//Creating matrix for calculations with Armadillo
mat mainMatrix(int dimensions, double step_length, double(*potential)(double,int,double), double omega_r)
{
double diagonal_fixed = 2./(step_length*step_length);
double off_diagonal = -1./(step_length*step_length);
mat A(dimensions, dimensions, fill::zeros);
A(0,0) = diagonal_fixed+potential(step_length, 1, omega_r);
A(0,1) = off_diagonal;
A(dimensions-1,dimensions-1) = diagonal_fixed + potential(step_length,dimensions,omega_r);
A(dimensions-1, dimensions-2) = off_diagonal;
for(int i = 1; i < dimensions-1; i++){
A(i,i) = diagonal_fixed + potential(step_length,i+1,omega_r);
A(i,i+1) = off_diagonal;
A(i,i-1) = off_diagonal;
}
return A;
}
void MainWindow::on_saveButton_clicked()
{
int size = nc*3/4;
char potentialFilename[]="out/potential-%1.txt";
char concFilename[]="out/ni_ne-%1.txt";
//Save potential
QVector<double> r(size), potential(size);
for (int i=0; i<size; ++i)
{
r[i] = r_array[i];
potential[i] = phi[i];
}
saveToFile(r,potential,QString(potentialFilename).arg((t/dt)));
//Save concentration of the electrons and ions
QVector<double> /*r(size),*/ ne(size),ni(size);
for (int i=0; i<size; ++i)
{
r[i] = r_array[i];
ne[i] = srho[0][i];
ni[i] = srho[1][i];
}
saveToFile2(r,ne,ni, QString(concFilename).arg((t/dt)));
}
double theory_t::hamiltonian(conf_t &conf,double t)
{
double K=conf.kinetic_energy();
double V=potential(conf.X,t);
return K+V;
}
//------------------------------------------------------------------------------
CoulombInteractionNucleus::CoulombInteractionNucleus(Config *cfg, const Grid &grid):
Potential(cfg, grid)
{
double b = 1;
double Z = 2;
try{
b = cfg->lookup("oneBodyPotential.coulombInteractionNucleus.b");
Z = cfg->lookup("oneBodyPotential.coulombInteractionNucleus.Z");
} catch (const SettingNotFoundException &nfex) {
cerr << "CoulombInteractionNucleus::CoulombInteractionNucleus(Config *cfg)"
<< "::Error reading from config object." << endl;
}
potential = vec(nGrid);
// Setting the potential
for(int j=0; j<nGrid; j++){
vec r = grid.at(j);
double r2 = 0;
for(int i=0; i<dim; i++){
r2 += r(i)*r(i);
}
potential(j) = - Z/sqrt(r2 + b*b);
}
}
double a3_pot(double r)
{
double V_0 = -60.0 * pow(10,6),
r_0 = 3.0 * pow(10,-15),
a_0 = 0.4 * pow(10,-15);
return potential(r, r_0, a_0, V_0);
}
double find_minimum(double *x, double *y, int i) {
double dx = 0.001;
double xmax = 1.0;
double xcur = 0.0;
double pcur = 0.0;
double xopt = 0.0;
double popt = 0.0;
while (dx > 1e-9) {
while (xcur < xmax) {
pcur = potential(x, y, i, xcur);
// printf("%f, %f, %f\n", xcur, y[i], pcur);
if (pcur < popt) {
xopt = xcur;
popt = pcur;
}
xcur += dx;
}
xcur = xopt-dx;
xmax = xopt+dx;
dx /= 10.0;
}
if (xopt > 1.0) {
xopt -= 1.0;
} else if (xopt < 0.0) {
xopt += 1.0;
}
return xopt;
}
/*Function of the 1th (radial) momentum component differential equation for the geodesics.
