In [1]:

"""Demonstrate particle-resolved Brownian coagulation.

Generates a modest bimodal particle-resolved sample, configures Brownian
coagulation with ``distribution_type="particle_resolved"``, runs a short
step, and plots histograms of radii before/after execution to show how the
sample redistributes. Uses a small sample size to keep runtime fast.

Example:
    Run the script to visualize how Brownian coagulation redistributes a
    set of sampled radii in a particle-resolved representation via the
    public ``par.dynamics`` API.
"""

"""Demonstrate particle-resolved Brownian coagulation. Generates a modest bimodal particle-resolved sample, configures Brownian coagulation with ``distribution_type="particle_resolved"``, runs a short step, and plots histograms of radii before/after execution to show how the sample redistributes. Uses a small sample size to keep runtime fast. Example: Run the script to visualize how Brownian coagulation redistributes a set of sampled radii in a particle-resolved representation via the public ``par.dynamics`` API. """

Out[1]:

'Demonstrate particle-resolved Brownian coagulation.\n\nGenerates a modest bimodal particle-resolved sample, configures Brownian\ncoagulation with ``distribution_type="particle_resolved"``, runs a short\nstep, and plots histograms of radii before/after execution to show how the\nsample redistributes. Uses a small sample size to keep runtime fast.\n\nExample:\n    Run the script to visualize how Brownian coagulation redistributes a\n    set of sampled radii in a particle-resolved representation via the\n    public ``par.dynamics`` API.\n'

Coagulation Pattern 3: Particle Resolved¶

Brownian coagulation using the public par.dynamics API with a particle-resolved representation:

1. Build a Brownian coagulation strategy with distribution_type="particle_resolved".
2. Wrap it in par.dynamics.Coagulation.
3. Run a short, fast step on a sampled aerosol and visualize the change.

In [2]:

# In Colab uncomment the following command to install particula:
#!pip install particula[extra] --quiet
import matplotlib.pyplot as plt
import numpy as np
import particula as par

# In Colab uncomment the following command to install particula: #!pip install particula[extra] --quiet import matplotlib.pyplot as plt import numpy as np import particula as par

Build a particle-resolved aerosol¶

Sample a modest bimodal lognormal distribution, assign mass/density, and combine with a simple atmosphere.

In [3]:

# Sample radii (small sample for speed)
radii_sample = par.particles.get_lognormal_sample_distribution(
    mode=np.array([80e-9, 200e-9]),
    geometric_standard_deviation=np.array([1.4, 1.5]),
    number_of_particles=np.array([4e4, 2e4]),
    number_of_samples=50_000,
)

density = np.array([1_000.0])
mass_sample = 4 / 3 * np.pi * radii_sample**3 * density

# Atmosphere (ambient)
atmosphere = (
    par.gas.AtmosphereBuilder()
    .set_temperature(25, "degC")
    .set_pressure(1, "atm")
    .build()
)

# Particle-resolved representation
particles_resolved = (
    par.particles.ResolvedParticleMassRepresentationBuilder()
    .set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
    .set_activity_strategy(par.particles.ActivityIdealMass())
    .set_surface_strategy(par.particles.SurfaceStrategyVolume())
    .set_mass(mass_sample, mass_units="kg")
    .set_density(density, density_units="kg/m^3")
    .set_charge(0)
    .set_volume(1e-3, volume_units="m^3")
    .build()
)

aerosol_resolved = par.Aerosol(
    atmosphere=atmosphere, particles=particles_resolved
)

# Sample radii (small sample for speed) radii_sample = par.particles.get_lognormal_sample_distribution( mode=np.array([80e-9, 200e-9]), geometric_standard_deviation=np.array([1.4, 1.5]), number_of_particles=np.array([4e4, 2e4]), number_of_samples=50_000, ) density = np.array([1_000.0]) mass_sample = 4 / 3 * np.pi * radii_sample**3 * density # Atmosphere (ambient) atmosphere = ( par.gas.AtmosphereBuilder() .set_temperature(25, "degC") .set_pressure(1, "atm") .build() ) # Particle-resolved representation particles_resolved = ( par.particles.ResolvedParticleMassRepresentationBuilder() .set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass()) .set_activity_strategy(par.particles.ActivityIdealMass()) .set_surface_strategy(par.particles.SurfaceStrategyVolume()) .set_mass(mass_sample, mass_units="kg") .set_density(density, density_units="kg/m^3") .set_charge(0) .set_volume(1e-3, volume_units="m^3") .build() ) aerosol_resolved = par.Aerosol( atmosphere=atmosphere, particles=particles_resolved )

Configure coagulation (particle_resolved)¶

In [4]:

coagulation_strategy = (
    par.dynamics.BrownianCoagulationBuilder()
    .set_distribution_type("particle_resolved")
    .build()
)
coagulation_process = par.dynamics.Coagulation(
    coagulation_strategy=coagulation_strategy
)

print(coagulation_process)

coagulation_strategy = ( par.dynamics.BrownianCoagulationBuilder() .set_distribution_type("particle_resolved") .build() ) coagulation_process = par.dynamics.Coagulation( coagulation_strategy=coagulation_strategy ) print(coagulation_process)

<particula.dynamics.particle_process.Coagulation object at 0x7fc4de1f2ab0>

Execute a short coagulation step¶

In [5]:

time_step = 3600  # seconds (1 hour)
sub_steps = 20

radii_before = aerosol_resolved.particles.get_radius()

aerosol_after = coagulation_process.execute(
    aerosol_resolved, time_step=time_step, sub_steps=sub_steps
)
radii_after = aerosol_after.particles.get_radius()

time_step = 3600 # seconds (1 hour) sub_steps = 20 radii_before = aerosol_resolved.particles.get_radius() aerosol_after = coagulation_process.execute( aerosol_resolved, time_step=time_step, sub_steps=sub_steps ) radii_after = aerosol_after.particles.get_radius()

Plot: particle-resolved histogram before/after¶

In [6]:

bins = np.logspace(np.log10(radii_before.min()), -5, 80).tolist()

fig, ax = plt.subplots(figsize=(8, 5))
ax.hist(
    radii_before,
    bins=bins,
    histtype="step",
    color="tab:blue",
    label="Before",
    density=True,
)
ax.hist(
    radii_after,
    bins=bins,
    histtype="step",
    color="tab:orange",
    label="After",
    density=True,
)
ax.set_xscale("log")
ax.set_xlim(1e-8, 1e-5)
ax.set_xlabel("Particle radius (m)")
ax.set_ylabel("PDF of sampled particles")
ax.set_title("Particle-resolved coagulation (Brownian)")
ax.legend()
ax.grid(alpha=0.3)
plt.show()

bins = np.logspace(np.log10(radii_before.min()), -5, 80).tolist() fig, ax = plt.subplots(figsize=(8, 5)) ax.hist( radii_before, bins=bins, histtype="step", color="tab:blue", label="Before", density=True, ) ax.hist( radii_after, bins=bins, histtype="step", color="tab:orange", label="After", density=True, ) ax.set_xscale("log") ax.set_xlim(1e-8, 1e-5) ax.set_xlabel("Particle radius (m)") ax.set_ylabel("PDF of sampled particles") ax.set_title("Particle-resolved coagulation (Brownian)") ax.legend() ax.grid(alpha=0.3) plt.show()

Summary¶

• Strategy: BrownianCoagulationBuilder().set_distribution_type("particle_resolved")
• Runnable: par.dynamics.Coagulation
• Representation: particle-resolved sampled radii/mass
• Runtime guardrails: ~50k samples, 1-hour horizon, 20 sub-steps