def run_kepler(mass, semi, ecc, time): kep = Kepler(redirection='none') kep.initialize_code() kep.set_longitudinal_unit_vector(1.0, 1.0, 0.0) kep.initialize_from_elements(mass, semi, ecc) a,e = kep.get_elements() p = kep.get_periastron() print "elements:", a, e, p kep.transform_to_time(time) x,y,z = kep.get_separation_vector() print "separation:", x,y,z x,y,z = kep.get_longitudinal_unit_vector() print "longitudinal:", x,y,z pos = [1, 0, 0] | nbody_system.length vel = [0, 0.5, 0] | nbody_system.speed kep.initialize_from_dyn(mass, pos[0], pos[1], pos[2], vel[0], vel[1], vel[2]) a,e = kep.get_elements() p = kep.get_periastron() print "elements:", a, e, p kep.transform_to_time(time) x,y,z = kep.get_separation_vector() print "separation:", x,y,z x,y,z = kep.get_velocity_vector() print "velocity:", x,y,z x,y,z = kep.get_longitudinal_unit_vector() print "longitudinal:", x,y,z kep.set_random(42) kep.make_binary_scattering(0.5 | nbody_system.mass, 0.5, 0.5 | nbody_system.mass, 0.0 | nbody_system.speed, 0.0 | nbody_system.length, 1.e-6, 0) kep.stop()
def get_galaxies_in_orbit(m_a=10.e11|units.MSun, m_b=10.e11|units.MSun, ecc=0.5, r_min=25.|units.kpc, t_start=None): """ binary galaxy with orbit of given parameters -- if ecc=>1, start at t_start (p625, t_start=-10=-10*100Myr) -- if ecc<1, start at apocenter (p644) """ converter=nbody_system.nbody_to_si(m_a+m_b,1|units.kpc) semi = r_min/(1.-ecc) # relative position and velocity vectors at the pericenter using kepler kepler = Kepler_twobody(converter) kepler.initialize_code() kepler.initialize_from_elements(mass=(m_a+m_b), semi=semi, ecc=ecc, periastron=r_min) # at periastron # evolve back till initial position if ( ecc<1. ): kepler.return_to_apastron() else: kepler.transform_to_time(t_start) # get time of the orbit t_orbit = kepler.get_time() rl = kepler.get_separation_vector() r = [rl[0].value_in(units.AU), rl[1].value_in(units.AU), rl[2].value_in(units.AU)] | units.AU vl = kepler.get_velocity_vector() v = [vl[0].value_in(units.kms), vl[1].value_in(units.kms), vl[2].value_in(units.kms)] | units.kms kepler.stop() # assign particle atributes galaxies = Particles(2) galaxies[0].mass = m_a galaxies[0].position = (0,0,0) | units.AU galaxies[0].velocity = (0,0,0) | units.kms galaxies[1].mass = m_b galaxies[1].position = r galaxies[1].velocity = v # identification galaxies[0].id = 'a0' galaxies[1].id = 'b0' galaxies.move_to_center() return galaxies, t_orbit
def relative_position_and_velocity_from_orbital_elements( mass1, mass2, semimajor_axis, eccentricity, mean_anomaly, seed=None): """ Function that returns relative positions and velocity vectors or orbiters with masses mass2 of the central body with mass mass1 in Cartesian coordinates; for vectors of orbital elements -- semi-major axes, eccentricities, mean anomalies. 3D orientation of orbits (inclination, longitude of ascending node and argument of periapsis) are random. (cos(incl) is uniform -1--1, longitude of ascending node and argument of periapsis are uniform 0--2pi) Assuming mass1 is static in the center [0,0,0] m, [0,0,0] km/s (that is mass2<<mass1) """ position_vectors = [] velocity_vectors = [] converter = nbody_system.nbody_to_si(1 | units.MSun, 1 | units.AU) kepler = Kepler(converter) kepler.initialize_code() r_vec = (0., 0., 0.) | units.AU v_vec = (0., 0., 0.) | units.kms # to change seed for each particle if seed is not None: i = 0 for m2_i, a_i, ecc_i, ma_i in zip(mass2, semimajor_axis, eccentricity, mean_anomaly): #print m2_i, a_i, ecc_i, ma_i if seed is not None: kepler.set_random(seed + i) i = i + 1 kepler.initialize_from_elements(mass=(mass1 + m2_i), semi=a_i, ecc=ecc_i, mean_anomaly=ma_i, random_orientation=-1) ri = kepler.get_separation_vector() vi = kepler.get_velocity_vector() # this is to get ~half of the orbits retrograde (that is with inclination # of 90--180 degrees) --> velocity = -velocity vel_vec_dir = numpy.random.random() if (vel_vec_dir <= 0.5): vel_orientation = 1. else: vel_orientation = -1. position_vectors.append([ri[0], ri[1], ri[2]]) velocity_vectors.append([ vel_orientation * vi[0], vel_orientation * vi[1], vel_orientation * vi[2] ]) kepler.stop() return position_vectors, velocity_vectors
def relative_position_and_velocity_from_orbital_elements(mass1, mass2, semimajor_axis, eccentricity, mean_anomaly, seed=None): """ Function that returns relative positions and velocity vectors or orbiters with masses mass2 of the central body with mass mass1 in Cartesian coordinates; for vectors of orbital elements -- semi-major axes, eccentricities, mean anomalies. 