${p1}^{dot} = f1(x^{\alpha},p^{\alpha})$.*/
mydbl geodesic_equation_r(gsl_spline *spline1, gsl_interp_accel *acc1, gsl_spline *spline2, gsl_interp_accel *acc2, mydbl p0, mydbl pr, mydbl x0, mydbl r)
{
double t = (double)(1.0*x0/C);
mydbl a = (mydbl) 1.0*interpolator(spline1, t, acc1);
mydbl adot = (mydbl) 1.0*interpolator(spline2, t, acc2);
mydbl f = - (der_potential(r)*p0*p0)/(a*a*C*C*(1.0 - 2.0*potential(r)/(C*C))) - (2.0*adot*p0*pr)/(C*a) + (der_potential(r)/(C*C))*(pr*pr)/(1.0 - 2.0*potential(r)/(C*C));
return f;
}
int main(int, char **) {
FILE *o = fopen("paper/figs/constrained-water.dat", "w");
Functional f = OfEffectivePotential(SaftFluidSlow(water_prop.lengthscale,
water_prop.epsilonAB, water_prop.kappaAB,
water_prop.epsilon_dispersion,
water_prop.lambda_dispersion, water_prop.length_scaling, 0));
double mu_satp = find_chemical_potential(f, water_prop.kT,
water_prop.liquid_density);
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.1);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint,
OfEffectivePotential(SaftFluidSlow(water_prop.lengthscale,
water_prop.epsilonAB, water_prop.kappaAB,
water_prop.epsilon_dispersion,
water_prop.lambda_dispersion, water_prop.length_scaling, mu_satp)));
Minimizer min = Precision(0, PreconditionedConjugateGradient(f, gd, water_prop.kT, &potential,
QuadraticLineMinimizer));
potential = water_prop.liquid_density*constraint
+ water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
//potential = water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
potential = -water_prop.kT*potential.cwise().log();
const int numiters = 50;
for (int i=0;i<numiters && min.improve_energy(true);i++) {
fflush(stdout);
Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
density.epsNative1d("paper/figs/1d-constrained-plot.eps",
Cartesian(0,0,0), Cartesian(0,0,zmax),
water_prop.liquid_density, 1, "Y axis: , x axis: ");
}
min.print_info();
double energy = min.energy()/width/width;
printf("Energy is %.15g\n", energy);
double N = 0;
{
Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) N += density[i]*gd.dvolume;
}
N = N/width/width;
printf("N is %.15g\n", N);
Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
density.epsNative1d("paper/figs/1d-constrained-plot.eps", Cartesian(0,0,0), Cartesian(0,0,zmax), water_prop.liquid_density, 1, "Y axis: , x axis: ");
//potential.epsNative1d("hard-wall-potential.eps", Cartesian(0,0,0), Cartesian(0,0,zmax), 1, 1);
fclose(o);
}
bool finalState(HyperRectangle* rect)
{
double points[16][4] =
{
{rect->dims[0].min, rect->dims[1].min, rect->dims[2].min, rect->dims[3].min},
{rect->dims[0].min, rect->dims[1].min, rect->dims[2].min, rect->dims[3].max},
{rect->dims[0].min, rect->dims[1].min, rect->dims[2].max, rect->dims[3].min},
{rect->dims[0].min, rect->dims[1].min, rect->dims[2].max, rect->dims[3].max},
{rect->dims[0].min, rect->dims[1].max, rect->dims[2].min, rect->dims[3].min},
{rect->dims[0].min, rect->dims[1].max, rect->dims[2].min, rect->dims[3].max},
{rect->dims[0].min, rect->dims[1].max, rect->dims[2].max, rect->dims[3].min},
{rect->dims[0].min, rect->dims[1].max, rect->dims[2].max, rect->dims[3].max},
{rect->dims[0].max, rect->dims[1].min, rect->dims[2].min, rect->dims[3].min},
{rect->dims[0].max, rect->dims[1].min, rect->dims[2].min, rect->dims[3].max},
{rect->dims[0].max, rect->dims[1].min, rect->dims[2].max, rect->dims[3].min},
{rect->dims[0].max, rect->dims[1].min, rect->dims[2].max, rect->dims[3].max},
{rect->dims[0].max, rect->dims[1].max, rect->dims[2].min, rect->dims[3].min},
{rect->dims[0].max, rect->dims[1].max, rect->dims[2].min, rect->dims[3].max},
{rect->dims[0].max, rect->dims[1].max, rect->dims[2].max, rect->dims[3].min},
{rect->dims[0].max, rect->dims[1].max, rect->dims[2].max, rect->dims[3].max},
};
double maxPotential = potential(points[0][0], points[0][1], points[0][2], points[0][3]);
for (int i = 1; i < 16; ++i)
{
