def evolve_model(self):
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun,
149.5e6 | units.km)
hermite = Hermite(convert_nbody)
hermite.initialize_code()
hermite.parameters.epsilon_squared = 0.0 | units.AU**2
stars = self.new_system_of_sun_and_earth()
earth = stars[1]
sun = stars[0]
Earth = blender.Primitives.sphere(10, 10, 0.1) # Make the earth avatar
Sun = blender.Primitives.sphere(32, 32, 1) # Make the sun avatar
hermite.particles.add_particles(stars)
for i in range(1 * 365):
hermite.evolve_model(i | units.day)
hermite.particles.copy_values_of_all_attributes_to(stars)
# update avatar positions:
Earth.loc = (1 * earth.position.value_in(units.AU)[0],
1 * earth.position.value_in(units.AU)[1],
earth.position.value_in(units.AU)[2])
Sun.loc = (1 * sun.position.value_in(units.AU)[0],
1 * sun.position.value_in(units.AU)[1],
sun.position.value_in(units.AU)[2])
blender.Redraw()
hermite.print_refs()
hermite.stop()
def test13(self):
particles = plummer.new_plummer_model(31)
instance = Hermite(number_of_workers=1)#, debugger="xterm")
instance.initialize_code()
instance.parameters.epsilon_squared = 0.01 | nbody_system.length ** 2
instance.particles.add_particles(particles)
instance.evolve_model(0.1 | nbody_system.time)
instance.synchronize_model()
expected_positions = instance.particles.position
instance.stop()
positions_per_workers = []
for n in [2,3,4,5]:
instance = Hermite(number_of_workers=n)
instance.initialize_code()
instance.parameters.epsilon_squared = 0.01 | nbody_system.length ** 2
instance.particles.add_particles(particles)
instance.evolve_model(0.1 | nbody_system.time)
instance.synchronize_model()
positions_per_workers.append(instance.particles.position)
instance.stop()
for index, n in enumerate([2,3,4,5]):
self.assertAlmostEqual(expected_positions, positions_per_workers[index], 15)
def simulate_small_cluster(number_of_stars=1000,
end_time=40 | nbody_system.time,
number_of_workers=1):
particles = new_plummer_model(number_of_stars)
particles.scale_to_standard()
gravity = Hermite(number_of_workers=number_of_workers)
gravity.parameters.epsilon_squared = 0.15 | nbody_system.length**2
gravity.particles.add_particles(particles)
from_gravity_to_model = gravity.particles.new_channel_to(particles)
time = 0.0 * end_time
total_energy_at_t0 = gravity.kinetic_energy + gravity.potential_energy
positions_at_different_times = []
positions_at_different_times.append(particles.position)
times = []
times.append(time)
print("evolving the model until t = " + str(end_time))
while time < end_time:
time += end_time / 3.0
gravity.evolve_model(time)
from_gravity_to_model.copy()
positions_at_different_times.append(particles.position)
times.append(time)
print_log(time, gravity, particles, total_energy_at_t0)
gravity.stop()
return times, positions_at_different_times
def test3(self):
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun, 149.5e6 | units.km)
instance = Hermite(convert_nbody)
instance.initialize_code()
instance.parameters.epsilon_squared = 0.00001 | units.AU**2
instance.dt_dia = 5000
stars = datamodel.Stars(2)
star1 = stars[0]
star2 = stars[1]
star1.mass = units.MSun(1.0)
star1.position = units.AU(numpy.array((-1.0,0.0,0.0)))
star1.velocity = units.AUd(numpy.array((0.0,0.0,0.0)))
star1.radius = units.RSun(1.0)
star2.mass = units.MSun(1.0)
star2.position = units.AU(numpy.array((1.0,0.0,0.0)))
star2.velocity = units.AUd(numpy.array((0.0,0.0,0.0)))
star2.radius = units.RSun(100.0)
instance.particles.add_particles(stars)
for x in range(1,2000,10):
instance.evolve_model(x | units.day)
instance.particles.copy_values_of_all_attributes_to(stars)
stars.savepoint()
instance.cleanup_code()
instance.stop()
def test12(self):
particles = datamodel.Particles(2)
particles.x = [0.0, 1.00] | nbody_system.length
particles.y = [0.0, 0.0] | nbody_system.length
particles.z = [0.0, 0.0] | nbody_system.length
particles.radius = 0.005 | nbody_system.length
particles.vx = [5.1, 0.0] | nbody_system.speed
particles.vy = [0.0, 0.0] | nbody_system.speed
particles.vz = [0.0, 0.0] | nbody_system.speed
particles.mass = [0.1, 0.1] | nbody_system.mass
instance = Hermite()
instance.initialize_code()
instance.parameters.stopping_conditions_out_of_box_size = .5 | nbody_system.length
self.assertEqual(
instance.parameters.stopping_conditions_out_of_box_size,
.5 | nbody_system.length)
instance.particles.add_particles(particles)
instance.stopping_conditions.out_of_box_detection.enable()
instance.evolve_model(0.1 | nbody_system.time)
self.assertTrue(
instance.stopping_conditions.out_of_box_detection.is_set())
self.assertAlmostEqual(
instance.stopping_conditions.out_of_box_detection.particles(0).x,
1.0 | nbody_system.length, 3)
instance.stop()
def test22(self):
hermite = Hermite()
hermite.parameters.epsilon_squared = 0.0 | nbody_system.length**2
