int main(int argc, char* argv[]) {
struct reb_simulation* r = reb_create_simulation();
// Setup constants
r->opening_angle2 = .5; // This determines the precission of the tree code gravity calculation.
r->integrator = REB_INTEGRATOR_SEI;
r->boundary = REB_BOUNDARY_SHEAR;
r->gravity = REB_GRAVITY_TREE;
r->collision = REB_COLLISION_TREE;
double OMEGA = 0.00013143527; // 1/s
r->ri_sei.OMEGA = OMEGA;
r->G = 6.67428e-11; // N / (1e-5 kg)^2 m^2
r->softening = 0.1; // m
r->dt = 1e-3*2.*M_PI/OMEGA; // s
// This example uses two root boxes in the x and y direction.
// Although not necessary in this case, it allows for the parallelization using MPI.
// See Rein & Liu for a description of what a root box is in this context.
double surfacedensity = 600; // kg/m^2
double particle_density = 400; // kg/m^3
double particle_radius_min = 1; // m
double particle_radius_max = 4; // m
double particle_radius_slope = -3;
double boxsize = 100; // m
if (argc>1){ // Try to read boxsize from command line
boxsize = atof(argv[1]);
}
reb_configure_box(r, boxsize, 2, 2, 1);
r->nghostx = 2;
r->nghosty = 2;
r->nghostz = 0;
// Use Bridges et al coefficient of restitution.
r->coefficient_of_restitution = coefficient_of_restitution_bridges;
// When two particles collide and the relative velocity is zero, the might sink into each other in the next time step.
// By adding a small repulsive velocity to each collision, we prevent this from happening.
r->minimum_collision_velocity = particle_radius_min*OMEGA*0.001; // small fraction of the shear accross a particle
// Add all ring paricles
double total_mass = surfacedensity*r->boxsize.x*r->boxsize.y;
double mass = 0;
while(mass<total_mass){
struct reb_particle pt = {0.};
pt.x = reb_random_uniform(-r->boxsize.x/2.,r->boxsize.x/2.);
pt.y = reb_random_uniform(-r->boxsize.y/2.,r->boxsize.y/2.);
pt.z = reb_random_normal(1.); // m
pt.vx = 0;
pt.vy = -1.5*pt.x*OMEGA;
pt.vz = 0;
pt.ax = 0;
pt.ay = 0;
pt.az = 0;
double radius = reb_random_powerlaw(particle_radius_min,particle_radius_max,particle_radius_slope);
pt.r = radius; // m
double particle_mass = particle_density*4./3.*M_PI*radius*radius*radius;
pt.m = particle_mass; // kg
reb_add(r, pt);
mass += particle_mass;
}
reb_integrate(r, 2./OMEGA);
}
int main(int argc, char* argv[]){
// Setup constants
G = 1;
integrator = LEAPFROG;
softening = 0.01;
dt = 3e-3;
boxsize = 1.2;
root_nx = 1; root_ny = 1; root_nz = 1;
nghostx = 0; nghosty = 0; nghostz = 0;
init_box();
// Setup particles
double disc_mass = 2e-1;
int _N = 10000;
// Initial conditions
struct reb_particle star;
star.x = 0; star.y = 0; star.z = 0;
star.vx = 0; star.vy = 0; star.vz = 0;
star.ax = 0; star.ay = 0; star.az = 0;
star.m = 1;
reb_add(r, star);
while(N<_N){
struct reb_particle pt;
double a = reb_random_powerlaw(boxsize/10.,boxsize/2./1.2,-1.5);
double phi = reb_random_uniform(0,2.*M_PI);
pt.x = a*cos(phi);
pt.y = a*sin(phi);
pt.z = a*reb_random_normal(0.001);
double mu = star.m + disc_mass * (pow(a,-3./2.)-pow(boxsize/10.,-3./2.))/(pow(boxsize/2./1.2,-3./2.)-pow(boxsize/10.,-3./2.));
double vkep = sqrt(G*mu/a);
pt.vx = vkep * sin(phi);
pt.vy = -vkep * cos(phi);
pt.vz = 0;
pt.ax = 0;
pt.ay = 0;
pt.az = 0;
pt.m = disc_mass/(double)_N;
reb_add(r, pt);
}
}
void run_sim(){
struct reb_simulation* const r = reb_create_simulation();
// Setup constants
r->integrator = REB_INTEGRATOR_LEAPFROG;
r->gravity = REB_GRAVITY_BASIC;
r->boundary = REB_BOUNDARY_OPEN;
r->opening_angle2 = 1.5; // This constant determines the accuracy of the tree code gravity estimate.
