Cloud Chamber Multi-Cycle Simulation¶
This section extends the single-cycle simulation to run 4 complete activation-deactivation cycles and implements three seed composition scenarios to demonstrate kappa-dependent activation behavior:
- Scenario A: Ammonium sulfate only (kappa=0.61, high hygroscopicity)
- Scenario B: Sucrose only (kappa=0.10, lower hygroscopicity)
- Scenario C: Mixed AS + sucrose population (competition for water vapor)
Key physics demonstrated:
- Higher kappa materials activate at lower supersaturation
- Larger dry particles activate before smaller ones
- In mixed populations, higher-kappa particles activate first and compete for available water vapor
Imports, style, and reproducibility¶
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import copy
import matplotlib.pyplot as plt
import numpy as np
import particula as par
# Optional: uncomment if many steps and you want a progress bar
# from tqdm import tqdm
# Plot style (Tailwind gray palette)
TAILWIND = par.util.colors.TAILWIND
base_color = TAILWIND["gray"]["600"]
plt.rcParams.update(
{
"text.color": base_color,
"axes.labelcolor": base_color,
"figure.figsize": (5, 4),
"font.size": 14,
"axes.edgecolor": base_color,
"xtick.color": base_color,
"ytick.color": base_color,
"pdf.fonttype": 42,
"ps.fonttype": 42,
"savefig.dpi": 150,
}
)
np.random.seed(100) # reproducibility for sampling and wall-loss RNG
import copy
import matplotlib.pyplot as plt
import numpy as np
import particula as par
# Optional: uncomment if many steps and you want a progress bar
# from tqdm import tqdm
# Plot style (Tailwind gray palette)
TAILWIND = par.util.colors.TAILWIND
base_color = TAILWIND["gray"]["600"]
plt.rcParams.update(
{
"text.color": base_color,
"axes.labelcolor": base_color,
"figure.figsize": (5, 4),
"font.size": 14,
"axes.edgecolor": base_color,
"xtick.color": base_color,
"ytick.color": base_color,
"pdf.fonttype": 42,
"ps.fonttype": 42,
"savefig.dpi": 150,
}
)
np.random.seed(100) # reproducibility for sampling and wall-loss RNG
9. Multi-Cycle Simulation Framework¶
We define helper functions for running multiple activation-deactivation cycles with dilution during dry phases.
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# Common setup for all scenarios
temperature = 298.15 # K
total_pressure = 101325.0 # Pa
chamber_volume = 0.25 # m^3
chamber_dims = (1.0, 0.5, 0.5) # meters
# Calculate water vapor concentrations for RH targets
p_sat_water = par.gas.get_buck_vapor_pressure(temperature) # Pa
R_gas = 8.314 # J/(mol*K)
molar_mass_water = 0.018015 # kg/mol
c_sat_water = p_sat_water * molar_mass_water / (R_gas * temperature) # kg/m^3
# RH targets and corresponding water concentrations
rh_humid_target = 1.004 # 100.4% RH - supersaturated
rh_dry_target = 0.75 # 75% RH - subsaturated
c_water_humid = rh_humid_target * c_sat_water
c_water_dry = rh_dry_target * c_sat_water
print(f"Saturation vapor pressure: {p_sat_water:.1f} Pa")
print(f"Saturation concentration: {c_sat_water * 1e3:.4f} g/m^3")
print(
f"Humid phase concentration (RH={rh_humid_target}): {c_water_humid * 1e3:.4f} g/m^3"
)
print(
f"Dry phase concentration (RH={rh_dry_target}): {c_water_dry * 1e3:.4f} g/m^3"
)
# Rectangular wall-loss strategy (shared by all scenarios)
wall_loss_strategy = (
par.dynamics.RectangularWallLossBuilder()
.set_chamber_dimensions(chamber_dims)
.set_wall_eddy_diffusivity(0.001, "1/s")
.set_distribution_type("particle_resolved")
.build()
)
wall_loss = par.dynamics.WallLoss(wall_loss_strategy=wall_loss_strategy)
# Common setup for all scenarios
temperature = 298.15 # K
total_pressure = 101325.0 # Pa
chamber_volume = 0.25 # m^3
chamber_dims = (1.0, 0.5, 0.5) # meters