particles = datamodel.Particles(2)
particles.position = ([0, 0, 0], [1, 0, 0]) | nbody_system.length
particles.velocity = ([-2, 0, 0], [2, 0, 0]) | nbody_system.speed
particles.radius = 0 | nbody_system.length
particles.mass = 0.1 | nbody_system.mass
hermite.particles.add_particles(particles)
hermite.stopping_conditions.out_of_box_detection.enable()
hermite.parameters.stopping_conditions_out_of_box_size = 2 | nbody_system.length
hermite.parameters.stopping_conditions_out_of_box_use_center_of_mass = False
hermite.evolve_model(1 | nbody_system.time)
print(hermite.particles.x)
print(hermite.particles.key, particles[1].key)
print(hermite.stopping_conditions.out_of_box_detection.particles(0))
self.assertTrue(
hermite.stopping_conditions.out_of_box_detection.is_set())
self.assertEqual(
len(hermite.stopping_conditions.out_of_box_detection.particles(0)),
1)
self.assertEqual(
hermite.stopping_conditions.out_of_box_detection.particles(0)
[0].key, particles[1].key)
hermite.stop()
def simulate_system_until(particles, end_time):
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun,
149.5e6 | units.km)
instance = Hermite(convert_nbody)
instance.parameters.epsilon_squared = 0.0 | units.AU**2
instance.particles.add_particles(particles)
t0 = 0 | units.day
dt = 10 | units.day
t = t0
earth = instance.particles[1]
x_values = quantities.AdaptingVectorQuantity()
y_values = quantities.AdaptingVectorQuantity()
while t < end_time:
instance.evolve_model(t)
x_values.append(earth.x)
y_values.append(earth.y)
t += dt
instance.stop()
return x_values, y_values
def evolve_model(end_time, double_star, stars):
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
# from_stars = stars.new_channel_to(gravity.particles)
time = 0 | units.yr
dt = end_time / 100.
a = [] | units.au
t = [] | units.yr
while time < end_time:
time += dt
gravity.evolve_model(1 | units.yr)
to_stars.copy()
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
a.append(orbital_elements[2])
t.append(time)
gravity.stop()
from matplotlib import pyplot
pyplot.scatter(t.value_in(units.yr), a.value_in(units.au))
pyplot.show()
def test18(self):
particles = datamodel.Particles(2)
particles.x = [0.0,1.0] | nbody_system.length
particles.y = 0.0 | nbody_system.length
particles.z = 0.0 | nbody_system.length
particles.vx = 0.0 | nbody_system.speed
particles.vy = 0.0 | nbody_system.speed
particles.vz = 0.0 | nbody_system.speed
particles.mass = 1.0 | nbody_system.mass
instance = Hermite()
instance.particles.add_particles(particles)
instance.commit_particles()
self.assertEqual(instance.particles[0].radius, 0.0 | nbody_system.length)
instance.parameters.end_time_accuracy_factor = 1.0
instance.evolve_model(0.1 | nbody_system.time)
self.assertAlmostRelativeEquals(instance.model_time, 0.10563767746 |nbody_system.time, 5)
instance.parameters.end_time_accuracy_factor = -1.0
instance.evolve_model(0.3 | nbody_system.time)
self.assertAlmostRelativeEquals(instance.model_time, 0.266758127609 |nbody_system.time, 5)
instance.parameters.end_time_accuracy_factor = 0.0
instance.evolve_model(0.4 | nbody_system.time)
self.assertAlmostRelativeEquals(instance.model_time, 0.4 |nbody_system.time, 6)
instance.parameters.end_time_accuracy_factor = -0.5
instance.evolve_model(0.5 | nbody_system.time)
self.assertAlmostRelativeEquals(instance.model_time, 0.48974930698 |nbody_system.time, 6)
instance.parameters.end_time_accuracy_factor = +0.5
instance.evolve_model(0.6 | nbody_system.time)
self.assertAlmostRelativeEquals(instance.model_time, 0.6042733579 |nbody_system.time, 6)
instance.stop()
def test8(self):
print("Testing Hermite collision_detection")
particles = datamodel.Particles(7)
particles.mass = 0.001 | nbody_system.mass
particles.radius = 0.01 | nbody_system.length
particles.x = [-101.0, -100.0, -0.5, 0.5, 100.0, 101.0, 104.0] | nbody_system.length
particles.y = 0 | nbody_system.length
particles.z = 0 | nbody_system.length
particles.velocity = [[2, 0, 0], [-2, 0, 0]]*3 + [[-4, 0, 0]] | nbody_system.speed
instance = Hermite()
instance.initialize_code()
instance.parameters.set_defaults()
instance.particles.add_particles(particles)
collisions = instance.stopping_conditions.collision_detection
collisions.enable()
instance.evolve_model(1.0 | nbody_system.time)
self.assertTrue(collisions.is_set())
self.assertTrue(instance.model_time < 0.5 | nbody_system.time)
self.assertEqual(len(collisions.particles(0)), 3)
self.assertEqual(len(collisions.particles(1)), 3)
self.assertEqual(len(particles - collisions.particles(0) - collisions.particles(1)), 1)
self.assertEqual(abs(collisions.particles(0).x - collisions.particles(1).x) <=
(collisions.particles(0).radius + collisions.particles(1).radius),
[True, True, True])
sticky_merged = datamodel.Particles(len(collisions.particles(0)))
