(x, 0, 1.0+delta/2);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
fclose(out_path);
fclose(out_back);
}
for (int version = 0; version < numplots; version++) {
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-path-inbetween-%s-%04.2f.dat",
fun[version], eta);
FILE *out_path = fopen(plotname_path, "w");
if (!out_path) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-back-inbetween-%s-%04.2f.dat",
fun[version], eta);
FILE *out_back = fopen(plotname_path, "w");
if (!out_back) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
fprintf(out_path, "# unused\tg3\tz\tx\n");
fprintf(out_back, "# unused\tg3\tz\tx\n");
const Cartesian r0(0,0, 4.0+2*delta);
const double max_theta = M_PI;
for (double z = 11; z >= 3*(2.0 + delta); z-=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double z = -10; z <= -(2.0 + delta); z+=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
const double dtheta = ds/2;
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, (2.0+delta)*(2+cos(theta)));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, -(2.0+delta)*cos(theta));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double x = 0; x>=-6; x-=ds){
const Cartesian r1(x, 0, 2.0+delta);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
fclose(out_path);
fclose(out_back);
}
delete[] plotname_path;
}
int main(int, char **) {
for (double eta = 0.3; eta < 0.35; eta += 0.1) {
// Generates a data file for the pair distribution function, for filling fraction eta
// and distance of first sphere from wall of z0. Data saved in a table such that the
// columns are x values and rows are z1 values.
printf("Now starting sphere_with_wall with eta = %g\n",eta);
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width+2*spacing));
GridDescription gd(lat, dx); //the resolution here dramatically affects our memory use
Functional f = OfEffectivePotential(WB + IdealGas());
double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
f = OfEffectivePotential(WB + IdealGas()
+ ChemicalPotential(mu));
Grid potential(gd);
Grid constraint(gd);
constraint.Set(*notinwall_or_sphere);
constraint.epsNativeSlice("myconstraint.eps",
Cartesian(0, 0, 2*(width+2*spacing)),
Cartesian(2*width, 0, 0),
Cartesian(0, 0, 0));
f = constrain(constraint, f);
potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
potential = -potential.cwise().log();
const double approx_energy = (WB + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*dw*dw*width;
const double precision = fabs(approx_energy*1e-4);
//printf("Minimizing to %g absolute precision...\n", precision);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, 1,
&potential,
QuadraticLineMinimizer));
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
for (int i=0; min.improve_energy(true) && i<100; i++) {
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
char *plotname = new char[1024];
sprintf(plotname, "papers/pair-correlation/figs/walls/wallsWB-sphere-dft-%04.2f.dat", eta);
pair_plot(plotname, density);
delete[] plotname;
char *plotname_path = new char[1024];
sprintf(plotname_path, "papers/pair-correlation/figs/walls/wallsWB-sphere-dft-path-%04.2f.dat", eta);
path_plot(plotname_path, density, constraint);
delete[] plotname_path;
fflush(stdout);
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
fflush(stdout);
}
fflush(stdout);
// Just create this file so make knows we have run.
if (!fopen("papers/pair-correlation/figs/walls_sphere.dat", "w")) {
printf("Error creating walls.dat!\n");
return 1;
}
fflush(stdout);
return 1;
}
int main(int argc, char *argv[]) {
if (argc == 5) {
if (sscanf(argv[1], "%lg", &xmax) != 1) {
printf("Got bad x argument: %s\n", argv[1]);
return 1;
}
if (sscanf(argv[2], "%lg", &ymax) != 1) {
printf("Got bad y argument: %s\n", argv[2]);
return 1;
}
if (sscanf(argv[3], "%lg", &zmax) != 1) {
printf("Got bad z argument: %s\n", argv[3]);
return 1;
}
if (sscanf(argv[4], "%lg", &N) != 1) {
printf("Got bad N argument: %s\n", argv[4]);
return 1;
}
using_default_box = false;
printf("Box is %g x %g x %g hard sphere diameters, and it holds %g of them\n", xmax, ymax, zmax, N);
}
char *datname = (char *)malloc(1024);
sprintf(datname, "papers/contact/figs/box-%02.0f,%02.0f,%02.0f-%02.0f-energy.dat", xmax, ymax, zmax, N);
FILE *o = fopen(datname, "w");
const double myvolume = (xmax+2)*(ymax+2)*(zmax+2);
const double meandensity = N/myvolume;
Functional f = OfEffectivePotential(HS + IdealGas());
double mu = find_chemical_potential(f, 1, meandensity);
f = OfEffectivePotential(HS + IdealGas()
+ ChemicalPotential(mu));
