def calculate_angular_momentum_flux(lambda0, G_ring, shear_viscosity,
bulk_viscosity, c, r, t, vr, vt, wt,
fast_gravity):
#select two central streamlines
total_number_of_outputs, number_of_streamlines, particles_per_streamline = r.shape
middle_index = number_of_streamlines / 2
rc = r[:, middle_index - 1:middle_index + 1, :]
tc = t[:, middle_index - 1:middle_index + 1, :]
vrc = vr[:, middle_index - 1:middle_index + 1, :]
vtc = vt[:, middle_index - 1:middle_index + 1, :]
wtc = wt[:, middle_index - 1:middle_index + 1, :]
lambdac = lambda0[middle_index - 1:middle_index + 1, :]
#compute angular momentum flux and luminosity
twopi = 2 * np.pi
angular_momentum_flux_list = []
angular_momentum_luminosity_list = []
for t_idx in range(total_number_of_outputs):
Ar, At = accelerations(lambdac, G_ring, shear_viscosity,
bulk_viscosity, c, rc[t_idx], tc[t_idx],
vrc[t_idx], vtc[t_idx], fast_gravity)
angular_momentum_flux = lambdac * rc[t_idx] * At
torque_per_particle = angular_momentum_flux * rc[t_idx] / twopi
torque_per_particle = torque_per_particle[-1]
angular_momentum_flux = angular_momentum_flux[-1]
angular_momentum_flux_list += [angular_momentum_flux]
angular_momentum_luminosity_list += [torque_per_particle.sum()]
#convert lists to arrays
angular_momentum_flux = np.array(angular_momentum_flux_list)
angular_momentum_luminosity = np.array(angular_momentum_luminosity_list)
#select central streamline
rc = rc[:, -1, :]
tc = tc[:, -1, :]
wtc = wtc[:, -1, :]
return angular_momentum_flux, angular_momentum_luminosity, rc, tc, wtc
def calculate_angular_momentum_flux(lambda0, G_ring, shear_viscosity,
bulk_viscosity, c, r, t, vr, vt, wt,
fast_gravity, confine_edges):
#select two central streamlines
total_number_of_outputs, number_of_streamlines, particles_per_streamline = r.shape
middle_index = number_of_streamlines / 2
rc = r[:, middle_index - 1:middle_index + 1, :]
tc = t[:, middle_index - 1:middle_index + 1, :]
vrc = vr[:, middle_index - 1:middle_index + 1, :]
vtc = vt[:, middle_index - 1:middle_index + 1, :]
wtc = wt[:, middle_index - 1:middle_index + 1, :]
lambdac = lambda0[middle_index - 1:middle_index + 1, :]
#compute angular momentum flux and luminosity
twopi = 2 * np.pi
angular_momentum_flux_list = []
angular_momentum_luminosity_list = []
for t_idx in range(total_number_of_outputs):
#compute one-sided acceleration=acceleration of middle streamline due to interior neighbor
r_now = rc[t_idx]
t_now = tc[t_idx]
vr_now = vrc[t_idx]
vt_now = vtc[t_idx]
Ar, At = accelerations(lambdac, G_ring, shear_viscosity,
bulk_viscosity, c, r_now, t_now, vr_now, vt_now,
fast_gravity, confine_edges)
angular_momentum_flux = lambdac * r_now * At
angular_momentum_flux = angular_momentum_flux[-1]
angular_momentum_flux_list += [angular_momentum_flux]
#compute one-sided torque
delta_ell = twopi * r_now[-1].mean() / particles_per_streamline
torque = angular_momentum_flux.sum() * delta_ell
angular_momentum_luminosity_list += [torque]
#convert lists to arrays
angular_momentum_flux = np.array(angular_momentum_flux_list)
angular_momentum_luminosity = np.array(angular_momentum_luminosity_list)
#select central streamline
rc = rc[:, -1, :]
tc = tc[:, -1, :]
wtc = wtc[:, -1, :]
return angular_momentum_flux, angular_momentum_luminosity, rc, tc, wtc
def calculate_energy_flux(lambda0, G_ring, shear_viscosity, bulk_viscosity, c,
r, t, vr, vt, wt, fast_gravity, confine_edges):
#select two central streamlines
total_number_of_outputs, number_of_streamlines, particles_per_streamline = r.shape
middle_index = number_of_streamlines / 2
rc = r[:, middle_index - 1:middle_index + 1, :]
tc = t[:, middle_index - 1:middle_index + 1, :]
vrc = vr[:, middle_index - 1:middle_index + 1, :]
vtc = vt[:, middle_index - 1:middle_index + 1, :]
wtc = wt[:, middle_index - 1:middle_index + 1, :]
lambdac = lambda0[middle_index - 1:middle_index + 1, :]
#compute energy flux and luminosity
twopi = 2 * np.pi
energy_flux_list = []
energy_luminosity_list = []
for t_idx in range(total_number_of_outputs):
r_now = rc[t_idx]
t_now = tc[t_idx]
vr_now = vrc[t_idx]
vt_now = vtc[t_idx]
Ar, At = accelerations(lambdac, G_ring, shear_viscosity,
bulk_viscosity, c, r_now, t_now, vr_now, vt_now,
fast_gravity, confine_edges)
energy_flux = lambdac * (Ar * vr_now + At * vt_now)
energy_flux = energy_flux[-1]
energy_flux_list += [energy_flux]
#compute one-sided work
delta_ell = twopi * r_now[-1].mean() / particles_per_streamline
work = energy_flux.sum() * delta_ell
energy_luminosity_list += [work]
#convert lists to arrays
energy_flux = np.array(energy_flux_list)
energy_luminosity = np.array(energy_luminosity_list)
#select central streamline
rc = rc[:, -1, :]
tc = tc[:, -1, :]
wtc = wtc[:, -1, :]
return energy_flux, energy_luminosity, rc, tc, wtc