sticky_merged.mass = collisions.particles(0).mass + collisions.particles(1).mass
sticky_merged.radius = collisions.particles(0).radius
for p1, p2, merged in zip(collisions.particles(0), collisions.particles(1), sticky_merged):
merged.position = (p1 + p2).center_of_mass()
merged.velocity = (p1 + p2).center_of_mass_velocity()
print(instance.model_time)
print(instance.particles)
instance.particles.remove_particles(collisions.particles(0) + collisions.particles(1))
instance.particles.add_particles(sticky_merged)
instance.evolve_model(1.0 | nbody_system.time)
print()
print(instance.model_time)
print(instance.particles)
self.assertTrue(collisions.is_set())
self.assertTrue(instance.model_time < 1.0 | nbody_system.time)
self.assertEqual(len(collisions.particles(0)), 1)
self.assertEqual(len(collisions.particles(1)), 1)
self.assertEqual(len(instance.particles - collisions.particles(0) - collisions.particles(1)), 2)
self.assertEqual(abs(collisions.particles(0).x - collisions.particles(1).x) <=
(collisions.particles(0).radius + collisions.particles(1).radius),
[True])
instance.stop()
def test19(self):
particles = datamodel.Particles(2)
particles.x = [0.0,200.0] | nbody_system.length
particles.y = 0.0 | nbody_system.length
particles.z = 0.0 | nbody_system.length
particles.vx = 0.0 | nbody_system.speed
particles.vy = 0.0 | nbody_system.speed
particles.vz = 0.0 | nbody_system.speed
particles.mass = 1.0 | nbody_system.mass
instance = Hermite()
instance.particles.add_particles(particles)
instance.commit_particles()
self.assertEqual(instance.particles[0].radius, 0.0 | nbody_system.length)
instance.parameters.end_time_accuracy_factor = 0.0
instance.evolve_model(0.1 | nbody_system.time)
self.assertAlmostRelativeEquals(instance.model_time, 0.1 |nbody_system.time, 5)
instance.stop()
def test7(self):
print("Test7: Testing effect of Hermite parameter epsilon_squared")
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun,
1.0 | units.AU)
particles = datamodel.Particles(2)
sun = particles[0]
sun.mass = 1.0 | units.MSun
sun.position = [0.0, 0.0, 0.0] | units.AU
sun.velocity = [0.0, 0.0, 0.0] | units.AU / units.yr
sun.radius = 1.0 | units.RSun
earth = particles[1]
earth.mass = 5.9736e24 | units.kg
earth.radius = 6371.0 | units.km
earth.position = [0.0, 1.0, 0.0] | units.AU
earth.velocity = [2.0 * numpy.pi, -0.0001, 0.0] | units.AU / units.yr
initial_direction = math.atan((earth.velocity[0] / earth.velocity[1]))
final_direction = []
for log_eps2 in range(-9, 10, 2):
instance = Hermite(convert_nbody)
instance.parameters.end_time_accuracy_factor = 0.0
instance.parameters.epsilon_squared = 10.0**log_eps2 | units.AU**2
instance.particles.add_particles(particles)
instance.commit_particles()
instance.evolve_model(0.25 | units.yr)
final_direction.append(
math.atan((instance.particles[1].velocity[0] /
instance.particles[1].velocity[1])))
instance.stop()
# Small values of epsilon_squared should result in normal earth-sun dynamics: rotation of 90 degrees
self.assertAlmostEqual(abs(final_direction[0]),
abs(initial_direction + math.pi / 2.0), 2)
# Large values of epsilon_squared should result in ~ no interaction
self.assertAlmostEqual(final_direction[-1], initial_direction, 2)
# Outcome is most sensitive to epsilon_squared when epsilon_squared = d(earth, sun)^2
delta = [
abs(final_direction[i + 1] - final_direction[i])
for i in range(len(final_direction) - 1)
]
self.assertEqual(delta[len(final_direction) // 2 - 1], max(delta))
def test23(self):
hermite = Hermite()
hermite.parameters.epsilon_squared = 0.0 | nbody_system.length**2
particles = datamodel.Particles(1)
particles.position = ([0,0,0] )| nbody_system.length
particles.velocity = ([1,0,0] )| nbody_system.speed
particles.radius = 0| nbody_system.length
particles.mass = 0.1| nbody_system.mass
hermite.particles.add_particles(particles)
hermite.evolve_model(1 | nbody_system.time)
print(hermite.particles.x)
self.assertAlmostRelativeEquals(hermite.model_time, 1 | nbody_system.time)
self.assertAlmostRelativeEquals(hermite.particles[0].x, 1 | nbody_system.length)
hermite.evolve_model(1.5 | nbody_system.time)
print(hermite.particles.x)
self.assertAlmostRelativeEquals(hermite.model_time, 1.5 | nbody_system.time)
self.assertAlmostRelativeEquals(hermite.particles[0].x, 1.5 | nbody_system.length)
hermite.stop()
def test2(self):
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun, 149.5e6 | units.km)
instance = Hermite(convert_nbody)
instance.initialize_code()
instance.parameters.epsilon_squared = 0.0 | units.AU**2
instance.dt_dia = 5000
stars = self.new_system_of_sun_and_earth()
earth = stars[1]
instance.particles.add_particles(stars)
for x in range(1, 500, 10):
instance.evolve_model(x | units.day)
instance.particles.copy_values_of_all_attributes_to(stars)
stars.savepoint()
if HAS_MATPLOTLIB:
figure = pyplot.figure()
