def new_plummer_distribution(number_of_particles,
total_mass = 1.0|nbody_system.mass,
virial_radius = 1.0|nbody_system.length,
mass_cutoff = 0.999,
G = None,
**keyword_arguments): # optional arguments for UniformSphericalDistribution
"""
Create a plummer model with the given number of particles. Returns a set
of particles with equal masses and positions distributed to fit a plummer
distribution model. Velocities are sampled using von Neumann's rejection
method (Aarseth et al. 1974), balancing the gravitational forces between
the particles.
"""
particles = new_plummer_spatial_distribution(number_of_particles, total_mass=total_mass,
virial_radius=virial_radius, **keyword_arguments)
if G is None:
G = nbody_system.G if generic_unit_system.is_generic_unit(total_mass.unit) else constants.G
velocity_unit = (G*total_mass/virial_radius).sqrt().unit.base_unit()
plummer_radius = 0.1875 * numpy.pi * virial_radius
escape_velocity = (1 + particles.position.lengths_squared()/plummer_radius**2)**(-0.25) | velocity_unit
velocity = escape_velocity * sample_from_velocity_distribution(number_of_particles)
velocity *= numpy.sqrt((G*total_mass*number_of_particles) / (2*virial_radius*velocity.length_squared()))
particles.velocity = velocity.reshape((-1,1)) * random_direction(number_of_particles)
return particles
def new_plummer_distribution(number_of_particles,
total_mass = 1.0|nbody_system.mass,
virial_radius = 1.0|nbody_system.length,
mass_cutoff = 0.999,
G = None,
**keyword_arguments): # optional arguments for UniformSphericalDistribution
"""
Create a plummer model with the given number of particles. Returns a set
of particles with equal masses and positions distributed to fit a plummer
distribution model. Velocities are sampled using von Neumann's rejection
method (Aarseth et al. 1974), balancing the gravitational forces between
the particles.
"""
particles = new_plummer_spatial_distribution(number_of_particles, total_mass=total_mass,
virial_radius=virial_radius, **keyword_arguments)
if G is None:
G = nbody_system.G if generic_unit_system.is_generic_unit(total_mass.unit) else constants.G
velocity_unit = (G*total_mass/virial_radius).sqrt().unit.base_unit()
plummer_radius = 0.1875 * numpy.pi * virial_radius
escape_velocity = (1 + particles.position.lengths_squared()/plummer_radius**2)**(-0.25) | velocity_unit
velocity = escape_velocity * sample_from_velocity_distribution(number_of_particles)
velocity *= numpy.sqrt((G*total_mass*number_of_particles) / (2*virial_radius*velocity.length_squared()))
particles.velocity = velocity.reshape((-1,1)) * random_direction(number_of_particles)
return particles
def new_gas_plummer_distribution(
number_of_particles,
total_mass=1.0 | nbody_system.mass,
virial_radius=1.0 | nbody_system.length,
G=None,
**keyword_arguments
): # optional arguments for UniformSphericalDistribution
"""
Create a plummer gas model with the given number of particles. Returns a set
of SPH particles with equal masses and positions distributed to fit a plummer
distribution model. Velocities are set to zero, and internal energies are set
to balance the gravitational forces between the gas particles.
"""
particles = new_plummer_spatial_distribution(number_of_particles,
total_mass=total_mass,
virial_radius=virial_radius,
**keyword_arguments)
if G is None:
G = nbody_system.G if generic_unit_system.is_generic_unit(
total_mass.unit) else constants.G
velocity_unit = (G * total_mass / virial_radius).sqrt().unit.base_unit()
particles.velocity = [0.0, 0.0, 0.0] | velocity_unit
plummer_radius = 0.1875 * numpy.pi * virial_radius
u_unit = (velocity_unit**2).base_unit()
particles.u = (1 + particles.position.lengths_squared() /
plummer_radius**2)**(-0.5) | u_unit
particles.u *= 0.25 * (G * total_mass**2 /
virial_radius) / particles.thermal_energy()
return particles
def new_gas_plummer_distribution(number_of_particles,
total_mass = 1.0|nbody_system.mass,
virial_radius = 1.0|nbody_system.length,
G = None,
**keyword_arguments): # optional arguments for UniformSphericalDistribution
"""
Create a plummer gas model with the given number of particles. Returns a set
of SPH particles with equal masses and positions distributed to fit a plummer
distribution model. Velocities are set to zero, and internal energies are set
to balance the gravitational forces between the gas particles.
"""
particles = new_plummer_spatial_distribution(number_of_particles, total_mass=total_mass,
virial_radius=virial_radius, **keyword_arguments)
if G is None:
G = nbody_system.G if generic_unit_system.is_generic_unit(total_mass.unit) else constants.G
velocity_unit = (G*total_mass/virial_radius).sqrt().unit.base_unit()
particles.velocity = [0.0, 0.0, 0.0] | velocity_unit
plummer_radius = 0.1875 * numpy.pi * virial_radius
u_unit = (velocity_unit**2).base_unit()
particles.u = (1 + particles.position.lengths_squared()/plummer_radius**2)**(-0.5) | u_unit
particles.u *= 0.25 * (G*total_mass**2/virial_radius) / particles.thermal_energy()
return particles