double p = potential(points[i][0], points[i][1], points[i][2], points[i][3]);
if (p > maxPotential)
maxPotential = p;
}
hyperrectangle_to_file(f_final, rect,2);
printf("---> potential of final state = %f\n", maxPotential);
return maxPotential < 1;
}
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 solve_even(double h, double x_right, double E){
fp = fopen( "output.txt", "w" );
/* boundary condition */
x = x_left;
psi[0] = 1;
psi[1] = 1 + pow(h, 2)/2*potential(x_left, E) + pow(h, 4)/24*(2 + pow(potential(x_left, E), 2));
printf( "%f %f\n%f %f\n ", x_left, psi[0], x_left + h, psi[1] );
fprintf(fp, "%e %e\n%e %e\n ", x_left, psi[0], x_left + h, psi[1]);
/* recursion */
while (x <= x_right) {
x += h;
psi[2] = ((2 + 5 * pow(h, 2) * potential(x, E)/6.0)*psi[1] - (1.0 - pow(h, 2) * potential(x - h, E)/12.0)*psi[0])/(1 - pow(h, 2) * potential(x + h, E)/12.0);
printf("%f %f\n ", x + h, psi[2]);
fprintf(fp, "%e %e\n ", x+h, psi[2]);
psi[0] = psi[1];
psi[1] = psi[2];
}
fclose( fp );
return 0;
}
int
mem_pool_alloc(struct mem_pool * pool, size_t size) {
size_t sz = size >= ND_MIN_SZ ? size : ND_MIN_SZ;
sz = IS_POW2(sz) ? sz : NEXT_POW2(sz);
printf("aligning requested size %d to %d...\n", size, sz);
unsigned order = pool->order + 4 - LOG2(sz);
printf("requested order is %d\n", order);
unsigned i = 0, rval = 0;
if (!potential(pool, i, order)) {
return -1;
}
for (;;) {
printf("checking node %d ...\n", i);
struct node * n = &pool->nl[i];
if (n->status == FREE && HEIGHT(i) == order) {
n->status = FULL;
mark_parent(pool, i);
while (i < pool->valid_nr) {
rval = i;
i = LEFT(i);
}
return rval - LEFT_LEAF(pool->order); //good
} else if (potential(pool, LEFT(i), order)) {
i = LEFT(i);
} else if (potential(pool, RIGHT(i), order)) {
i = RIGHT(i);
} else {
break;
}
}
return -1;
}
//Function utilizing the function tqli() in lib.cpp to calculate eigenvalues and eigenvectors
void tqliEigensolver(double *off_diagonal, double *diagonal, double **output_matrix, int n, double step_length,
double omega_r,double(*potential)(double,int,double))
{
double constant_diagonal = 2./(step_length*step_length);
double constant_off_diagonal = -1./(step_length*step_length);
for(int i = 0; i < n; i++){
diagonal[i] = constant_diagonal+potential(step_length,i+1,omega_r);
off_diagonal[i] = constant_off_diagonal;
output_matrix[i][i] = 1;
for(int j = i + 1; j < n; j++){
output_matrix[i][j] = 0;
}
}
tqli(diagonal, off_diagonal, n, output_matrix);
}
int PlasmaBunch::interaction(int m, int sum){
register int i, j,k;
static Vector_3 r;
int ret=Plasma::interaction(m,sum);
// now interacting with bunch particles
int type=0; // ion-ion
double dEcoul,dEpotent,dQuant;
double df;
for(i=0;i<(m<0 ? n : m+1);i++){
if(i>=ni)type|=0x1;// setting electron-? interaction type
else type&=0x2;// setting ion-? interaction type
if(is_ion)type&=0x1; // setting ?-ion interaction type
else type|=0x2;// setting ?-electron interaction type
for(j=0;j<nb;j++){
for(k=0;k<3;k++){ // determining the closest
//distance and correspondent direction
r[k]=xx[i][k]-xb[j][k];
if(r[k]>L/2)r[k]-=L;
if(r[k]<-L/2)r[k]+=L;
}
double R=r.norm();
if(R<1e-20)printf("Got small distance to bunch (%d,b%d) !\n",i,j);
r/=R;
dEcoul=qb/R;
df=potential(type,R,dEpotent,dQuant);
for(k=0;k<3;k++){ // to avoid vector copying
f[i][k]+=df*r[k];
//f[j][k]-=df*r[k];
}
Ecoul+=dEcoul;
Quant+=dQuant;
Epotent+=dEpotent;
}
}
return ret;
}
int main(int argc,char **argv)
{
int i,n=100;
double x0 = 0.75;
for (i=0 ; i<n ; i++)
{
double x = i/((double)(n-1));
printf("%f %f %f\n",
x,
potential(x,x0),
potential_derivative(x,x0));
}
return EXIT_SUCCESS;
}
bool shouldStop(double state[NUM_DIMS], double simTime, void* p)
{
bool rv = false;
double pot = potential(state[0], state[1], state[2], state[3]);
double maxTime = 2.0;
if (pot < 1)
{
rv = true;
double* stopTime = (double*)p;
*stopTime = simTime;
}
if (simTime >= maxTime)
{
rv = true;