plot = figure.add_subplot(1,1,1)
x_points = earth.get_timeline_of_attribute("x")
y_points = earth.get_timeline_of_attribute("y")
x_points_in_AU = [t_x[1].value_in(units.AU) for t_x in x_points]
y_points_in_AU = [t_x1[1].value_in(units.AU) for t_x1 in y_points]
plot.scatter(x_points_in_AU,y_points_in_AU, color="b", marker='o')
plot.set_xlim(-1.5, 1.5)
plot.set_ylim(-1.5, 1.5)
test_results_path = self.get_path_to_results()
output_file = os.path.join(test_results_path, "hermite-earth-sun2.svg")
figure.savefig(output_file)
instance.cleanup_code()
instance.stop()
def test10(self):
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun, 149.5e6 | units.km)
instance = Hermite(convert_nbody)
instance.initialize_code()
instance.parameters.epsilon_squared = 0.0 | units.AU**2
instance.parameters.stopping_conditions_number_of_steps = 10
self.assertEqual(instance.parameters.stopping_conditions_number_of_steps,10)
stars = self.new_system_of_sun_and_earth()
earth = stars[1]
instance.particles.add_particles(stars)
instance.stopping_conditions.number_of_steps_detection.enable()
instance.evolve_model(365.0 | units.day)
self.assertTrue(instance.stopping_conditions.number_of_steps_detection.is_set())
instance.particles.copy_values_of_all_attributes_to(stars)
instance.cleanup_code()
instance.stop()
def test1(self):
convert_nbody = nbody_system.nbody_to_si(1.0 | units.MSun, 149.5e6 | units.km)
hermite = Hermite(convert_nbody)
hermite.initialize_code()
hermite.parameters.epsilon_squared = 0.0 | units.AU**2
hermite.parameters.end_time_accuracy_factor = 0.0
hermite.dt_dia = 5000
stars = self.new_system_of_sun_and_earth()
earth = stars[1]
hermite.particles.add_particles(stars)
hermite.evolve_model(365.0 | units.day)
hermite.particles.copy_values_of_all_attributes_to(stars)
position_at_start = earth.position.value_in(units.AU)[0]
position_after_full_rotation = earth.position.value_in(units.AU)[0]
self.assertAlmostRelativeEqual(position_at_start, position_after_full_rotation, 6)
hermite.evolve_model(365.0 + (365.0 / 2) | units.day)
hermite.particles.copy_values_of_all_attributes_to(stars)
position_after_half_a_rotation = earth.position.value_in(units.AU)[0]
self.assertAlmostRelativeEqual(-position_at_start, position_after_half_a_rotation, 3)
hermite.evolve_model(365.0 + (365.0 / 2) + (365.0 / 4) | units.day)
hermite.particles.copy_values_of_all_attributes_to(stars)
position_after_half_a_rotation = earth.position.value_in(units.AU)[1]
self.assertAlmostRelativeEqual(-position_at_start, position_after_half_a_rotation, 3)
hermite.cleanup_code()
hermite.stop()
def test11(self):
particles = datamodel.Particles(2)
particles.x = [0.0,10.0] | nbody_system.length
particles.y = 0 | nbody_system.length
particles.z = 0 | nbody_system.length
particles.radius = 0.005 | nbody_system.length
particles.vx = 0 | nbody_system.speed
particles.vy = 0 | nbody_system.speed
particles.vz = 0 | nbody_system.speed
particles.mass = 1.0 | nbody_system.mass
instance = Hermite()
instance.initialize_code()
instance.parameters.stopping_conditions_number_of_steps = 2
self.assertEqual(instance.parameters.stopping_conditions_number_of_steps, 2)
instance.particles.add_particles(particles)
instance.stopping_conditions.number_of_steps_detection.enable()
instance.evolve_model(10 | nbody_system.time)
self.assertTrue(instance.stopping_conditions.number_of_steps_detection.is_set())
self.assertTrue(instance.model_time < 10 | nbody_system.time)
instance.stop()
def supernova_in_binary_nbody(M0, m0, a0, tsn):
stars = make_circular_binary(M0, m0, a0)
M, m, a, e, ta_out, inc, lan_out, aop_out = orbital_elements_from_binary(
stars, G=constants.G)
print("Initial binary: a=", a.in_(
units.AU), "e=", e, "M=", stars[0].mass, "and m=", stars[1].mass)
converter = nbody_system.nbody_to_si(M + m, a)
gravity = Hermite(converter)
gravity.particles.add_particles(stars)
print("Integrate binary to t=", tsn.in_(units.day))
gravity.evolve_model(tsn)
M, m, a, e, ta_out, inc, lan_out, aop_out = orbital_elements_from_binary(
stars, G=constants.G)
print("Pre supernova orbit: a=", a.in_(units.AU), "e=", e)
stars[0].mass *= 0.1
print("Reduce stellar mass to: M=", stars[0].mass, "and m=", stars[1].mass)
v_kick = (0, 0, 0) | units.kms
stars[0].velocity += v_kick
gravity.evolve_model(2 * tsn)
M, m, a, e, ta_out, inc, lan_out, aop_out = orbital_elements_from_binary(
stars, G=constants.G)
print("Post supernova orbit: a=", a.in_(units.AU), "e=", e)
r0 = a
a_ana = post_supernova_semimajor_axis(
M0, m0, stars[0].mass, stars[1].mass, a, r0)
e_ana = post_supernova_eccentricity(
M0, m0, stars[0].mass, stars[1].mass, a, r0)
print(
"Analytic solution to post orbit orbital parameters: a=",
a_ana, "e=", e_ana,
)
gravity.stop()
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5*end_time/1000.