3D orientation of orbits (inclination, longitude of ascending node and argument of periapsis) are random. (cos(incl) is uniform -1--1, longitude of ascending node and argument of periapsis are uniform 0--2pi) Assuming mass1 is static in the center [0,0,0] m, [0,0,0] km/s (that is mass2<<mass1) """ position_vectors = [] velocity_vectors = [] converter = nbody_system.nbody_to_si(1|units.MSun,1|units.AU) kepler = Kepler(converter) kepler.initialize_code() r_vec = (0.,0.,0.) | units.AU v_vec = (0.,0.,0.) | units.kms # to change seed for each particle if seed is not None: i=0 for m2_i, a_i, ecc_i, ma_i in zip(mass2, semimajor_axis, eccentricity, mean_anomaly): #print m2_i, a_i, ecc_i, ma_i if seed is not None: kepler.set_random(seed+i) i=i+1 kepler.initialize_from_elements(mass=(mass1+m2_i),semi=a_i,ecc=ecc_i,mean_anomaly=ma_i,random_orientation=-1) ri = kepler.get_separation_vector() vi = kepler.get_velocity_vector() # this is to get ~half of the orbits retrograde (that is with inclination # of 90--180 degrees) --> velocity = -velocity vel_vec_dir = numpy.random.random() if (vel_vec_dir<=0.5): vel_orientation = 1. else: vel_orientation = -1. position_vectors.append([ri[0], ri[1], ri[2]]) velocity_vectors.append([vel_orientation*vi[0], vel_orientation*vi[1], vel_orientation*vi[2]]) kepler.stop() return position_vectors, velocity_vectors
def test11(self): """ testing orbital_elements_for_rel_posvel_arrays for unbound orbits """ from amuse.community.kepler.interface import Kepler numpy.random.seed(66) N = 10 mass_sun = 1. | units.MSun mass1 = numpy.ones(N) * mass_sun mass2 = numpy.zeros(N) | units.MSun semi_major_axis=-1000.*(random.random(N)) | units.AU eccentricity = (1.+random.random(N))*10.-9. inclination = numpy.pi*random.random(N) longitude_of_the_ascending_node = 2.*numpy.pi*random.random(N)-numpy.pi argument_of_periapsis = 2.*numpy.pi*random.random(N)-numpy.pi # kepler.initialize_from_elements initializes orbits with mean_anomaly=0 and true_anomaly=0 true_anomaly = 0.*(360.*random.random(N)-180.) comets = datamodel.Particles(N) converter = nbody_system.nbody_to_si(1|units.MSun,1|units.AU) kepler = Kepler(converter) kepler.initialize_code() for i,arg in enumerate(zip(mass1,mass2,semi_major_axis,eccentricity,true_anomaly,inclination, longitude_of_the_ascending_node,argument_of_periapsis)): kepler.initialize_from_elements(mass=(mass1[i]+mass2[i]), semi=semi_major_axis[i], ecc=eccentricity[i]) ri = kepler.get_separation_vector() vi = kepler.get_velocity_vector() om = longitude_of_the_ascending_node[i] w = argument_of_periapsis[i] incl = inclination[i] a1 = ([numpy.cos(om), -numpy.sin(om), 0.0], [numpy.sin(om), numpy.cos(om), 0.0], [0.0, 0.0, 1.0]) a2 = ([1.0, 0.0, 0.0], [0.0, numpy.cos(incl), -numpy.sin(incl)], [0.0, numpy.sin(incl), numpy.cos(incl)]) a3 = ([numpy.cos(w), -numpy.sin(w), 0.0], [numpy.sin(w), numpy.cos(w), 0.0], [0.0, 0.0, 1.0]) A = numpy.dot(numpy.dot(a1,a2),a3) r_vec = numpy.dot(A,numpy.reshape(ri,3,1)) v_vec = numpy.dot(A,numpy.reshape(vi,3,1)) r = (0.0, 0.0, 0.0) | units.AU v = (0.0, 0.0, 0.0) | (units.AU / units.day) r[0] = r_vec[0] r[1] = r_vec[1] r[2] = r_vec[2] v[0] = v_vec[0] v[1] = v_vec[1] v[2] = v_vec[2] comets[i].mass = mass2[i] comets[i].position = r_vec comets[i].velocity = v_vec kepler.stop() semi_major_axis_ext, eccentricity_ext, ta_ext, inclination_ext, \ longitude_of_the_ascending_node_ext, argument_of_periapsis_ext = \ orbital_elements(comets.position, comets.velocity, comets.mass + mass_sun, G=constants.G) self.assertAlmostEqual(semi_major_axis,semi_major_axis_ext.in_(units.AU)) self.assertAlmostEqual(eccentricity,eccentricity_ext) self.assertAlmostEqual(inclination,inclination_ext) self.assertAlmostEqual(longitude_of_the_ascending_node,longitude_of_the_ascending_node_ext) self.assertAlmostEqual(argument_of_periapsis,argument_of_periapsis_ext) self.assertAlmostEqual(true_anomaly,ta_ext)
def run_ph4(infile = None, outfile = None, number_of_stars = 100, number_of_binaries = 0, end_time = 10 | nbody_system.time, delta_t = 1 | nbody_system.time, n_workers = 1, use_gpu = 1, gpu_worker = 1, salpeter = 0, accuracy_parameter = 0.1, softening_length = 0.0 | nbody_system.length, manage_encounters = 1, random_seed = 1234): if random_seed <= 0: numpy.random.seed() random_seed = numpy.random.randint(1, pow(2,31)-1) numpy.random.seed(random_seed) print "random seed =", random_seed if infile != None: print "input file =", infile print "end_time =", end_time.number print "delta_t =", delta_t.number print "n_workers =", n_workers print "use_gpu =", use_gpu print "manage_encounters =", manage_encounters print "\ninitializing the gravity module" sys.stdout.flush() init_smalln() # Note that there are actually three GPU options: # # 1. use the GPU code and allow GPU use (default) # 2. use the GPU code but disable GPU use (-g) # 3. use the non-GPU code (-G) if gpu_worker == 1: try: gravity = grav(number_of_workers = n_workers, redirection = "none", mode = "gpu") except Exception as ex: gravity = grav(number_of_workers = n_workers, redirection = "none") else: gravity = grav(number_of_workers = n_workers, redirection = "none") gravity.initialize_code() gravity.parameters.set_defaults() #----------------------------------------------------------------- if infile == None: print "making a Plummer model" stars = new_plummer_model(number_of_stars) id = numpy.arange(number_of_stars) stars.id = id+1 print "setting particle masses and radii" if salpeter == 0: print 'equal masses' total_mass = 1.0 | nbody_system.mass