r->G = 1;
r->softening = 0.02; // Gravitational softening length
r->dt = 3e-2; // Timestep
const double boxsize = 10.2;
reb_configure_box(r,boxsize,1,1,1);
// Setup particles
double disc_mass = 2e-1; // Total disc mass
int N = 2000; // Number of particles
// Initial conditions
struct reb_particle star = {0};
star.m = 1;
reb_add(r, star);
for (int i=0;i<N;i++){
struct reb_particle pt = {0};
double a = reb_random_powerlaw(boxsize/10.,boxsize/2./1.2,-1.5);
double phi = reb_random_uniform(0,2.*M_PI);
pt.x = a*cos(phi);
pt.y = a*sin(phi);
pt.z = a*reb_random_normal(0.001);
double mu = star.m + disc_mass * (pow(a,-3./2.)-pow(boxsize/10.,-3./2.))/(pow(boxsize/2./1.2,-3./2.)-pow(boxsize/10.,-3./2.));
double vkep = sqrt(r->G*mu/a);
pt.vx = vkep * sin(phi);
pt.vy = -vkep * cos(phi);
pt.vz = 0;
pt.m = disc_mass/(double)N;
reb_add(r, pt);
}
reb_integrate(r, 1.0);
reb_free_simulation(r);
}
int main(int argc, char* argv[]){
struct reb_simulation* const r = reb_create_simulation();
// Setup constants
r->integrator = REB_INTEGRATOR_LEAPFROG;
r->gravity = REB_GRAVITY_TREE;
r->boundary = REB_BOUNDARY_OPEN;
r->opening_angle2 = 1.5; // This constant determines the accuracy of the tree code gravity estimate.
r->G = 1;
r->softening = 0.02; // Gravitational softening length
r->dt = 3e-2; // Timestep
const double boxsize = 10.2;
// Setup root boxes for gravity tree.
// Here, we use 2x2=4 root boxes (each with length 'boxsize')
// This allows you to use up to 4 MPI nodes.
reb_configure_box(r,boxsize,2,2,1);
// Initialize MPI
// This can only be done after reb_configure_box.
reb_mpi_init(r);
// Setup particles only on master node
// In the first timestep, the master node will
// distribute particles to other nodes.
// Note that this is not the most efficient method
// for very large particle numbers.
double disc_mass = 2e-1/r->mpi_num; // Total disc mass
int N = 10000/r->mpi_num; // Number of particles
// Initial conditions
struct reb_particle star = {0};
star.m = 1;
if (r->mpi_id==0){
reb_add(r, star);
}
for (int i=0;i<N;i++){
struct reb_particle pt = {0};
double a = reb_random_powerlaw(boxsize/10.,boxsize/2./1.2,-1.5);
double phi = reb_random_uniform(0,2.*M_PI);
pt.x = a*cos(phi);
pt.y = a*sin(phi);
pt.z = a*reb_random_normal(0.001);
double mu = star.m + disc_mass * (pow(a,-3./2.)-pow(boxsize/10.,-3./2.))/(pow(boxsize/2./1.2,-3./2.)-pow(boxsize/10.,-3./2.));
double vkep = sqrt(r->G*mu/a);
pt.vx = vkep * sin(phi);
pt.vy = -vkep * cos(phi);
pt.vz = 0;
pt.m = disc_mass/(double)N;
reb_add(r, pt);
}
r->heartbeat = heartbeat;
#ifdef OPENGL
// Hack to artificially increase particle array.
// This cannot be done once OpenGL is activated.
r->allocatedN *=8;
r->particles = realloc(r->particles,sizeof(struct reb_particle)*r->allocatedN);
#endif // OPENGL
// Start the integration
reb_integrate(r, INFINITY);
// Cleanup
reb_mpi_finalize(r);
reb_free_simulation(r);
}
void reb_tools_megno_init(struct reb_simulation* const r, double delta){
int N_var = r->N;
r->calculate_megno = 1;
r->megno_Ys = 0.;
r->megno_Yss = 0.;
r->megno_cov_Yt = 0.;
r->megno_var_t = 0.;
r->megno_n = 0;
r->megno_mean_Y = 0;
r->megno_mean_t = 0;
for (int i=0;i<N_var;i++){
struct reb_particle megno = {
.m = r->particles[i].m,
.x = reb_random_normal(1.),
.y = reb_random_normal(1.),
.z = reb_random_normal(1.),
.vx = reb_random_normal(1.),
.vy = reb_random_normal(1.),
.vz = reb_random_normal(1.) };
double deltad = delta/sqrt(megno.x*megno.x + megno.y*megno.y + megno.z*megno.z + megno.vx*megno.vx + megno.vy*megno.vy + megno.vz*megno.vz); // rescale
megno.x *= deltad;
megno.y *= deltad;
megno.z *= deltad;
megno.vx *= deltad;
megno.vy *= deltad;