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
period = (
2*numpy.pi
* (
double_star.semimajor_axis*double_star.semimajor_axis*double_star.semimajor_axis
/ (constants.G*double_star.mass)
).sqrt()
)
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period/dt))
a_an = [] | units.au
e_an = []
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
print(atemp)
a = [] | units.au
e = []
m = [] | units.MSun
t = [] | units.yr
while time<end_time:
time += dt
gravity.evolve_model(time)
to_stars.copy()
dmdt = mass_loss_rate(stars.mass)
dadt = dadt_masschange(atemp, stars.mass, dmdt)
dedt = dedt_masschange(etemp, stars.mass, dmdt)
atemp = atemp + dadt*dt
etemp = etemp + dedt*dt
a_an.append(atemp)
e_an.append(etemp)
stars.mass += dmdt * dt
from_stars.copy()
orbital_elements = orbital_elements_from_binary(stars,
G=constants.G)
a.append(orbital_elements[2])
e.append(orbital_elements[3])
m.append(stars.mass.sum())
t.append(time)
print("time=", time.in_(units.yr),
"a=", a[-1].in_(units.RSun),
"e=", e[-1],
"m=", stars.mass.in_(units.MSun), end="\r")
gravity.stop()
from matplotlib import pyplot
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True)
axis[0][0].plot(t.value_in(units.yr), a.value_in(units.RSun), label="nbody")
axis[0][0].plot(t.value_in(units.yr), a_an.value_in(units.RSun), label="analytic")
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][0].legend()
axis[0][1].plot(t.value_in(units.yr), m.value_in(units.MSun))
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[1][1].plot(t.value_in(units.yr), e)
axis[1][1].plot(t.value_in(units.yr), e_an)
axis[1][1].set_ylabel("e")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.savefig("mloss.png")
pyplot.show()
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5 * end_time / 1000. * 2
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
stars2 = stars.copy()
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
gravity2 = Hermite(converter)
gravity2.particles.add_particle(stars2)
to_stars2 = gravity2.particles.new_channel_to(stars2)
from_stars2 = stars2.new_channel_to(gravity2.particles)
period = (2 * numpy.pi *
(double_star.semimajor_axis * double_star.semimajor_axis *
double_star.semimajor_axis /
(constants.G * double_star.mass)).sqrt())
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period / dt))
a_an = [] | units.au
e_an = []
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
a = [] | units.au
e = []
ome = []
a2 = [] | units.au
e2 = []
ome2 = []
m1 = [] | units.MSun
m2 = [] | units.MSun
t = [] | units.yr
while time < end_time:
time += dt
gravity.evolve_model(time)
gravity2.evolve_model(time)
to_stars.copy()
to_stars2.copy()
dmdtloss = mass_loss_rate(stars.mass)
dmdtacc = dmdt_acc(dmdtloss)
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
orbital_elements2 = orbital_elements_from_binary(stars2, G=constants.G)
# etemp = orbital_elements[3]
# atemp = orbital_elements[2]
dadt = dadt_masschange(atemp, stars.mass, dmdtloss + dmdtacc)
dedt = dedt_masschange(etemp, stars.mass, dmdtloss + dmdtacc)
dadt += dadt_momentumchange(atemp, etemp, stars.mass, dmdtacc)
dedt += dedt_momentumchange(etemp, stars.mass, dmdtacc)
h = (constants.G * stars.mass.sum() * atemp * (1 - etemp * etemp))**0.5
dhdt = dhdt_momentumchange(h, stars.mass, dmdtacc)
atemp = atemp + dadt * dt
etemp = etemp + dedt * dt
a_an.append(atemp)
e_an.append(etemp)
kick_from_accretion(stars, dmdtacc, dt)
dhdt_dadt_to_kick(stars2, dhdt, dadt, dmdtloss + dmdtacc, dt)
stars.mass += (dmdtloss + dmdtacc) * dt
stars2.mass += (dmdtloss + dmdtacc) * dt
from_stars.copy()
from_stars2.copy()
a.append(orbital_elements[2])
e.append(orbital_elements[3])
ome.append(orbital_elements[7])
a2.append(orbital_elements2[2])
e2.append(orbital_elements2[3])
ome2.append(orbital_elements2[7])
m1.append(stars[0].mass)
m2.append(stars[1].mass)
t.append(time)
print("time=", time.in_(units.yr), "a=", a[-1].in_(units.RSun), "e=",
e[-1], "m=", stars.mass.in_(units.MSun), "end=\r")
gravity.stop()
gravity2.stop()
from matplotlib import pyplot
pyplot.rc('text', usetex=True)
pyplot.rcParams.update({'font.size': 16})
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True, figsize=(13, 6))
axis[0][0].plot(t.value_in(units.yr),
a.value_in(units.RSun),
label="nbody (direct)",
lw=2)
axis[0][0].plot(t.value_in(units.yr),
a2.value_in(units.RSun),
label="nbody (heuristic)",
lw=2,
ls="--")
axis[0][0].plot(t.value_in(units.yr),
a_an.value_in(units.RSun),
label="analytic",
lw=2,
ls="-.")
