In [1]:

"""Showcase a PMF-based Brownian coagulation example.

Builds a lognormal PMF aerosol, configures Brownian coagulation with
``distribution_type="discrete"``, runs a short guarded step, and plots PMF
concentration before/after execution to visualize redistribution. Designed
for quick execution with a small grid and modest sub-steps.

Example:
    Run the script to generate before/after concentration curves for a
    discrete PMF aerosol using the public ``par.dynamics`` API.
"""

"""Showcase a PMF-based Brownian coagulation example. Builds a lognormal PMF aerosol, configures Brownian coagulation with ``distribution_type="discrete"``, runs a short guarded step, and plots PMF concentration before/after execution to visualize redistribution. Designed for quick execution with a small grid and modest sub-steps. Example: Run the script to generate before/after concentration curves for a discrete PMF aerosol using the public ``par.dynamics`` API. """

Out[1]:

'Showcase a PMF-based Brownian coagulation example.\n\nBuilds a lognormal PMF aerosol, configures Brownian coagulation with\n``distribution_type="discrete"``, runs a short guarded step, and plots PMF\nconcentration before/after execution to visualize redistribution. Designed\nfor quick execution with a small grid and modest sub-steps.\n\nExample:\n    Run the script to generate before/after concentration curves for a\n    discrete PMF aerosol using the public ``par.dynamics`` API.\n'

Coagulation Pattern 1: PMF¶

Brownian coagulation using the public par.dynamics API with a discrete/PMF representation:

1. Build a Brownian coagulation strategy with distribution_type="discrete".
2. Wrap it in par.dynamics.Coagulation.
3. Run a short, fast step on a PMF 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 PMF aerosol¶

We create a modest lognormal PMF and attach it to an ambient atmosphere.

In [3]:

# Radius bins (log-spaced, extended to 10 microns for visibility)
radius_bins = np.logspace(-8, -5, 150)  # m (10 nm to 10 um)

# Lognormal PMF (concentration per bin) - higher concentration for visible change
concentration_pmf = par.particles.get_lognormal_pmf_distribution(
    x_values=radius_bins,
    mode=np.array([80e-9]),
    geometric_standard_deviation=np.array([1.5]),
    number_of_particles=np.array(
        [1e10]
    ),  # m^-3 total (increased for visibility)
)

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

# PMF particle representation
particles_pmf = (
    par.particles.PresetParticleRadiusBuilder()
    .set_distribution_type("pmf")
    .set_radius_bins(radius_bins, radius_bins_units="m")
    .set_concentration(concentration_pmf, concentration_units="m^-3")
    .set_density(np.array([1_000.0]), density_units="kg/m^3")
    .set_charge(np.zeros_like(radius_bins))
    .build()
)

# Aerosol object
pmf_aerosol = par.Aerosol(atmosphere=atmosphere, particles=particles_pmf)

# Radius bins (log-spaced, extended to 10 microns for visibility) radius_bins = np.logspace(-8, -5, 150) # m (10 nm to 10 um) # Lognormal PMF (concentration per bin) - higher concentration for visible change concentration_pmf = par.particles.get_lognormal_pmf_distribution( x_values=radius_bins, mode=np.array([80e-9]), geometric_standard_deviation=np.array([1.5]), number_of_particles=np.array( [1e10] ), # m^-3 total (increased for visibility) ) # Atmosphere (ambient, non-condensing) atmosphere = ( par.gas.AtmosphereBuilder() .set_temperature(25, "degC") .set_pressure(1, "atm") .build() ) # PMF particle representation particles_pmf = ( par.particles.PresetParticleRadiusBuilder() .set_distribution_type("pmf") .set_radius_bins(radius_bins, radius_bins_units="m") .set_concentration(concentration_pmf, concentration_units="m^-3") .set_density(np.array([1_000.0]), density_units="kg/m^3") .set_charge(np.zeros_like(radius_bins)) .build() ) # Aerosol object pmf_aerosol = par.Aerosol(atmosphere=atmosphere, particles=particles_pmf)

Configure coagulation (discrete)¶

Use the Brownian builder with distribution_type="discrete", then wrap in the public Coagulation runnable.