double* stopTime = (double*)p;
*stopTime = -1;
}
return rv;
}
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;
}
pair<Cost,Flow> mincost(Index s, Index t, Flow f = InfCapacity, bool bellmanFord = false)
{
int n = g.size();
vector<Cost> dist(n);
vector<Index> prev(n);
vector<Index> prevEdge(n);
pair<Cost,Flow> total = make_pair(0, 0);
vector<Cost> potential(n);
while(f > 0)
{
fill(dist.begin(), dist.end(), InfCost);
if(bellmanFord || total.second == 0)
{
dist[s] = 0;
for(int k=0; k<n; k++)
{
bool update = false;
for(int i=0; i<n; i++)
if(dist[i] != InfCost)
for(Index ei = 0; ei < (Index)g[i].size(); ei ++)
{
const Edge &e = g[i][ei];
if(e.capacity <= 0) continue;
Index j = e.to;
Cost d = dist[i] + e.cost;
if(dist[j] > d )
{
dist[j] = d;
prev[j] = i;
prevEdge[j] = ei;
update = true;
}
}
if(!update) break;
}
}
else
{
vector<bool> vis(n);
priority_queue<pair<Cost,Index> > q;
q.push(make_pair(-0, s));
dist[s] = 0;
while(!q.empty())
{
Index i = q.top().second;
q.pop();
if(vis[i]) continue;
vis[i] = true;
for(Index ei = 0; ei < (Index)g[i].size(); ei ++)
{
const Edge &e = g[i][ei];
if(e.capacity <= 0) continue;
Index j = e.to;
Cost d = dist[i] + e.cost + potential[i] - potential[j];
if(d < dist[i]) d = dist[i];
if(dist[j] > d)
{
dist[j] = d;
prev[j] = i;
prevEdge[j] = ei;
q.push(make_pair(-d, j));
}
}
}
}
if(dist[t] == InfCost) break;
if(!bellmanFord) for(Index i = 0; i < n; i ++) potential[i] += dist[i];
Flow d = f;
Cost distt = 0;
for(Index v = t; v != s; )
{
Index u = prev[v];
const Edge &e = g[u][prevEdge[v]];
d = min(d, e.capacity);
distt += e.cost;
v = u;
}
f -= d;
total.first += d * distt;
total.second += d;
for(Index v = t; v != s; v = prev[v])
{
Edge &e = g[prev[v]][prevEdge[v]];
e.capacity -= d;
g[e.to][e.rev].capacity += d;
}
}
return total;
}
double surface_tension(Minimizer min, Functional f0, LiquidProperties prop,
bool verbose, const char *plotname) {
int numptspersize = 100;
int size = 64;
const int gas_size = 10;
Lattice lat(Cartesian(1,0,0), Cartesian(0,1,0), Cartesian(0,0,size*prop.lengthscale));
GridDescription gd(lat, 1, 1, numptspersize*size);
Grid potential(gd);
// Set the density to range from vapor to liquid
const double Veff_liquid = -prop.kT*log(prop.liquid_density);
const double Veff_gas = -prop.kT*log(prop.vapor_density);
for (int i=0; i<gd.NxNyNz*gas_size/size; i++) potential[i] = Veff_gas;
for (int i=gd.NxNyNz*gas_size/size; i<gd.NxNyNz; i++) potential[i] = Veff_liquid;
// Enable the following line for debugging...
//f0.run_finite_difference_test("f0", prop.kT, potential);
min.minimize(f0, gd, &potential);
while (min.improve_energy(verbose))
if (verbose) {
printf("Working on liberated interface...\n");
fflush(stdout);
}
const double Einterface = f0.integral(prop.kT, potential);
double Ninterface = 0;
Grid interface_density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) Ninterface += interface_density[i]*gd.dvolume;
if (verbose) printf("Got interface energy of %g.\n", Einterface);
for (int i=0; i<gd.NxNyNz; i++) potential[i] = Veff_gas;
min.minimize(f0, gd, &potential);
while (min.improve_energy(verbose))
if (verbose) {
printf("Working on gas...\n");
fflush(stdout);
}
const double Egas = f0.integral(prop.kT, potential);
double Ngas = 0;
{
Grid density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) Ngas += density[i]*gd.dvolume;
}
for (int i=0; i<gd.NxNyNz; i++) potential[i] = Veff_liquid;
if (verbose) {
printf("\n\n\nWorking on liquid...\n");
fflush(stdout);
}
min.minimize(f0, gd, &potential);
while (min.improve_energy(verbose))
if (verbose) {
printf("Working on liquid...\n");
fflush(stdout);
}
const double Eliquid = f0.integral(prop.kT, potential);
double Nliquid = 0;
{
Grid density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) Nliquid += density[i]*gd.dvolume;
}
const double X = Ninterface/Nliquid; // Fraction of volume effectively filled with liquid.