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][0].legend()
axis[0][1].plot(t.value_in(units.yr),
m1.value_in(units.MSun),
label="m1",
lw=2,
c="tab:red")
axis[0][1].plot(t.value_in(units.yr),
m2.value_in(units.MSun),
label="m2",
lw=2,
c="tab:cyan")
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[0][1].legend()
axis[1][1].plot(t.value_in(units.yr), e, lw=2)
axis[1][1].plot(t.value_in(units.yr), e2, lw=2, ls="--")
axis[1][1].plot(t.value_in(units.yr), e_an, lw=2, ls="-.")
axis[1][1].set_ylabel("e")
axis[1][0].plot(t.value_in(units.yr), ome, lw=2, label="nbody (direct)")
axis[1][0].plot(t.value_in(units.yr),
ome2,
lw=2,
ls="--",
label="nbody (heuristic)")
axis[1][0].set_ylabel("$\omega$ [degrees]")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.tight_layout()
pyplot.subplots_adjust(hspace=0, top=0.93, bottom=0.1)
pyplot.suptitle("mloss+macc+momentum change, same model")
pyplot.savefig("comparisons.png")
pyplot.show()
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
#time = 10.0017596364 | units.yr
#inname = "binstar_10.0017596364.hdf5"
#stars = read_set_from_file(inname, "hdf5")
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
period = (2 * numpy.pi *
(double_star.semimajor_axis * double_star.semimajor_axis *
double_star.semimajor_axis /
(constants.G * double_star.mass)).sqrt())
print("Period =", period.as_string_in(units.yr))
dt = period / 32.
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period / dt))
print("Radii", stars.radius)
print("Taulag", stars.taulag)
print("K", stars.kaps)
QT = QuickTides(double_star.semimajor_axis, double_star.eccentricity,
stars[0].mass, stars[1].mass, stars[0].radius,
stars[1].radius, stars[0].kaps, stars[1].kaps,
stars[0].taulag, stars[1].taulag)
print(stars)
a_an = [] | units.au
e_an = []
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
a = [] | units.au
e = []
m = [] | units.MSun
t = [] | units.yr
while time < end_time:
time += dt
gravity.evolve_model(time)
to_stars.copy()
dadt, dedt = QT.dadt_dedt(atemp, etemp)
atemp = atemp + dadt * dt
etemp = etemp + dedt * dt
a_an.append(atemp)
e_an.append(etemp)
kick_stars_tides(stars, dt)
from_stars.copy()
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
a.append(orbital_elements[2])
e.append(orbital_elements[3])
m.append(stars.mass.sum())
t.append(time)
if check_collision(stars): break
print("time=",
time.in_(units.yr),
"a=",
a[-1].in_(units.RSun),
"e=",
e[-1],
"m=",
stars.mass.in_(units.MSun),
end="\r")
gravity.stop()
from matplotlib import pyplot
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True)
axis[0][0].plot(t.value_in(units.yr), a.value_in(units.au), label="nbody")
axis[0][0].plot(t.value_in(units.yr),
a_an.value_in(units.au),
label="analytic")
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][0].legend()
write_set_to_file(stars,
"binstar_" + str(time.value_in(units.yr)) + ".hdf5",
"hdf5")
numpy.savetxt(
"ae_{:d}.txt".format(numpy.random.randint(0, 1000)),
numpy.vstack([t.value_in(units.yr),
a.value_in(units.au), e]).T)
axis[0][1].plot(t.value_in(units.yr), m.value_in(units.MSun))
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[1][1].plot(t.value_in(units.yr), e)
axis[1][1].plot(t.value_in(units.yr), e_an)
axis[1][1].set_ylabel("e")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.savefig("mloss.png")
pyplot.show()
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5 * end_time / 1000.
