def scale_to_standard(particles,
convert_nbody=None,
smoothing_length_squared=zero,
virial_ratio=0.5):
"""
Scale the particles to a standard NBODY model with G=1,
total_mass=1, and virial_radius=1 (or potential_energy=-0.5).
In virial equilibrium (virial_ratio=0.5, default) the
kinetic_energy=0.25 and the velocity_dispersion=1/sqrt(2).
:argument convert_nbody: the scaling is in nbody units,
when the particles are in si units a convert_nbody is needed
:argument smoothing_length_squared: needed for calculating
the potential energy correctly.
:argument virial_ratio: scale velocities to Q=K/|U|, (kinetic/potential energy);
Q = virial_ratio > 0.5: supervirial, will expand
Q = virial_ratio < 0.5: subvirial, will collapse
"""
if not convert_nbody is None:
particles = ParticlesWithUnitsConverted(
particles, convert_nbody.as_converter_from_generic_to_si())
if not smoothing_length_squared is zero:
smoothing_length_squared = convert_nbody.to_nbody(
smoothing_length_squared)
# Proper order is to scale mass, then length, then velocities.
# Simple length scaling for the potential works only in the
# unsoftened case. In general, it may not be possible to force
# the potential to -0.5, so perhaps best to stop after the simple
# scaling. We can always scale the velocities to get the correct
# virial ratio (and hence virial equilibrium).
total_mass = particles.mass.sum()
scale_factor = ((1 | total_mass.unit) / total_mass)
particles.mass *= scale_factor
potential_energy \
= particles.potential_energy(G=nbody_system.G,
smoothing_length_squared = smoothing_length_squared)
target_energy = -0.5 | nbody_system.energy
scale_factor = (potential_energy / target_energy) # unsoftened only...
particles.position *= scale_factor
if smoothing_length_squared == zero:
potential_energy = target_energy
else:
potential_energy = particles.potential_energy(
G=nbody_system.G,
smoothing_length_squared=smoothing_length_squared)
if virial_ratio == 0:
scale_factor = 0
else:
scale_factor = numpy.sqrt(
abs(virial_ratio * potential_energy) / particles.kinetic_energy())
particles.velocity *= scale_factor
def scale_to_standard(particles, convert_nbody = None,
smoothing_length_squared = zero,
virial_ratio = 0.5):
"""
Scale the particles to a standard NBODY model with G=1,
total_mass=1, and virial_radius=1 (or potential_energy=-0.5).
In virial equilibrium (virial_ratio=0.5, default) the
kinetic_energy=0.25 and the velocity_dispersion=1/sqrt(2).
:argument convert_nbody: the scaling is in nbody units,
when the particles are in si units a convert_nbody is needed
:argument smoothing_length_squared: needed for calculating
the potential energy correctly.
:argument virial_ratio: scale velocities to Q=K/|U|, (kinetic/potential energy);
Q = virial_ratio > 0.5: supervirial, will expand
Q = virial_ratio < 0.5: subvirial, will collapse
"""
if not convert_nbody is None:
particles = ParticlesWithUnitsConverted(particles, convert_nbody.as_converter_from_generic_to_si())
if not smoothing_length_squared is zero:
smoothing_length_squared = convert_nbody.to_nbody(smoothing_length_squared)
# Proper order is to scale mass, then length, then velocities.
# Simple length scaling for the potential works only in the
# unsoftened case. In general, it may not be possible to force
# the potential to -0.5, so perhaps best to stop after the simple
# scaling. We can always scale the velocities to get the correct
# virial ratio (and hence virial equilibrium).
total_mass = particles.mass.sum()
scale_factor = ((1 | total_mass.unit) / total_mass)
particles.mass *= scale_factor
potential_energy \
= particles.potential_energy(G=nbody_system.G,
smoothing_length_squared = smoothing_length_squared)
target_energy = -0.5 | nbody_system.energy
scale_factor = (potential_energy / target_energy) # unsoftened only...
particles.position *= scale_factor
if smoothing_length_squared == zero:
potential_energy = target_energy
else:
potential_energy = particles.potential_energy(G=nbody_system.G,
smoothing_length_squared = smoothing_length_squared)
if virial_ratio == 0:
scale_factor = 0
else:
scale_factor = numpy.sqrt(abs(virial_ratio*potential_energy) / particles.kinetic_energy())
particles.velocity *= scale_factor