const double surface_tension = (Einterface - Eliquid*X - Egas*(1-X))/2;
if (verbose) {
printf("\n\n");
printf("interface energy is %.15g\n", Einterface);
printf("gas energy is %.15g\n", Egas);
printf("liquid energy is %.15g\n", Eliquid);
printf("Ninterface/liquid/gas = %g/%g/%g\n", Ninterface, Nliquid, Ngas);
printf("X is %g\n", X);
printf("surface tension is %.10g\n", surface_tension);
}
if (plotname)
interface_density.Dump1D(plotname, Cartesian(0,0,0),
Cartesian(0,0,size*prop.lengthscale));
return surface_tension;
}
int Plasma::interaction(int m, int sum){
register int i, j,k;
static Vector_3 r;
//static Vector_3 df;
int type=0; // ion-ion
for(i=(m<0 ? 0 : m);i<n;i++){
for(k=0;k<3;k++){
f[i][k]=0; // reducing to elementary cell
if(x[i][k]>0)xx[i][k]=amod1(x[i][k]+L/2,L)-L/2;
else xx[i][k]=amod1(x[i][k]-L/2,L)+L/2;
}
if(m>=0)break;
}
Quant=Ecoul=0;
double dEcoul,dEpotent,dQuant;
double df;
if(!is_matr || m<0)Epotent=0;
for(i=0;i<(m<0 ? n : m+1);i++){
if(i>=ni)type|=0x1;// setting electron-? interaction type
type&=0x1; // setting ?-ion interaction type
for(j=((m<0 || i==m) ? i+1: m); j<n;j++){
if(j>=ni)type|=0x2;// setting ?-electron interaction type
//r=xx[i]-xx[j];
for(k=0;k<3;k++){ // determining the closest
//distance and correspondent direction
r[k]=xx[i][k]-xx[j][k];
if(r[k]>L/2)r[k]-=L;
if(r[k]<-L/2)r[k]+=L;
}
double R=r.norm();
if(R<1e-20){
printf("Got small distance (%d,%d) !\n",i,j);
}
r/=R;
dEcoul=-1/R;
if(type==ELCELC || type ==IONION){
dEcoul=-dEcoul;
if(write_distr){
if(non_symm && type==IONION)DRRpp.point(R,1.);
else DRRee.point(R,1.);
}
}
else if(write_distr)DRRep.point(R,1.);
df=potential(type,R,dEpotent,dQuant);
///df=PotentialKELBG(type,R,dEpotent,dQuant);
//f[i]+=df;
//f[j]-=df;
for(k=0;k<3;k++){ // to avoid vector copying
f[i][k]+=df*r[k];
f[j][k]-=df*r[k];
}
Ecoul+=dEcoul;
Quant+=dQuant;
if(is_matr && m>=0)Epotent+=dEpotent-(*umatr)(i,j);
else Epotent+=dEpotent;
if(is_matr){
if(m>=0){
int l=(i< m ? i : j);
(*umatr)(l,l)=(*umatr)(i,j); //(l,l) used for storing temporary
//fucktmp[l]=(*umatr)(i,j);
//printf("%d <- (%d, %d)[%f]\n",l,i,j,fucktmp[l]);
}
(*umatr)(i,j)=dEpotent;
}
if(m>=0 && i!=m)break;
}
}
if(is_matr && m>=0 && sum){
Epotent=0;
for(i=0;i<n;i++){
for(j=i+1;j<n;j++){
Epotent+=(*umatr)(i,j);
}
}
}
return 0;
}
/*To set the initial value of pr, it must hold $g_{\mu\nu}p^{\mu}p^{\nu} = 0$.
This factor multiplies p0 to guarantee that p1 fulfill the null geodesic condition.*/
mydbl condition_factor(mydbl r, double a)
{
return (mydbl)(1.0/a)*sqrtl((1.0+2.0*potential(r)/(C*C))/(1.0 - 2.0*potential(r)/(C*C)));
}
void schroedinger(int n,double x,double y[2],double yp[2])
{
/* Calculate first order derivatives for R-K4 algorithm*/
yp[0] = y[1];
yp[1] = 5.1363071e13 * 0.5110e6 * (potential(x) - E) * y[0];
}
int main(int argc, char *argv[]) {
if (argc > 1) {
if (sscanf(argv[1], "%lg", &diameter) != 1) {
printf("Got bad argument: %s\n", argv[1]);
return 1;
}
diameter *= nm;
using_default_diameter = false;
printf("Diameter is %g bohr\n", diameter);
}
const double ptransition =(3.0*M_PI-4.0)*(diameter/2.0)/2.0;
const double dmax = ptransition + 0.6*nm;
double zmax = 2*diameter+dmax+2*nm;
double ymax = 2*diameter+dmax+2*nm;
char *datname = new char[1024];
snprintf(datname, 1024, "papers/water-saft/figs/four-rods-in-water-%04.1fnm.dat", diameter/nm);
FILE *o = fopen(datname, "w");
delete[] datname;
Functional f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
new_water_prop.epsilonAB, new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling, 0));
double n_1atm = pressure_to_density(f, new_water_prop.kT, atmospheric_pressure,
0.001, 0.01);
double mu_satp = find_chemical_potential(f, new_water_prop.kT, n_1atm);
f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
new_water_prop.epsilonAB, new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling, mu_satp));
const double EperVolume = f(new_water_prop.kT, -new_water_prop.kT*log(n_1atm));
const double EperCell = EperVolume*(zmax*ymax - 4*0.25*M_PI*diameter*diameter)*width;
//Functional X = Xassociation(new_water_prop.lengthscale, new_water_prop.epsilonAB,
// new_water_prop.kappaAB, new_water_prop.epsilon_dispersion,
// new_water_prop.lambda_dispersion,
// new_water_prop.length_scaling);
Functional S = OfEffectivePotential(EntropySaftFluid2(new_water_prop.lengthscale,
new_water_prop.epsilonAB,
new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling));
//dmax, dstep already in bohrs (so it doesn't need to be converted from nm)
double dstep = 0.25*nm;
for (distance=0.0*nm; distance<=dmax; distance += dstep) {
if ((distance >= ptransition - 0.5*nm) && (distance <= ptransition + 0.05*nm)) {
if (distance >= ptransition - 0.25*nm) {
dstep = 0.03*nm;
} else {
dstep = 0.08*nm;
}
} else {
dstep = 0.25*nm;
}
Lattice lat(Cartesian(width,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.2);
printf("Grid is %d x %d x %d\n", gd.Nx, gd.Ny, gd.Nz);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
new_water_prop.epsilonAB, new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling, mu_satp));
f = constrain(constraint, f);
printf("Diameter is %g bohr (%g nm)\n", diameter, diameter/nm);
printf("Distance between rods = %g bohr (%g nm)\n", distance, distance/nm);
potential = new_water_prop.liquid_density*constraint
+ 400*new_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
//potential = new_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
potential = -new_water_prop.kT*potential.cwise().log();
const double surface_tension = 5e-5; // crude guess from memory...