scaled_mass = total_mass / number_of_stars else: print 'salpeter mass function' scaled_mass = new_salpeter_mass_distribution_nbody(number_of_stars) stars.mass = scaled_mass print "centering stars" stars.move_to_center() print "scaling stars to virial equilibrium" stars.scale_to_standard(smoothing_length_squared = gravity.parameters.epsilon_squared) else: # Read the input data. Units are dynamical (sorry). # Format: id mass pos[3] vel[3] print "reading file", infile id = [] mass = [] pos = [] vel = [] f = open(infile, 'r') count = 0 for line in f: if len(line) > 0: count += 1 cols = line.split() if count == 1: snap = int(cols[0]) elif count == 2: number_of_stars = int(cols[0]) elif count == 3: time = float(cols[0]) | nbody_system.time else: if len(cols) >= 8: id.append(int(cols[0])) mass.append(float(cols[1])) pos.append((float(cols[2]), float(cols[3]), float(cols[4]))) vel.append((float(cols[5]), float(cols[6]), float(cols[7]))) f.close() stars = datamodel.Particles(number_of_stars) stars.id = id stars.mass = mass | nbody_system.mass stars.position = pos | nbody_system.length stars.velocity = vel | nbody_system.speed #stars.radius = 0. | nbody_system.length total_mass = stars.mass.sum() ke = pa.kinetic_energy(stars) kT = ke/(1.5*number_of_stars) if number_of_binaries > 0: # Turn selected stars into binary components. # Only tested for equal-mass case. kep = Kepler(redirection = "none") kep.initialize_code() added_mass = 0.0 | nbody_system.mass # Work with energies rather than semimajor axes. Emin = 10*kT Emax = 20*kT ecc = 0.1 id_count = number_of_stars nbin = 0 for i in range(0, number_of_stars, number_of_stars/number_of_binaries): # Star i is CM, becomes component, add other star at end. nbin += 1 mass = stars[i].mass new_mass = numpy.random.uniform()*mass # uniform q? mbin = mass + new_mass fac = new_mass/mbin E = Emin + numpy.random.uniform()*(Emax-Emin) a = 0.5*nbody_system.G*mass*new_mass/E kep.initialize_from_elements(mbin, a, ecc) dr = quantities.AdaptingVectorQuantity() dr.extend(kep.get_separation_vector()) dv = quantities.AdaptingVectorQuantity() dv.extend(kep.get_velocity_vector()) newstar = datamodel.Particles(1) newstar.mass = new_mass newstar.position = stars[i].position + (1-fac)*dr newstar.velocity = stars[i].velocity + (1-fac)*dv # stars[i].mass = mass stars[i].position = stars[i].position - fac*dr stars[i].velocity = stars[i].velocity - fac*dv id_count += 1 newstar.id = id_count stars.add_particles(newstar) added_mass += new_mass if nbin >= number_of_binaries: break kep.stop() print 'created', nbin, 'binaries' sys.stdout.flush() stars.mass = stars.mass * total_mass/(total_mass+added_mass) number_of_stars += nbin # Set dynamical radii (assuming virial equilibrium and standard # units). Note that this choice should be refined, and updated # as the system evolves. Probably the choice of radius should be # made entirely in the multiples module. TODO. In these units, # M = 1 and <v^2> = 0.5, so the mean 90-degree turnaround impact # parameter is # # b_90 = G (m_1+m_2) / vrel^2 # = 2 <m> / 2<v^2> # = 2 / N for equal masses # # Taking r_i = m_i / 2<v^2> = m_i in virial equilibrium means # that, approximately, "contact" means a 90-degree deflection (r_1 # + r_2 = b_90). A more conservative choice with r_i less than # this value will isolates encounters better, but also place more # load on the large-N dynamical module. stars.radius = stars.mass.number | nbody_system.length time = 0.0 | nbody_system.time # print "IDs:", stars.id.number print "recentering stars" stars.move_to_center() sys.stdout.flush() #----------------------------------------------------------------- if softening_length < 0.0 | nbody_system.length: # Use ~interparticle spacing. Assuming standard units here. TODO eps2 = 0.25*(float(number_of_stars))**(-0.666667) \ | nbody_system.length**2 else: eps2 = softening_length*softening_length print 'softening length =', eps2.sqrt() gravity.parameters.timestep_parameter = accuracy_parameter gravity.parameters.epsilon_squared = eps2 gravity.parameters.use_gpu = use_gpu # gravity.parameters.manage_encounters = manage_encounters print '' print "adding particles" # print stars sys.stdout.flush() gravity.particles.add_particles(stars) gravity.commit_particles() print '' print "number_of_stars =", number_of_stars print "evolving to time =", end_time.number, \ "in steps of", delta_t.number sys.stdout.flush() # Channel to copy values from the code to the set in memory. channel = gravity.particles.new_channel_to(stars) stopping_condition = gravity.stopping_conditions.collision_detection stopping_condition.enable() # Debugging: prevent the multiples code from being called. if 0: stopping_condition.disable() print 'stopping condition disabled' sys.stdout.flush() # ----------------------------------------------------------------- # Create the coupled code and integrate the system to the desired # time, managing interactions internally. kep = init_kepler(stars[0], stars[1]) multiples_code = multiples.Multiples(gravity, new_smalln, kep) multiples_code.neighbor_perturbation_limit = 0.1 #multiples_code.neighbor_distance_factor = 1.0 #multiples_code.neighbor_veto = False #multiples_code.neighbor_distance_factor = 2.0 multiples_code.neighbor_veto = True print '' print 'multiples_code.initial_scale_factor =', \ multiples_code.initial_scale_factor print 'multiples_code.neighbor_perturbation_limit =', \ multiples_code.neighbor_perturbation_limit print 'multiples_code.neighbor_veto =', \ multiples_code.neighbor_veto print 'multiples_code.final_scale_factor =', \ multiples_code.final_scale_factor print 'multiples_code.initial_scatter_factor =', \ multiples_code.initial_scatter_factor print 'multiples_code.final_scatter_factor =', \ multiples_code.final_scatter_factor print 'multiples_code.retain_binary_apocenter =', \ multiples_code.retain_binary_apocenter print 'multiples_code.wide_perturbation_limit =', \ multiples_code.wide_perturbation_limit pre = "%%% " E0,cpu0 = print_log(pre, time, multiples_code) while time < end_time: time += delta_t multiples_code.evolve_model(time) # Copy values from the module to the set in memory. channel.copy() # Copy the index (ID) as used in the module to the id field in # memory. The index is not copied by default, as different # codes may have different indices for the same particle and # we don't want to overwrite silently. channel.copy_attribute("index_in_code", "id") print_log(pre, time, multiples_code, E0, cpu0) sys.stdout.flush() #----------------------------------------------------------------- if not outfile == None: # Write data to a file. f = open(outfile, 'w') #-------------------------------------------------- # Need to save top-level stellar data and parameters. # Need to save multiple data and parameters. f.write('%.15g\n'%(time.number)) for s in multiples_code.stars: write_star(s, f) #-------------------------------------------------- f.close() print 'wrote file', outfile print '' gravity.stop()
def compress_binary_components(comp1, comp2, scale): # Compress the two-body system consisting of comp1 and comp2 to # lie within distance scale of one another. pos1 = comp1.position pos2 = comp2.position sep12 = ((pos2-pos1)**2).sum() if sep12 > scale*scale: print '\ncompressing components', int(comp1.id.number), \ 'and', int(comp2.id.number), 'to separation', scale.number sys.stdout.flush() mass1 = comp1.mass mass2 = comp2.mass total_mass = mass1 + mass2 vel1 = comp1.velocity vel2 = comp2.velocity cmpos = (mass1*pos1+mass2*pos2)/total_mass cmvel = (mass1*vel1+mass2*vel2)/total_mass # For now, create and delete a temporary kepler # process to handle the transformation. Obviously # more efficient to define a single kepler at the # start of the calculation and reuse it. kep = Kepler(redirection = "none") kep.initialize_code() mass = comp1.mass + comp2.mass rel_pos = pos2 - pos1 rel_vel = vel2 - vel1 kep.initialize_from_dyn(mass, rel_pos[0], rel_pos[1], rel_pos[2], rel_vel[0], rel_vel[1], rel_vel[2]) M,th = kep.get_angles() a,e = kep.get_elements() if e < 1: peri = a*(1-e) apo = a*(1+e) else: peri = a*(e-1) apo = 2*a # OK - used ony to reset scale limit = peri + 0.01*(apo-peri) if scale < limit: scale = limit if M < 0: # print 'approaching' kep.advance_to_periastron() kep.advance_to_radius(limit) else: # print 'receding' if kep.get_separation() < scale: kep.advance_to_radius(limit) else: kep.return_to_radius(scale) # a,e = kep.get_elements() # r = kep.get_separation() # E,J = kep.get_integrals() # print 'kepler: a,e,r =', a.number, e.number, r.number # print 'E, J =', E, J # Note: if periastron > scale, we are now just past periastron. new_rel_pos = kep.get_separation_vector() new_rel_vel = kep.get_velocity_vector() kep.stop() # Enew = 0 # r2 = 0 # for k in range(3): # Enew += 0.5*(new_rel_vel[k].number)**2 # r2 += (new_rel_pos[k].number)**2 # rnew = math.sqrt(r2) # Enew -= mass.number/r1 # print 'E, Enew, rnew =', E.number, E1, r1 # Problem: the vectors returned by kepler are lists, # not numpy arrays, and it looks as though we can say # comp1.position = pos, but not comp1.position[k] = # xxx, as we'd like... Also, we don't know how to # copy a numpy array with units... TODO newpos1 = pos1 - pos1 # stupid trick to create zero vectors newpos2 = pos2 - pos2 # with the proper form and units... newvel1 = vel1 - vel1 newvel2 = vel2 - vel2 frac2 = mass2/total_mass for k in range(3): dxk = new_rel_pos[k] dvk = new_rel_vel[k] newpos1[k] = cmpos[k] - frac2*dxk newpos2[k] = cmpos[k] + (1-frac2)*dxk newvel1[k] = cmvel[k] - frac2*dvk newvel2[k] = cmvel[k] + (1-frac2)*dvk # Perform the changes to comp1 and comp2, and recursively # transmit them to the (currently absolute) coordinates of # all lower components. offset_particle_tree(comp1, newpos1-pos1, newvel1-vel1) offset_particle_tree(comp2, newpos2-pos2, newvel2-vel2)