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
a_an = [] | units.au
e_an = []
# dt_an = dt/1000.
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
print(atemp)
a = [] | units.au
e = []
m = [] | units.MSun
t = [] | units.yr
while time < end_time:
# ana_time = time
# ana_time_end = time + dt
# while ana_time < ana_time_end:
# dmdt_ana = -1*mass_loss_rate(stars.mass)
# print(atemp)
# dadt = dadt_massloss(atemp, stars.mass, dmdt_ana)
# dedt = dedt_massloss(etemp, stars.mass, dmdt_ana)
# atemp = dadt*dt
# etemp = dedt*dt
# ana_time += dt_an
time += dt
gravity.evolve_model(time)
to_stars.copy()
dmdt = mass_loss_rate(stars.mass)
dadt = dadt_massloss(atemp, stars.mass, dmdt)
dedt = dedt_massloss(etemp, stars.mass, dmdt)
atemp = atemp + dadt * dt
etemp = etemp + dedt * dt
a_an.append(atemp)
e_an.append(etemp)
stars.mass -= dmdt * dt
from_stars.copy()
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
a.append(orbital_elements[2])
e.append(orbital_elements[3])
m.append(stars.mass.sum())
t.append(time)
print("time=", time.in_(units.yr), "a=", a[-1].in_(units.RSun), "e=",
e[-1], "m=", stars.mass.in_(units.MSun))
gravity.stop()
from matplotlib import pyplot
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True)
axis[0][0].scatter(t.value_in(units.yr), a.value_in(units.RSun))
axis[0][0].scatter(t.value_in(units.yr), a_an.value_in(units.RSun))
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][1].scatter(t.value_in(units.yr), m.value_in(units.MSun))
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[1][1].scatter(t.value_in(units.yr), e)
axis[1][1].scatter(t.value_in(units.yr), e_an)
axis[1][1].set_ylabel("e")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.show()
pyplot.savefig("mloss.png")
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.05 * end_time / 1000.
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
period = get_period(double_star)
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period / dt))
a_an = [] | units.au
e_an = []
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
###### COMMON ENVELOPE STUFF ###############
final_a = 40 | units.RSun
mu = double_star.mass * constants.G
Eps0 = mu / (2 * double_star.semimajor_axis)
Eps1 = mu / (2 * final_a)
# Eps_ce should come from alpha lambda model, but we just fix the final semimajor axis here for simplicity
Eps_ce = Eps1 - Eps0
print("Eps_ce/Eps0", Eps_ce / Eps0)
Tce = 1000 | units.yr
Kce = K_from_eps(Eps0, Eps_ce, Tce, mu)
print("Kce", Kce)
Avisc = -Kce * Tce
print("Avisc", Avisc.as_string_in(units.RSun**2))
Rvisc = Avisc.sqrt() / (4 * constants.pi)
print("Rvisc", Rvisc.as_string_in(units.RSun))
vorb = (mu / double_star.semimajor_axis).sqrt()
###### END COMMON ENVELOPE STUFF ###############
collision = False
a = [] | units.au
e = []
m = [] | units.MSun
t = [] | units.yr
while time < end_time:
time += dt
if not collision:
gravity.evolve_model(time)
to_stars.copy()
kick_stars_comenv2(stars, dt, Kce, Avisc)
from_stars.copy()
from_stars.copy()
orbital_elements = orbital_elements_from_binary(stars,
G=constants.G)
collision = check_collisions(stars)
if atemp.number > 0:
dadt = dadt_comenv_k0(atemp, etemp, Kce / Avisc)
dedt = dedt_comenv_k0(atemp, etemp, Kce / Avisc)
atemp = atemp + dadt * dt
etemp = etemp + dedt * dt
if collision and atemp.number < 0: break
a_an.append(atemp)
e_an.append(etemp)
a.append(orbital_elements[2])
e.append(orbital_elements[3])
m.append(stars.mass.sum())
t.append(time)
print("time=",
time.in_(units.yr),
"a=",
a[-1].in_(units.RSun),
"e=",
e[-1],
"m=",
stars.mass.in_(units.MSun),
end="\r")
gravity.stop()
from matplotlib import pyplot
import seaborn as sns
sns.set(font_scale=1.33)
sns.set_style("ticks")
fig, axis = pyplot.subplots(nrows=2, sharex=True)
axis[0].plot(t.value_in(units.yr),
a.value_in(units.RSun),
label="nbody k=0")
axis[0].plot(t.value_in(units.yr),
a_an.value_in(units.RSun),
label="analytic")
axis[0].set_ylabel("semimajor axis [$R_\odot$]")
axis[0].legend()
axis[1].plot(t.value_in(units.yr), e)
axis[1].plot(t.value_in(units.yr), e_an)
axis[1].set_ylabel("eccentricity")
axis[1].set_xlabel("time [yr]")
axis[0].set_xlabel("time [yr]")
pyplot.tight_layout()
pyplot.subplots_adjust(hspace=0.0)
pyplot.savefig("comenv2.png")
pyplot.show()
)
subplot.set_xlim(-1, 1)
subplot.set_ylim(-1, 1)
subplot.set_xlabel('x (nbody length)')
subplot.set_ylabel('y (nbody length)')
pyplot.show()
if __name__ == "__main__":
numpy.random.seed(1212)
particles = new_cluster(128)
code = Hermite()
code.particles.add_particles(particles)
stopping_condition = code.stopping_conditions.collision_detection
stopping_condition.enable()
code.evolve_model(4 | nbody_system.time)
if not stopping_condition.is_set():
raise Exception(
"No stopping collision detected in the given timeframe.")