const double surfprecision = 1e-5*(4*M_PI*diameter)*width*surface_tension; // five digits accuracy
const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision for small rods
const double precision = bulkprecision + surfprecision;
printf("Precision limit from surface tension is to %g based on %g and %g\n",
precision, surfprecision, bulkprecision);
Minimizer min = Precision(precision, PreconditionedConjugateGradient(f, gd, new_water_prop.kT,
&potential,
QuadraticLineMinimizer));
const int numiters = 200;
for (int i=0;i<numiters && min.improve_energy(false);i++) {
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);
// }
}
Grid potential2(gd);
Grid constraint2(gd);
constraint2.Set(notinmiddle);
potential2 = new_water_prop.liquid_density*(constraint2.cwise()*constraint)
+ 400*new_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
potential2 = -new_water_prop.kT*potential2.cwise().log();
Minimizer min2 = Precision(1e-12, PreconditionedConjugateGradient(f, gd, new_water_prop.kT,
&potential2,
QuadraticLineMinimizer));
for (int i=0;i<numiters && min2.improve_energy(false);i++) {
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);
// }
}
char *plotnameslice = new char[1024];
snprintf(plotnameslice, 1024, "papers/water-saft/figs/four-rods-%04.1f-%04.2f.dat", diameter/nm, distance/nm);
printf("The bulk energy per cell should be %g\n", EperCell);
double energy;
if (min.energy() < min2.energy()) {
energy = (min.energy() - EperCell)/width;
Grid density(gd, EffectivePotentialToDensity()(new_water_prop.kT, gd, potential));
printf("Using liquid in middle initially.\n");
plot_grids_yz_directions(plotnameslice, density);
{
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);
}
} else {
energy = (min2.energy() - EperCell)/width;
Grid density(gd, EffectivePotentialToDensity()(new_water_prop.kT, gd, potential2));
printf("Using vapor in middle initially.\n");
plot_grids_yz_directions(plotnameslice, density);
{
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);
}
}
printf("Liquid energy is %.15g. Vapor energy is %.15g\n", min.energy(), min2.energy());
fprintf(o, "%g\t%.15g\n", distance/nm, energy);
//Grid entropy(gd, S(new_water_prop.kT, potential));
//Grid Xassoc(gd, X(new_water_prop.kT, density));
//plot_grids_y_direction(plotnameslice, density, energy_density, entropy, Xassoc);
//Grid energy_density(gd, f(new_water_prop.kT, gd, potential));
delete[] plotnameslice;
}
fclose(o);
{
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);
}
}
int main(int argc, char **argv)
{
printf("Mapping & Scaffolding module.\n");
if(argc == 1)
{
usage();
return 0;
}
int c = 0;
int inpseq, outseq;
//char optarg[256];
int mode = -1;
//char temp[100];
while((c = getopt(argc, argv, "s:g:p:L:t:i:u:c:P:K:MSBDO")) != EOF)
{
switch(c)
{
case 'M':
mode = MAPPING;
break;
case 'S':
mode = SCAFF;
break;
case 'B':
mode = BUNDLE;
break;
case 'D':
mode = PREPARE;
break;
case 'O':
mode = POTENT;
break;
case 's':
inpseq = 1;
shortrdsfile = (char *)ckalloc(256 * sizeof(char));
strcpy(shortrdsfile, optarg);
break;
case 'g':
outseq = 1;
graphfile = (char *)ckalloc(256 * sizeof(char));
strcpy(graphfile, optarg);
break;
case 'p':
thrd_num = atoi(optarg);
break;
case 'L':
ctg_short = atoi(optarg);
break;
case 'P':
OverlapPercent = atof (optarg);
break;
case 't':
close_threshold = atof (optarg);
break;
case 'i':
ins_size_var = atoi (optarg);
break;
case 'u':
bund_threshold = atoi (optarg);
break;
case 'c':
ctg_file = (char *)ckalloc(256 * sizeof(char));
strcpy(ctg_file, optarg);
break;
case 'K':
overlaplen = atoi(optarg);
break;
case 'h':
usage();