In [4]:

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

print(coagulation_process)

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

<particula.dynamics.particle_process.Coagulation object at 0x7f070164a990>

Execute a short coagulation step¶

Keep the time step and sub-steps small for quick execution. The runnable updates the aerosol in-place and returns it.

In [5]:

# Set up time and sub-steps for the coagulation process
# Longer time span for visible coagulation effect
time_step = 3600  # 1 hour per step
sub_steps = 100

radii = pmf_aerosol.particles.get_radius()
pmf_before = np.copy(pmf_aerosol.particles.concentration)

# Perform coagulation process for step 1
pmf_aerosol = coagulation_process.execute(
    pmf_aerosol, time_step=time_step, sub_steps=sub_steps
)
radii_after_step_1 = pmf_aerosol.particles.get_radius()
pmf_after_step_1 = np.copy(pmf_aerosol.particles.concentration)

# Perform coagulation process for step 2
pmf_aerosol = coagulation_process.execute(
    pmf_aerosol, time_step=time_step, sub_steps=sub_steps
)
radii_after_step_2 = pmf_aerosol.particles.get_radius()
pmf_after_step_2 = np.copy(pmf_aerosol.particles.concentration)

# Set up time and sub-steps for the coagulation process # Longer time span for visible coagulation effect time_step = 3600 # 1 hour per step sub_steps = 100 radii = pmf_aerosol.particles.get_radius() pmf_before = np.copy(pmf_aerosol.particles.concentration) # Perform coagulation process for step 1 pmf_aerosol = coagulation_process.execute( pmf_aerosol, time_step=time_step, sub_steps=sub_steps ) radii_after_step_1 = pmf_aerosol.particles.get_radius() pmf_after_step_1 = np.copy(pmf_aerosol.particles.concentration) # Perform coagulation process for step 2 pmf_aerosol = coagulation_process.execute( pmf_aerosol, time_step=time_step, sub_steps=sub_steps ) radii_after_step_2 = pmf_aerosol.particles.get_radius() pmf_after_step_2 = np.copy(pmf_aerosol.particles.concentration)

Plot: concentration before/after¶

In [6]:

fig, ax = plt.subplots(figsize=(8, 5))
ax.plot(radii, pmf_before, label="Initial", color="tab:blue")
ax.plot(
    radii_after_step_1,
    pmf_after_step_1,
    label="After step 1",
    color="tab:orange",
)
ax.plot(
    radii_after_step_2,
    pmf_after_step_2,
    label="After step 2",
    color="tab:green",
)
ax.set_xscale("log")
ax.set_xlim(1e-8, 1e-5)  # 10 nm to 10 um
ax.set_xlabel("Particle radius (m)")
ax.set_ylabel(r"Number concentration ($m^{-3}$)")
ax.set_title("PMF coagulation (Brownian, discrete)")
ax.legend()
ax.grid(alpha=0.3)
plt.show()

fig, ax = plt.subplots(figsize=(8, 5)) ax.plot(radii, pmf_before, label="Initial", color="tab:blue") ax.plot( radii_after_step_1, pmf_after_step_1, label="After step 1", color="tab:orange", ) ax.plot( radii_after_step_2, pmf_after_step_2, label="After step 2", color="tab:green", ) ax.set_xscale("log") ax.set_xlim(1e-8, 1e-5) # 10 nm to 10 um ax.set_xlabel("Particle radius (m)") ax.set_ylabel(r"Number concentration ($m^{-3}$)") ax.set_title("PMF coagulation (Brownian, discrete)") ax.legend() ax.grid(alpha=0.3) plt.show()

Summary¶

• Strategy: BrownianCoagulationBuilder().set_distribution_type("discrete")
• Runnable: par.dynamics.Coagulation
• Representation: PMF (bin-based number concentration)
• Runtime guardrails: small grid, short horizon for fast execution