def CutOrAdvance(enc_bodies, primary_sysID, converter=None): bodies = enc_bodies.copy() if converter==None: converter = nbody_system.nbody_to_si(bodies.mass.sum(), 2 * np.max(bodies.radius.number) | bodies.radius.unit) systems = stellar_systems.get_heirarchical_systems_from_set(bodies, converter=converter, RelativePosition=False) # Deal with Possible Key Issues with Encounters with 3+ Star Particles Being Run More than Other Systems ... if int(primary_sysID) not in systems.keys(): print "...: Error: Previously run binary system has been found! Not running this system ..." print primary_sysID print systems.keys() print "---------------------------------" return None # As this function is pulling from Multiples, there should never be more or less than 2 "Root" Particles ... if len(systems) != 2: print "...: Error: Encounter has more roots than expected! Total Root Particles:", len(systems) print bodies print "---------------------------------" return None # Assign the Primary System to #1 and Perturbing System to #2 sys_1 = systems[int(primary_sysID)] secondary_sysID = [key for key in systems.keys() if key!=int(primary_sysID)][0] sys_2 = systems[secondary_sysID] print 'All System Keys:', systems.keys() print 'Primary System Key:', primary_sysID print 'System 1 IDs:', sys_1.id print 'System 2 IDs:', sys_2.id # Calculate Useful Quantities mass_ratio = sys_2.mass.sum()/sys_1.mass.sum() total_mass = sys_1.mass.sum() + sys_2.mass.sum() rel_pos = sys_1.center_of_mass() - sys_2.center_of_mass() rel_vel = sys_1.center_of_mass_velocity() - sys_2.center_of_mass_velocity() # Initialize Kepler Worker kep = Kepler(unit_converter = converter, redirection = 'none') kep.initialize_code() kep.initialize_from_dyn(total_mass, rel_pos[0], rel_pos[1], rel_pos[2], rel_vel[0], rel_vel[1], rel_vel[2]) # Check to See if the Periastron is within the Ignore Distance for 10^3 Perturbation p = kep.get_periastron() ignore_distance = mass_ratio**(1./3.) * 600 | units.AU if p > ignore_distance: print "Encounter Ignored due to Periastron of", p.in_(units.AU), "and an IgnoreDistance of",ignore_distance kep.stop() print "---------------------------------" return None # Move the Particles to be Relative to their Respective Center of Mass cm_sys_1, cm_sys_2 = sys_1.center_of_mass(), sys_2.center_of_mass() cmv_sys_1, cmv_sys_2 = sys_1.center_of_mass_velocity(), sys_2.center_of_mass_velocity() for particle in sys_1: particle.position -= cm_sys_1 particle.velocity -= cmv_sys_1 for particle in sys_2: particle.position -= cm_sys_2 particle.velocity -= cmv_sys_2 # Check to See if the Planets are Closer than the Ignore Distance # Note: This shouldn't happen in the main code, but this prevents overshooting the periastron in debug mode. if kep.get_separation() > ignore_distance: kep.advance_to_radius(ignore_distance) # Advance the Center of Masses to the Desired Distance in Reduced Mass Coordinates x, y, z = kep.get_separation_vector() rel_pos_f = rel_pos.copy() rel_pos_f[0], rel_pos_f[1], rel_pos_f[2] = x, y, z vx, vy, vz = kep.get_velocity_vector() rel_vel_f = rel_vel.copy() rel_vel_f[0], rel_vel_f[1], rel_vel_f[2] = vx, vy, vz # Transform to Absolute Coordinates from Kepler Reduced Mass Coordinates cm_pos_1, cm_pos_2 = sys_2.mass.sum() * rel_pos_f / total_mass, -sys_1.mass.sum() * rel_pos_f / total_mass cm_vel_1, cm_vel_2 = sys_2.mass.sum() * rel_vel_f / total_mass, -sys_1.mass.sum() * rel_vel_f / total_mass # Move the Particles to the New Postions of their Respective Center of Mass for particle in sys_1: particle.position += cm_pos_1 particle.velocity += cm_vel_1 for particle in sys_2: particle.position += cm_pos_2 particle.velocity += cm_vel_2 # Stop Kepler and Return the Systems as a Particle Set kep.stop() # Collect the Collective Particle Set to be Returned Back final_set = Particles() final_set.add_particles(sys_1) final_set.add_particles(sys_2) print "---------------------------------" return final_set
def run_ph4(options, time=None, stars=None, mc_root_to_tree=None, randomize=True): infile = options.infile outfile = options.outfile restart_file = options.restart_file number_of_stars = options.N number_of_binaries = options.Nbin end_time = options.t_end | nbody_system.time delta_t = options.delta_t | nbody_system.time n_workers = options.n_workers use_gpu = options.use_gpu gpu_worker = options.gpu_worker salpeter = options.salpeter accuracy_parameter = options.accuracy_parameter softening_length = options.softening_length | nbody_system.length manage_encounters = options.manage_encounters random_seed = options.random_seed if randomize: if random_seed <= 0: numpy.random.seed() random_seed = numpy.random.randint(1, pow(2, 31) - 1) numpy.random.seed(random_seed) print "random seed =", random_seed if infile is not None: print "input file =", infile if restart_file is not None: print "restart file =", restart_file if restart_file is not None and infile is not None: print "restart file overrides input file" print "end_time =", end_time.number print "delta_t =", delta_t.number print "n_workers =", n_workers print "use_gpu =", use_gpu print "manage_encounters =", manage_encounters print "n =", number_of_stars print "nbin=", number_of_binaries print "\ninitializing the gravity module" sys.stdout.flush() init_smalln() # Note