break;
case '?':
usage();
exit(1);
default:
usage();
exit(1);
}
}
if(mode == -1)
{
usage();
exit(1);
}
else if(mode == MAPPING)
{
printf("[%s]Mapping mode selected .\n", __FUNCTION__);
if(outseq == 0 || inpseq == 0)
{
usage();
exit(1);
}
call_align();
}
else if(mode == SCAFF)
{
printf("[%s]Scaffolding mode selected .\n", __FUNCTION__);
if(outseq == 0)
{
usage();
exit(1);
}
call_scaffold();
}
else if(mode == BUNDLE)
{
printf("[%s]Bundling mode selected .\n", __FUNCTION__);
if(outseq == 0)
{
usage();
exit(1);
}
call_bundle();
}
else if(mode == PREPARE)
{
printf("[%s]Data prepare mode selected .\n", __FUNCTION__);
if(outseq == 0 || ctg_file == NULL)
{
usage();
exit(1);
}
data_prepare();
}
else if(mode == POTENT)
{
printf("[%s]Potential analysis mode selected .\n", __FUNCTION__) ;
if(outseq == NULL)
{
usage();
exit(1);
}
potential();
}
return 0;
}
/* Lagrangiana euclidea */
static double HOeLagrangian(double x1, double x2)
{
return M/2*(x2 - x1)*(x2 - x1) + (potential(x1) + potential(x2))/2;
}
int
main( int argc, const char *argv[] )
{
int i, j;
PLFLT xx, yy, argx, argy, distort;
static PLINT mark = 1500, space = 1500;
PLFLT **z, **w;
PLFLT xg1[XPTS], yg1[YPTS];
PLcGrid cgrid1;
PLcGrid2 cgrid2;
// Parse and process command line arguments
(void) plparseopts( &argc, argv, PL_PARSE_FULL );
// Initialize plplot
plinit();
// Set up function arrays
plAlloc2dGrid( &z, XPTS, YPTS );
plAlloc2dGrid( &w, XPTS, YPTS );
for ( i = 0; i < XPTS; i++ )
{
xx = (double) ( i - ( XPTS / 2 ) ) / (double) ( XPTS / 2 );
for ( j = 0; j < YPTS; j++ )
{
yy = (double) ( j - ( YPTS / 2 ) ) / (double) ( YPTS / 2 ) - 1.0;
z[i][j] = xx * xx - yy * yy;
w[i][j] = 2 * xx * yy;
}
}
// Set up grids
cgrid1.xg = xg1;
cgrid1.yg = yg1;
cgrid1.nx = XPTS;
cgrid1.ny = YPTS;
plAlloc2dGrid( &cgrid2.xg, XPTS, YPTS );
plAlloc2dGrid( &cgrid2.yg, XPTS, YPTS );
cgrid2.nx = XPTS;
cgrid2.ny = YPTS;
for ( i = 0; i < XPTS; i++ )
{
for ( j = 0; j < YPTS; j++ )
{
mypltr( (PLFLT) i, (PLFLT) j, &xx, &yy, NULL );
argx = xx * M_PI / 2;
argy = yy * M_PI / 2;
distort = 0.4;
cgrid1.xg[i] = xx + distort * cos( argx );
cgrid1.yg[j] = yy - distort * cos( argy );
cgrid2.xg[i][j] = xx + distort * cos( argx ) * cos( argy );
cgrid2.yg[i][j] = yy - distort * cos( argx ) * cos( argy );
}
}
// Plot using identity transform
//
// plenv(-1.0, 1.0, -1.0, 1.0, 0, 0);
// plcol0(2);
// plcont(z, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11, mypltr, NULL);
// plstyl(1, &mark, &space);
// plcol0(3);
// plcont(w, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11, mypltr, NULL);
// plstyl(0, &mark, &space);
// plcol0(1);
// pllab("X Coordinate", "Y Coordinate", "Streamlines of flow");
//
pl_setcontlabelformat( 4, 3 );
pl_setcontlabelparam( 0.006, 0.3, 0.1, 1 );
plenv( -1.0, 1.0, -1.0, 1.0, 0, 0 );
plcol0( 2 );
plcont( (const PLFLT * const *) z, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11, mypltr, NULL );
plstyl( 1, &mark, &space );
plcol0( 3 );
plcont( (const PLFLT * const *) w, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11, mypltr, NULL );
plstyl( 0, &mark, &space );
plcol0( 1 );
pllab( "X Coordinate", "Y Coordinate", "Streamlines of flow" );
pl_setcontlabelparam( 0.006, 0.3, 0.1, 0 );
// Plot using 1d coordinate transform
plenv( -1.0, 1.0, -1.0, 1.0, 0, 0 );
plcol0( 2 );
plcont( (const PLFLT * const *) z, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
pltr1, (void *) &cgrid1 );
plstyl( 1, &mark, &space );
plcol0( 3 );
plcont( (const PLFLT * const *) w, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
pltr1, (void *) &cgrid1 );
