double run_soft_sphere(double reduced_density, double temp) {
Functional f = SoftFluid(sigma, 1, 0);
const double mu = find_chemical_potential(OfEffectivePotential(f), temp, reduced_density*pow(2,-5.0/2.0));
printf("mu is %g for reduced_density = %g at temperature %g\n", mu, reduced_density, temp);
//printf("Filling fraction is %g with functional %s at temperature %g\n", reduced_density, teff);
//fflush(stdout);
temperature = temp;
//if (kT == 0) kT = ;1
Lattice lat(Cartesian(xmax,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid softspherepotential(gd);
softspherepotential.Set(soft_sphere_potential);
f = SoftFluid(sigma, 1, mu); // compute approximate energy with chemical potential mu
const double approx_energy = f(temperature, reduced_density*pow(2,-5.0/2.0))*xmax*ymax*zmax;
const double precision = fabs(approx_energy*1e-9);
f = OfEffectivePotential(SoftFluid(sigma, 1, mu) + ExternalPotential(softspherepotential));
static Grid *potential = 0;
potential = new Grid(gd);
*potential = softspherepotential - temperature*log(reduced_density*pow(2,-5.0/2.0)/(1.0*radius*radius*radius))*VectorXd::Ones(gd.NxNyNz); // Bad starting guess
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, temperature);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, temperature,
potential,
QuadraticLineMinimizer));
took("Setting up the variables");
for (int i=0; min.improve_energy(true) && i<100; i++) {
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(temperature, gd, *potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, reduced_density);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/radial-wca-%06.4f-%04.2f.dat", temp, reduced_density);
z_plot(plotname, Grid(gd, pow(2,5.0/2.0)*density));
free(plotname);
{
//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);
}
took("Plotting stuff");
printf("density %g gives ff %g for reduced_density = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, reduced_density, temp);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
double run_walls(double reduced_density, const char *name, Functional fhs, double teff) {
double kT = teff;
if (kT == 0) kT = 1;
Functional f = OfEffectivePotential(fhs);
const double zmax = width + 2*spacing;
Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint, f);
Grid potential(gd);
potential = pow(2,-5.0/2.0)*(reduced_density*constraint + 1e-4*reduced_density*VectorXd::Ones(gd.NxNyNz));
potential = -kT*potential.cwise().log();
const double approx_energy = fhs(kT, reduced_density*pow(2,-5.0/2.0))*dw*dw*width;
const double precision = fabs(approx_energy*1e-11);
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, kT,
&potential,
QuadraticLineMinimizer));
took("Setting up the variables");
if (strcmp(name, "hard") != 0 && false) {
printf("For now, SoftFluid doesn't work properly, so we're skipping the\n");
printf("minimization at temperature %g.\n", teff);
} else {
for (int i=0;min.improve_energy(false) && i<100;i++) {
}
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(kT, gd, potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, reduced_density);
z_plot(plotname, Grid(gd, density*pow(2,5.0/2.0)));
free(plotname);
took("Plotting stuff");
printf("density %g gives ff %g for reduced density = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, reduced_density, teff);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
double run_walls(double eta, const char *name, Functional fhs, double teff) {
//printf("Filling fraction is %g with functional %s at temperature %g\n", eta, name, teff);
//fflush(stdout);
double kT = teff;
if (kT == 0) kT = 1;
Functional f = OfEffectivePotential(fhs);
const double zmax = width + 2*spacing;
Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint, f);
// We reuse the potential, which should give us a better starting
// guess on each calculation.
static Grid *potential = 0;
if (strcmp(name, "hard") == 0) {
// start over for each potential
delete potential;
potential = 0;
}
if (!potential) {
potential = new Grid(gd);
*potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
*potential = -kT*potential->cwise().log();
}
// FIXME below I use the HS energy because of issues with the actual
// functional.
const double approx_energy = fhs(kT, eta/(4*M_PI/3))*dw*dw*width;
const double precision = fabs(approx_energy*1e-5);
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, kT,
potential,
QuadraticLineMinimizer));
took("Setting up the variables");
for (int i=0;min.improve_energy(false) && i<100;i++) {
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(kT, gd, *potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, eta);
z_plot(plotname, Grid(gd, 4*M_PI*density/3));
free(plotname);
{
GridDescription gdj = density.description();
double sep = gdj.dz*gdj.Lat.a3().norm();
int div = gdj.Nz;
int mid = int (div/2.0);
double Ntot_per_A = 0;
double mydist = 0;
for (int j=0; j<mid; j++){
Ntot_per_A += density(0,0,j)*sep;
mydist += sep;
}
double Extra_per_A = Ntot_per_A - eta/(4.0/3.0*M_PI)*width/2;
FILE *fout = fopen("papers/fuzzy-fmt/figs/wallsfillingfracInfo.txt", "a");
fprintf(fout, "walls%s-%04.2f.dat - If you want to match the bulk filling fraction of figs/walls%s-%04.2f.dat, than the number of extra spheres per area to add is %04.10f. So you'll want to multiply %04.2f by your cavity volume and divide by (4/3)pi. Then add %04.10f times the Area of your cavity to this number\n",
name, eta, name, eta, Extra_per_A, eta, Extra_per_A);
int wallslen = 20;
double Extra_spheres = (eta*wallslen*wallslen*wallslen/(4*M_PI/3) + Extra_per_A*wallslen*wallslen);
fprintf (fout, "For filling fraction %04.02f and walls of length %d you'll want to use %.0f spheres.\n\n", eta, wallslen, Extra_spheres);
fclose(fout);
}
{
//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);
}
took("Plotting stuff");
printf("density %g gives ff %g for eta = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, eta, teff);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