megno.vz *= deltad;
reb_add(r, megno);
}
r->N_var = N_var;
}
double reb_tools_calculate_megno(struct reb_simulation* r){ // Returns the MEGNO <Y>
if (r->t==0.) return 0.;
return r->megno_Yss/r->t;
}
double reb_tools_calculate_lyapunov(struct reb_simulation* r){ // Returns the largest Lyapunov characteristic number (LCN), or maximal Lyapunov exponent
if (r->t==0.) return 0.;
return r->megno_cov_Yt/r->megno_var_t;
}
double reb_tools_megno_deltad_delta(struct reb_simulation* const r){
const struct reb_particle* restrict const particles = r->particles;
const int N = r->N;
const int N_var = r->N_var;
double deltad = 0;
double delta2 = 0;
for (int i=N-N_var;i<N;i++){
deltad += particles[i].vx * particles[i].x;
deltad += particles[i].vy * particles[i].y;
deltad += particles[i].vz * particles[i].z;
deltad += particles[i].ax * particles[i].vx;
deltad += particles[i].ay * particles[i].vy;
deltad += particles[i].az * particles[i].vz;
delta2 += particles[i].x * particles[i].x;
delta2 += particles[i].y * particles[i].y;
delta2 += particles[i].z * particles[i].z;
delta2 += particles[i].vx * particles[i].vx;
delta2 += particles[i].vy * particles[i].vy;
delta2 += particles[i].vz * particles[i].vz;
}
return deltad/delta2;
}
void reb_tools_megno_update(struct reb_simulation* r, double dY){
// Calculate running Y(t)
r->megno_Ys += dY;
double Y = r->megno_Ys/r->t;
// Calculate averge <Y>
r->megno_Yss += Y * r->dt;
// Update covariance of (Y,t) and variance of t
r->megno_n++;
double _d_t = r->t - r->megno_mean_t;
r->megno_mean_t += _d_t/(double)r->megno_n;
double _d_Y = reb_tools_calculate_megno(r) - r->megno_mean_Y;
r->megno_mean_Y += _d_Y/(double)r->megno_n;
r->megno_cov_Yt += ((double)r->megno_n-1.)/(double)r->megno_n
*(r->t-r->megno_mean_t)
*(reb_tools_calculate_megno(r)-r->megno_mean_Y);
r->megno_var_t += ((double)r->megno_n-1.)/(double)r->megno_n
*(r->t-r->megno_mean_t)
*(r->t-r->megno_mean_t);
}
int main(int argc, char* argv[]){
struct reb_simulation* r = reb_create_simulation();
// Setup constants
r->dt = 1e-1;
r->gravity = REB_GRAVITY_NONE;
r->integrator = REB_INTEGRATOR_LEAPFROG;
r->collision = REB_COLLISION_TREE;
r->boundary = REB_BOUNDARY_PERIODIC;
// Override default collision handling to account for border particles
r->collision_resolve = collision_resolve_hardsphere_withborder;
r->heartbeat = heartbeat;
reb_configure_box(r, 20., 1, 1, 4);
r->nghostx = 1; r->nghosty = 1; r->nghostz = 0;
double N_part = 0.00937*r->boxsize.x*r->boxsize.y*r->boxsize.z;
// Add Border Particles
double radius = 1;
double mass = 1;
double border_spacing_x = r->boxsize.x/(floor(r->boxsize.x/radius/2.)-1.);
double border_spacing_y = r->boxsize.y/(floor(r->boxsize.y/radius/2.)-1.);
struct reb_particle pt = {0};
pt.r = radius;
pt.m = mass;
pt.id = 1;
for(double x = -r->boxsize.x/2.; x<r->boxsize.x/2.-border_spacing_x/2.;x+=border_spacing_x){
for(double y = -r->boxsize.y/2.; y<r->boxsize.y/2.-border_spacing_y/2.;y+=border_spacing_y){
pt.x = x;
pt.y = y;
// Add particle to bottom
pt.z = -r->boxsize.z/2.+radius;
pt.vy = 1;
reb_add(r, pt);
// Add particle to top
pt.z = r->boxsize.z/2.-radius;
pt.vy = -1;
reb_add(r, pt);
}
}
N_border = r->N;
// Add real particles
while(r->N-N_border<N_part){
struct reb_particle pt = {0};
pt.x = reb_random_uniform(-r->boxsize.x/2.,r->boxsize.x/2.);
pt.y = reb_random_uniform(-r->boxsize.y/2.,r->boxsize.y/2.);
pt.z = 0.758*reb_random_uniform(-r->boxsize.z/2.,r->boxsize.z/2.);
pt.vx = reb_random_normal(0.001);
pt.vy = reb_random_normal(0.001);
pt.vz = reb_random_normal(0.001);
pt.r = radius; // m
pt.m = 1;
pt.id = 2;
reb_add(r, pt);
}
reb_integrate(r, INFINITY);
}