that there are actually three GPU options: # # 1. use the GPU code and allow GPU use (default) # 2. use the GPU code but disable GPU use (-g) # 3. use the non-GPU code (-G) if gpu_worker == 1: try: #gravity = GravityModule(number_of_workers = n_workers, # redirection = "xterm") gravity = GravityModule(number_of_workers=n_workers, redirection="none", mode="gpu") except Exception as ex: gravity = GravityModule(number_of_workers=n_workers, redirection="none") else: gravity = GravityModule(number_of_workers=n_workers, redirection="none") gravity.initialize_code() gravity.parameters.set_defaults() if softening_length < 0.0 | nbody_system.length: # Use ~interparticle spacing. Assuming standard units here. TODO eps2 = 0.25*(float(number_of_stars))**(-0.666667) \ | nbody_system.length**2 else: eps2 = softening_length * softening_length print 'softening length =', eps2.sqrt() gravity.parameters.timestep_parameter = accuracy_parameter gravity.parameters.epsilon_squared = eps2 gravity.parameters.use_gpu = use_gpu kep = Kepler(redirection="none") kep.initialize_code() multiples_code = None Xtra = numpy.zeros(2) #----------------------------------------------------------------- if (restart_file is None or not os.path.exists(restart_file + ".stars.hdf5") ) and infile is None and stars is None: print "making a Plummer model" stars = new_plummer_model(number_of_stars) id = numpy.arange(number_of_stars) stars.id = id + 1 print "setting particle masses and radii" if salpeter == 0: print 'equal masses' total_mass = 1.0 | nbody_system.mass scaled_mass = total_mass / number_of_stars else: print 'salpeter mass function' scaled_mass = new_salpeter_mass_distribution_nbody(number_of_stars) stars.mass = scaled_mass print "centering stars" stars.move_to_center() print "scaling stars to virial equilibrium" stars.scale_to_standard( smoothing_length_squared=gravity.parameters.epsilon_squared) time = 0.0 | nbody_system.time total_mass = stars.mass.sum() ke = pa.kinetic_energy(stars) kT = ke / (1.5 * number_of_stars) # Set dynamical radii (assuming virial equilibrium and standard # units). Note that this choice should be refined, and updated # as the system evolves. Probably the choice of radius should be # made entirely in the multiples module. TODO. In these units, # M = 1 and <v^2> = 0.5, so the mean 90-degree turnaround impact # parameter is # # b_90 = G (m_1+m_2) / vrel^2 # = 2 <m> / 2<v^2> # = 2 / N for equal masses # # Taking r_i = m_i / 2<v^2> = m_i in virial equilibrium means # that, approximately, "contact" means a 90-degree deflection (r_1 # + r_2 = b_90). A more conservative choice with r_i less than # this value will isolates encounters better, but also place more # load on the large-N dynamical module. stars.radius = stars.mass.number | nbody_system.length if number_of_binaries > 0: # Turn selected stars into binary components. # Only tested for equal-mass case. added_mass = 0.0 | nbody_system.mass # Work with energies rather than semimajor axes. Emin = 10 * kT Emax = 20 * kT ecc = 0.1 id_count = number_of_stars nbin = 0 for i in range(0, number_of_stars, number_of_stars / number_of_binaries): # Star i is CM, becomes component, add other star at end. nbin += 1 mass = stars[i].mass #new_mass = numpy.random.uniform()*mass # uniform q? new_mass = mass # uniform q? mbin = mass + new_mass fac = new_mass / mbin E = Emin + numpy.random.uniform() * (Emax - Emin) a = 0.5 * nbody_system.G * mass * new_mass / E kep.initialize_from_elements(mbin, a, ecc) dr = quantities.AdaptingVectorQuantity() dr.extend(kep.get_separation_vector()) dv = quantities.AdaptingVectorQuantity() dv.extend(kep.get_velocity_vector()) newstar = datamodel.Particles(1) newstar.mass = new_mass newstar.position = stars[i].position + (1 - fac) * dr newstar.velocity = stars[i].velocity + (1 - fac) * dv newstar.radius = newstar.mass.number | nbody_system.length #newstar.radius = 3.0*stars[i].radius # HACK: try to force collision # stars[i].mass = mass stars[i].position = stars[i].position - fac * dr stars[i].velocity = stars[i].velocity - fac * dv id_count += 1 newstar.id = id_count stars.add_particles(newstar) added_mass += new_mass if nbin >= number_of_binaries: break kep.stop() print 'created', nbin, 'binaries' sys.stdout.flush() stars.mass = stars.mass * total_mass / (total_mass + added_mass) number_of_stars += nbin Xtra = numpy.zeros(2) print "recentering stars" stars.move_to_center() sys.stdout.flush() stars.savepoint(time) print '' print "adding particles" # print stars sys.stdout.flush() gravity.particles.add_particles(stars) gravity.commit_particles() else: print "Restart detected. Loading parameters from restart." new_end = options.t_end stars, time, multiples_code, Xtra = MRest.read_state_from_file( restart_file, gravity, new_smalln, kep) options.t_end = new_end total_mass = stars.mass.sum() ke = pa.kinetic_energy(stars) kT = ke / (1.5 * number_of_stars) # print "IDs:", stars.id.number print '' print "number_of_stars =", number_of_stars print "evolving to time =", end_time.number, \ "in steps of", delta_t.number sys.stdout.flush() # Channel to copy values from the code to the set in memory. channel = gravity.particles.new_channel_to(stars) stopping_condition = gravity.stopping_conditions.collision_detection stopping_condition.enable() # ----------------------------------------------------------------- # Create the coupled code and integrate the system to the desired # time, managing interactions internally. kep = init_kepler(stars[0], stars[1]) if not multiples_code: multiples_code = multiples.Multiples(gravity, new_smalln, kep) multiples_code.neighbor_distance_factor = 1.0 multiples_code.neighbor_veto = True #multiples_code.neighbor_distance_factor = 2.0 #multiples_code.neighbor_veto = True multiples_code.retain_binary_apocenter = False print '' print 'multiples_code.initial_scale_factor =', \ multiples_code.initial_scale_factor print 'multiples_code.neighbor_distance_factor =', \ multiples_code.neighbor_distance_factor print 'multiples_code.neighbor_veto =', \ multiples_code.neighbor_veto print 'multiples_code.final_scale_factor =', \ multiples_code.final_scale_factor print 'multiples_code.initial_scatter_factor =', \ multiples_code.initial_scatter_factor print 'multiples_code.final_scatter_factor =', \ multiples_code.final_scatter_factor print 'multiples_code.retain_binary_apocenter =', \ multiples_code.retain_binary_apocenter # if mc_root_to_tree is not None: # multiples_code.root_to_tree = mc_root_to_tree # print 'multiples code re-loaded with binary trees snapshot' pre = "%%% " E0, cpu0 = print_log(pre, time, multiples_code) while time < end_time: time += delta_t multiples_code.evolve_model(time) # Copy values from the module to the set in memory. channel.copy() # Copy the index (ID) as used in the module to the id field in # memory. The index is not copied by default, as different # codes may have different indices for the same particle and # we don't want to overwrite silently. channel.copy_attribute("index_in_code", "id") print_log(pre, time, multiples_code, E0, cpu0) stars.savepoint(time) MRest.write_state_to_file(time, stars, gravity, multiples_code, options.restart_file, Xtra, backup=1) sys.stdout.flush() #----------------------------------------------------------------- if not outfile is None: # Write data to a file. f = open(outfile, 'w') #-------------------------------------------------- # Need to save top-level stellar data and parameters. # Need to save multiple data and parameters. f.write('%.15g\n' % time.number) for s in multiples_code.stars: write_star(s, f) #-------------------------------------------------- f.close() print 'wrote file', outfile print '' gravity.stop()
def compress_binary_components(comp1, comp2, scale): # Compress the two-body system consisting of comp1 and comp2 to # lie within distance scale of one another. pos1 = comp1.position pos2 = comp2.position sep12 = ((pos2 - pos1)**2).sum() if sep12 > scale * scale: print('\ncompressing components', int(comp1.id.number), \ 'and', int(comp2.id.number), 'to separation', scale.number) sys.stdout.flush() mass1 = comp1.mass mass2 = comp2.mass total_mass = mass1 + mass2 vel1 = comp1.velocity vel2 = comp2.velocity cmpos = (mass1 * pos1 + mass2 * pos2) / total_mass cmvel = (mass1 * vel1 + mass2 * vel2) / total_mass # For now, create and delete a temporary kepler # process to handle the transformation. Obviously # more efficient to define a single kepler at the # start of the calculation and reuse it. kep = Kepler(redirection="none") kep.initialize_code() mass = comp1.mass + comp2.mass rel_pos = pos2 - pos1 rel_vel = vel2 - vel1 kep.initialize_from_dyn(mass, rel_pos[0], rel_pos[1], rel_pos[2], rel_vel[0], rel_vel[1], rel_vel[2]) M, th = kep.get_angles() a, e = kep.get_elements() if e < 1: peri = a * (1 - e) apo = a * (1 + e) else: peri = a * (e - 1) apo = 2 * a # OK - used ony to reset scale limit = peri + 0.01 * (apo - peri) if scale < limit: scale = limit if M < 0: # print 'approaching' kep.advance_to_periastron() kep.advance_to_radius(limit) else: # print 'receding' if kep.get_separation() < scale: kep.advance_to_radius(limit) else: kep.return_to_radius(scale) # a,e = kep.get_elements() # r = kep.get_separation() # E,J = kep.get_integrals() # print 'kepler: a,e,r =', a.number, e.number, r.number # print 'E, J =', E, J # Note: if periastron > scale, we are now just past periastron. new_rel_pos = kep.get_separation_vector() new_rel_vel = kep.get_velocity_vector() kep.stop() # Enew = 0 # r2 = 0 # for k in range(3): # Enew += 0.5*(new_rel_vel[k].number)**2 # r2 += (new_rel_pos[k].number)**2 # rnew = math.sqrt(r2) # Enew -= mass.number/r1 # print 'E, Enew, rnew =', E.number, E1, r1 # Problem: the vectors returned by kepler are lists, # not numpy arrays, and it looks as though we can say # comp1.position = pos, but not comp1.position[k] = # xxx, as we'd like... Also, we don't know how to # copy a numpy array with units... TODO newpos1 = pos1 - pos1 # stupid trick to create zero vectors newpos2 = pos2 - pos2 # with the proper form and units... newvel1 = vel1 - vel1 newvel2 = vel2 - vel2 frac2 = mass2 / total_mass for k in range(3): dxk = new_rel_pos[k] dvk = new_rel_vel[k] newpos1[k] = cmpos[k] - frac2 * dxk newpos2[k] = cmpos[k] + (1 - frac2) * dxk newvel1[k] = cmvel[k] - frac2 * dvk newvel2[k] = cmvel[k] + (1 - frac2) * dvk # Perform the changes to comp1 and comp2, and recursively # transmit them to the (currently absolute) coordinates of # all lower components. offset_particle_tree(comp1, newpos1 - pos1, newvel1 - vel1) offset_particle_tree(comp2, newpos2 - pos2, newvel2 - vel2)