plot_particles_and_highlight_collision(particles,
stopping_condition.particles(0),
stopping_condition.particles(1))
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5 * end_time / 1000. * 2
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
period = (2 * numpy.pi *
(double_star.semimajor_axis * double_star.semimajor_axis *
double_star.semimajor_axis /
(constants.G * double_star.mass)).sqrt())
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period / dt))
E_an = [] | (units.km / units.s)**2
h_an = [] | units.km**2 / units.s
Etemp = -double_star.mass * constants.G / (2 * double_star.semimajor_axis)
htemp = (double_star.mass * constants.G * double_star.semimajor_axis *
(1 - double_star.eccentricity * double_star.eccentricity))**0.5
E_num = [] | (units.km / units.s)**2
h_num = [] | units.km**2 / units.s
m1 = [] | units.MSun
m2 = [] | units.MSun
t = [] | units.yr
t_an = [] | units.yr
dt_an = period * 2.5
time_an = 0 | units.yr
while time < end_time:
time += dt
gravity.evolve_model(time)
to_stars.copy()
dmdtloss = mass_loss_rate(stars.mass)
dmdtacc = dmdt_acc(dmdtloss)
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
h = h_from_stars(stars)
E = E_from_stars(stars)
if time > time_an:
#atemp = orbital_elements[2]
#htemp = h
E_an.append(Etemp)
h_an.append(htemp)
t_an.append(time)
dEdt = dEdt_momentum_secular(htemp, Etemp, stars.mass, dmdtacc)
dhdt = dhdt_momentum_secular(htemp, stars.mass, dmdtacc)
Etemp = Etemp + dEdt * dt_an
htemp = htemp + dhdt * dt_an
E_an.append(Etemp)
h_an.append(htemp)
t_an.append(time + dt_an)
time_an += dt_an
kick_from_accretion(stars, dmdtacc, dt)
#stars.mass += (dmdtloss + dmdtacc) * dt
#stars2.mass += (dmdtloss + dmdtacc) * dt
from_stars.copy()
h_num.append(h)
E_num.append(E)
m1.append(stars[0].mass)
m2.append(stars[1].mass)
t.append(time)
print("time=",
time.in_(units.yr),
"h=",
h.in_(units.km**2 / units.s),
"E=",
E.in_((units.km / units.s)**2),
"m=",
stars.mass.in_(units.MSun),
end="\r")
gravity.stop()
from matplotlib import pyplot
pyplot.rc('text', usetex=True)
pyplot.rcParams.update({'font.size': 16})
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True, figsize=(13, 6))
axis[0][0].plot(t.value_in(units.yr),
E_num.value_in((units.km / units.s)**2),
label="nbody (direct)",
lw=2)
axis[0][0].plot(t_an.value_in(units.yr),
E_an.value_in((units.km / units.s)**2),
label="analytic",
lw=2,
ls="-.")
axis[0][0].set_ylabel("E [km/s]")
axis[0][0].legend()
axis[0][1].plot(t.value_in(units.yr),
m1.value_in(units.MSun),
label="m1",
lw=2,
c="tab:red")
axis[0][1].plot(t.value_in(units.yr),
m2.value_in(units.MSun),
label="m2",
lw=2,
c="tab:cyan")
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[0][1].legend()
axis[1][1].plot(t.value_in(units.yr),
h_num.value_in(units.km**2 / units.s),
lw=2)
axis[1][1].plot(t_an.value_in(units.yr),
h_an.value_in(units.km**2 / units.s),
lw=2,
ls="-.")
axis[1][1].set_ylabel("h [km$^2$/s]")
#axis[1][0].plot(t.value_in(units.yr), ome, lw=2, label="nbody (direct)")
#axis[1][0].set_ylabel("$\omega$ [degrees]")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.tight_layout()
pyplot.subplots_adjust(hspace=0, top=0.93, bottom=0.1)
pyplot.suptitle("mloss+macc+momentum change, same model")
pyplot.savefig("debug.png")
pyplot.show()
instance = Hermite(convert_nbody)
instance.particles.add_particles(particles)
channelp = instance.particles.new_channel_to(particles)
start = 0 | units.yr
end = 150 | units.yr
step = 10 | units.day
timerange = VectorQuantity.arange(start, end, step)
masses = [] | units.MSun
for i, time in enumerate(timerange):
instance.evolve_model(time)
channelp.copy()
particles.savepoint(time)
if (i % 220 == 0):
instance.particles[0].mass = simulate_massloss(time)
masses.append(instance.particles[0].mass)
instance.stop()
particle = particles[1]
t, pos = particle.get_timeline_of_attribute_as_vector("position")
distances = pos.lengths().as_quantity_in(units.AU)
plot(timerange, distances, timerange, masses)