plstyl( 0, &mark, &space );
plcol0( 1 );
pllab( "X Coordinate", "Y Coordinate", "Streamlines of flow" );
//
// pl_setcontlabelparam(0.006, 0.3, 0.1, 1);
// plenv(-1.0, 1.0, -1.0, 1.0, 0, 0);
// plcol0(2);
// plcont((const PLFLT **) z, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
// pltr1, (void *) &cgrid1);
//
// plstyl(1, &mark, &space);
// plcol0(3);
// plcont((const PLFLT **) w, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
// pltr1, (void *) &cgrid1);
// plstyl(0, &mark, &space);
// plcol0(1);
// pllab("X Coordinate", "Y Coordinate", "Streamlines of flow");
// pl_setcontlabelparam(0.006, 0.3, 0.1, 0);
//
// Plot using 2d coordinate transform
plenv( -1.0, 1.0, -1.0, 1.0, 0, 0 );
plcol0( 2 );
plcont( (const PLFLT * const *) z, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
pltr2, (void *) &cgrid2 );
plstyl( 1, &mark, &space );
plcol0( 3 );
plcont( (const PLFLT * const *) w, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
pltr2, (void *) &cgrid2 );
plstyl( 0, &mark, &space );
plcol0( 1 );
pllab( "X Coordinate", "Y Coordinate", "Streamlines of flow" );
//
// pl_setcontlabelparam(0.006, 0.3, 0.1, 1);
// plenv(-1.0, 1.0, -1.0, 1.0, 0, 0);
// plcol0(2);
// plcont((const PLFLT **) z, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
// pltr2, (void *) &cgrid2);
//
// plstyl(1, &mark, &space);
// plcol0(3);
// plcont((const PLFLT **) w, XPTS, YPTS, 1, XPTS, 1, YPTS, clevel, 11,
// pltr2, (void *) &cgrid2);
// plstyl(0, &mark, &space);
// plcol0(1);
// pllab("X Coordinate", "Y Coordinate", "Streamlines of flow");
//
pl_setcontlabelparam( 0.006, 0.3, 0.1, 0 );
polar();
//
// pl_setcontlabelparam(0.006, 0.3, 0.1, 1);
// polar();
//
pl_setcontlabelparam( 0.006, 0.3, 0.1, 0 );
potential();
//
// pl_setcontlabelparam(0.006, 0.3, 0.1, 1);
// potential();
//
// Clean up
plFree2dGrid( z, XPTS, YPTS );
plFree2dGrid( w, XPTS, YPTS );
plFree2dGrid( cgrid2.xg, XPTS, YPTS );
plFree2dGrid( cgrid2.yg, XPTS, YPTS );
plend();
exit( 0 );
}
/*$cp^{0}$ multiplied by this factor allows to obtain the energy for a local inertial observer in this spacetime.*/
mydbl energy_factor(mydbl r)
{
mydbl g = sqrtl(1.0 + 2.0*potential(r)/(C*C));
return g;
}
/*Violation of null geodesics condition $g_{\mu\nu}p^{\mu}p^{\nu} = 0$.*/
mydbl violation(mydbl r, mydbl p0, mydbl pr, double a)
{
mydbl f = -(1.0+2.0*potential(r)/(C*C))*p0*p0 + (mydbl)(1.0*a*a)*(1.0-2.0*potential(r)/(C*C))*pr*pr;
return f;
}
void interactionForce( latticeMesh* mesh, scalar Ff[3], scalar* rho, scalar* T, uint id ) {
uint i,
k;
/* // EOS Perturbation. Temporal */
/* scalar r = 1; */
/* if (mesh->mesh.points[id][1] == 0) { */
/* srand(id); */
/* r = (scalar)rand() / RAND_MAX; */
/* r = 0.9 + (1.1-0.9)*r; */
/* } */
scalar F[3] = {0.0, 0.0, 0.0};
// Initialize force term
for( i = 0 ; i < 3 ; i++) {
Ff[i] = 0 ;
}
// Do not use unexisting neighbour
if( mesh->mesh.isOnBnd[id] == 0 ) {
for( k = 1 ; k < mesh->lattice.Q ; k++ ) {
int neighId = mesh->mesh.nb[id][ mesh->lattice.reverse[k] ];
scalar alpha = mesh->lattice.weights[k] * potential(mesh, rho[neighId], T[neighId]);
for( i = 0 ; i < 3 ; i++ ) {
F[i] += alpha * (scalar)mesh->lattice.vel[k][i] ;
}
}
// Extra constant
scalar beta = -mesh->EOS.G * potential(mesh, rho[id], T[id]);
for( i = 0 ; i < 3 ; i++) {
Ff[i] = F[i] * beta;
}
}
}
/* Variazione di azione euclidea conseguente alla modifica di un elemento del
* vettore x
*/
static double deltaS(double *x, int dim, double x_new, int i)
{
return M*((x[i] - x_new)*(x[(i+1)%dim] + x[(i-1+dim)%dim]) +\
(x_new*x_new - x[i]*x[i])) + potential(x_new) - potential(x[i]);
}