Lattice lat(Cartesian(xmax+3,0,0), Cartesian(0,ymax+3,0), Cartesian(0,0,zmax+3));
GridDescription gd(lat, 0.05);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
took("Setting the constraint");
printf("xmax = %g\nymax = %g\nzmax = %g\nmeandensity=%g\n", xmax, ymax, zmax, meandensity);
f = constrain(constraint, f);
constraint.epsNativeSlice("papers/contact/figs/box-constraint.eps",
Cartesian(0,ymax+4,0), Cartesian(0,0,zmax+4),
Cartesian(0,-ymax/2-2,-zmax/2-2));
printf("Constraint has become a graph!\n");
potential = meandensity*constraint + 1e-4*meandensity*VectorXd::Ones(gd.NxNyNz);
potential = -potential.cwise().log();
Minimizer min = Precision(1e-6,
PreconditionedConjugateGradient(f, gd, 1,
&potential,
QuadraticLineMinimizer));
double mumax = mu, mumin = mu, dmu = 4.0/N;
double Nnow = N_from_mu(&min, &potential, constraint, mu);
const double fraccuracy = 1e-3;
if (fabs(Nnow/N - 1) > fraccuracy) {
if (Nnow > N) {
while (Nnow > N) {
mumin = mumax;
mumax += dmu;
dmu *= 2;
Nnow = N_from_mu(&min, &potential, constraint, mumax);
// Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
// density = EffectivePotentialToDensity()(1, gd, potential);
// density.epsNativeSlice("papers/contact/figs/box.eps",
// Cartesian(0,ymax+2,0), Cartesian(0,0,zmax+2),
// Cartesian(0,-ymax/2-1,-zmax/2-1));
// density.epsNativeSlice("papers/contact/figs/box-diagonal.eps",
// Cartesian(xmax+2,0,zmax+2), Cartesian(0,ymax+2,0),
// Cartesian(-xmax/2-1,-ymax/2-1,-zmax/2-1));
printf("mumax %g gives N %g\n", mumax, Nnow);
took("Finding N from mu");
}
printf("mu is between %g and %g\n", mumin, mumax);
} else {
while (Nnow < N) {
mumax = mumin;
if (mumin > dmu) {
mumin -= dmu;
dmu *= 2;
} else if (mumin > 0) {
mumin = -mumin;
} else {
mumin *= 2;
}
Nnow = N_from_mu(&min, &potential, constraint, mumin);
// density = EffectivePotentialToDensity()(1, gd, potential);
// density.epsNativeSlice("papers/contact/figs/box.eps",
// Cartesian(0,ymax+2,0), Cartesian(0,0,zmax+2),
// Cartesian(0,-ymax/2-1,-zmax/2-1));
// density.epsNativeSlice("papers/contact/figs/box-diagonal.eps",
// Cartesian(xmax+2,0,zmax+2), Cartesian(0,ymax+2,0),
// Cartesian(-xmax/2-1,-ymax/2-1,-zmax/2-1));
printf("mumin %g gives N %g\n", mumin, Nnow);
took("Finding N from mu");
}
printf("mu is between %g and %g\n", mumin, mumax);
}
while (fabs(N/Nnow-1) > fraccuracy) {
mu = 0.5*(mumin + mumax);
Nnow = N_from_mu(&min, &potential, constraint, mu);
// density = EffectivePotentialToDensity()(1, gd, potential);
// density.epsNativeSlice("papers/contact/figs/box.eps",
// Cartesian(0,ymax+2,0), Cartesian(0,0,zmax+2),
// Cartesian(0,-ymax/2-1,-zmax/2-1));
// density.epsNativeSlice("papers/contact/figs/box-diagonal.eps",
// Cartesian(xmax+2,0,zmax+2), Cartesian(0,ymax+2,0),
// Cartesian(-xmax/2-1,-ymax/2-1,-zmax/2-1));
printf("Nnow is %g vs %g with mu %g\n", Nnow, N, mu);
took("Finding N from mu");
if (Nnow > N) {
mumin = mu;
} else {
mumax = mu;
}
}
}
printf("N final is %g (vs %g) with mu = %g\n", Nnow, N, mu);
double energy = min.energy();
printf("Energy is %.15g\n", energy);
Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
double mean_contact_density = ContactDensitySimplest(1.0).integral(1, density)/myvolume;
fprintf(o, "%g\t%g\t%g\t%.15g\t%.15g\n", xmax, ymax, zmax, energy, mean_contact_density);
Grid energy_density(gd, f(1, gd, potential));
Grid contact_density(gd, ContactDensitySimplest(1.0)(1, gd, density));
Grid n0(gd, ShellConvolve(1)(1, density));
Grid wu_contact_density(gd, FuWuContactDensity(1.0)(1, gd, density));
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/contact/figs/box-100c--%02.0f,%02.0f,%02.0f-%02.0f.dat", xmax, ymax, zmax, N);
plot_grids_100_center(plotname, density, energy_density, contact_density);
sprintf(plotname, "papers/contact/figs/box-100s--%02.0f,%02.0f,%02.0f-%02.0f.dat", xmax, ymax, zmax, N);
plot_grids_100_side(plotname, density, energy_density, contact_density);
sprintf(plotname, "papers/contact/figs/box-110c--%02.0f,%02.0f,%02.0f-%02.0f.dat", xmax, ymax, zmax, N);
plot_grids_110(plotname, density, energy_density, contact_density);
sprintf(plotname, "papers/contact/figs/box-x-%02.0f,%02.0f,%02.0f-%02.0f.dat", xmax, ymax, zmax, N);
x_plot(plotname, density, energy_density, contact_density, wu_contact_density);
free(plotname);
density.epsNativeSlice("papers/contact/figs/box.eps",
Cartesian(0,ymax+2,0), Cartesian(0,0,zmax+2),
Cartesian(0,-ymax/2-1,-zmax/2-1));
density.epsNativeSlice("papers/contact/figs/box-diagonal.eps",
Cartesian(xmax+2,0,zmax+2), Cartesian(0,ymax+2,0),
Cartesian(-xmax/2-1,-ymax/2-1,-zmax/2-1));
took("Plotting stuff");
fclose(o);
}