def get_orbit_ini(m0, m1, peri, ecc, incl, omega, rel_force=0.01, r_disk=50|units.AU): converter=nbody_system.nbody_to_si(1|units.MSun,1|units.AU) # semi-major axis if ecc!=1.0: semi = peri/(1.0-ecc) else: semi = 1.0e10 | units.AU # relative position and velocity vectors at the pericenter using kepler kepler = Kepler_twobody(converter) kepler.initialize_code() kepler.initialize_from_elements(mass=(m0+m1), semi=semi, ecc=ecc, periastron=peri) # at pericenter # moving particle backwards to radius r where: F_m1(r) = rel_force*F_m0(r_disk) #r_disk = peri r_ini = r_disk*(1.0 + numpy.sqrt(m1/m0)/rel_force) kepler.return_to_radius(radius=r_ini) rl = kepler.get_separation_vector() r = [rl[0].value_in(units.AU), rl[1].value_in(units.AU), rl[2].value_in(units.AU)] | units.AU vl = kepler.get_velocity_vector() v = [vl[0].value_in(units.kms), vl[1].value_in(units.kms), vl[2].value_in(units.kms)] | units.kms period_kepler = kepler.get_period() time_peri = kepler.get_time() kepler.stop() # rotation of the orbital plane by inclination and argument of periapsis a1 = ([1.0, 0.0, 0.0], [0.0, numpy.cos(incl), -numpy.sin(incl)], [0.0, numpy.sin(incl), numpy.cos(incl)]) a2 = ([numpy.cos(omega), -numpy.sin(omega), 0.0], [numpy.sin(omega), numpy.cos(omega), 0.0], [0.0, 0.0, 1.0]) rot = numpy.dot(a1,a2) r_au = numpy.reshape(r.value_in(units.AU), 3, 1) v_kms = numpy.reshape(v.value_in(units.kms), 3, 1) r_rot = numpy.dot(rot, r_au) | units.AU v_rot = numpy.dot(rot, v_kms) | units.kms bodies = Particles(2) bodies[0].mass = m0 bodies[0].radius = 1.0|units.RSun bodies[0].position = (0,0,0) | units.AU bodies[0].velocity = (0,0,0) | units.kms bodies[1].mass = m1 bodies[1].radius = 1.0|units.RSun bodies[1].x = r_rot[0] bodies[1].y = r_rot[1] bodies[1].z = r_rot[2] bodies[1].vx = v_rot[0] bodies[1].vy = v_rot[1] bodies[1].vz = v_rot[2] bodies.age = 0.0 | units.yr bodies.move_to_center() print "\t r_rel_ini = ", r_rot.in_(units.AU) print "\t v_rel_ini = ", v_rot.in_(units.kms) print "\t time since peri = ", time_peri.in_(units.yr) a_orbit, e_orbit, p_orbit = orbital_parameters(r_rot, v_rot, (m0+m1)) print "\t a = ", a_orbit.in_(units.AU), "\t e = ", e_orbit, "\t period = ", p_orbit.in_(units.yr) return bodies, time_peri
def get_orbit_ini(m0, m1, peri, ecc, incl, omega, rel_force=0.01, r_disk=50 | units.AU): converter = nbody_system.nbody_to_si(1 | units.MSun, 1 | units.AU) # semi-major axis if ecc != 1.0: semi = peri / (1.0 - ecc) else: semi = 1.0e10 | units.AU # relative position and velocity vectors at the pericenter using kepler kepler = Kepler_twobody(converter) kepler.initialize_code() kepler.initialize_from_elements(mass=(m0 + m1), semi=semi, ecc=ecc, periastron=peri) # at pericenter # moving particle backwards to radius r where: F_m1(r) = rel_force*F_m0(r_disk) #r_disk = peri r_ini = r_disk * (1.0 + numpy.sqrt(m1 / m0) / rel_force) kepler.return_to_radius(radius=r_ini) rl = kepler.get_separation_vector() r = [ rl[0].value_in(units.AU), rl[1].value_in(units.AU), rl[2].value_in( units.AU) ] | units.AU vl = kepler.get_velocity_vector() v = [ vl[0].value_in(units.kms), vl[1].value_in(units.kms), vl[2].value_in( units.kms) ] | units.kms period_kepler = kepler.get_period() time_peri = kepler.get_time() kepler.stop() # rotation of the orbital plane by inclination and argument of periapsis a1 = ([1.0, 0.0, 0.0], [0.0, numpy.cos(incl), -numpy.sin(incl)], [0.0, numpy.sin(incl), numpy.cos(incl)]) a2 = ([numpy.cos(omega), -numpy.sin(omega), 0.0], [numpy.sin(omega), numpy.cos(omega), 0.0], [0.0, 0.0, 1.0]) rot = numpy.dot(a1, a2) r_au = numpy.reshape(r.value_in(units.AU), 3, 1) v_kms = numpy.reshape(v.value_in(units.kms), 3, 1) r_rot = numpy.dot(rot, r_au) | units.AU v_rot = numpy.dot(rot, v_kms) | units.kms bodies = Particles(2) bodies[0].mass = m0 bodies[0].radius = 1.0 | units.RSun bodies[0].position = (0, 0, 0) | units.AU bodies[0].velocity = (0, 0, 0) | units.kms bodies[1].mass = m1 bodies[1].radius = 1.0 | units.RSun bodies[1].x = r_rot[0] bodies[1].y = r_rot[1] bodies[1].z = r_rot[2] bodies[1].vx = v_rot[0] bodies[1].vy = v_rot[1] bodies[1].vz = v_rot[2] bodies.age = 0.0 | units.yr bodies.move_to_center() print "\t r_rel_ini = ", r_rot.in_(units.AU) print "\t v_rel_ini = ", v_rot.in_(units.kms) print "\t time since peri = ", time_peri.in_(units.yr) a_orbit, e_orbit, p_orbit = orbital_parameters(r_rot, v_rot, (m0 + m1)) print "\t a = ", a_orbit.in_( units.AU), "\t e = ", e_orbit, "\t period = ", p_orbit.in_(units.yr) return bodies, time_peri