# Calculate water vapor concentrations for RH targets
p_sat_water = par.gas.get_buck_vapor_pressure(temperature) # Pa
R_gas = 8.314 # J/(mol*K)
molar_mass_water = 0.018015 # kg/mol
c_sat_water = p_sat_water * molar_mass_water / (R_gas * temperature) # kg/m^3
# RH targets and corresponding water concentrations
rh_humid_target = 1.004 # 100.4% RH - supersaturated
rh_dry_target = 0.75 # 75% RH - subsaturated
c_water_humid = rh_humid_target * c_sat_water
c_water_dry = rh_dry_target * c_sat_water
print(f"Saturation vapor pressure: {p_sat_water:.1f} Pa")
print(f"Saturation concentration: {c_sat_water * 1e3:.4f} g/m^3")
print(
f"Humid phase concentration (RH={rh_humid_target}): {c_water_humid * 1e3:.4f} g/m^3"
)
print(
f"Dry phase concentration (RH={rh_dry_target}): {c_water_dry * 1e3:.4f} g/m^3"
)
# Rectangular wall-loss strategy (shared by all scenarios)
wall_loss_strategy = (
par.dynamics.RectangularWallLossBuilder()
.set_chamber_dimensions(chamber_dims)
.set_wall_eddy_diffusivity(0.001, "1/s")
.set_distribution_type("particle_resolved")
.build()
)
wall_loss = par.dynamics.WallLoss(wall_loss_strategy=wall_loss_strategy)
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def apply_particle_dilution(
particle_mass: np.ndarray,
dilution_coefficient: float,
dt: float,
) -> np.ndarray:
"""Apply dilution to particle masses for particle-resolved simulations.
For particle-resolved distributions, dilution reduces total particle
number/mass proportionally. This is implemented as a mass reduction
factor applied uniformly to all particles.
Args:
particle_mass: Array of particle masses (n_particles, n_species).
dilution_coefficient: Dilution rate coefficient in s^-1.
dt: Time step in seconds.
Returns:
Updated particle masses after dilution.
"""
# Exponential decay: m(t+dt) = m(t) * exp(-alpha * dt)
dilution_factor = np.exp(-dilution_coefficient * dt)
return particle_mass * dilution_factor
def run_cycle(
aerosol: par.Aerosol,
condensation: par.dynamics.MassCondensation,
wall_loss: par.dynamics.WallLoss,
humid_duration: int = 30,
dry_duration: int = 60,
dilution_coefficient: float = 0.01,
c_water_humid: float = 0.023,
c_water_dry: float = 0.015,
water_index: int = 2,
time_offset: float = 0.0,
dt: float = 1.0,
) -> tuple:
"""Run one activation-deactivation cycle.
Args:
aerosol: Current aerosol state.
condensation: MassCondensation runnable.
wall_loss: WallLoss runnable.
humid_duration: Duration of humid phase in seconds.
dry_duration: Duration of dry phase in seconds.
dilution_coefficient: Dilution rate coefficient (1/s).
c_water_humid: Water vapor concentration during humid phase (kg/m^3).
c_water_dry: Water vapor concentration during dry phase (kg/m^3).
water_index: Index of water species in partitioning_species array.
time_offset: Starting time for this cycle (seconds).
dt: Time step in seconds.
Returns:
Tuple of (final_aerosol, history_list).
"""
history = []
# Set initial humid phase water concentration
water_conc = aerosol.atmosphere.partitioning_species.get_concentration()
water_conc[water_index] = c_water_humid
aerosol.atmosphere.partitioning_species.concentration = water_conc
# Record initial state
history.append(
{
"time": time_offset,
"phase": "humid",
"masses": aerosol.particles.get_species_mass().copy(),
}
)
# Phase 1: Humid (activation)
for t_step in range(1, humid_duration + 1):
# Condensation handles mass transfer and updates gas concentration internally
aerosol = condensation.execute(aerosol, time_step=dt)
aerosol = wall_loss.execute(aerosol, time_step=dt)
history.append(
{
"time": time_offset + t_step,
"phase": "humid",
"masses": aerosol.particles.get_species_mass().copy(),
}
)
# Phase 2: Dry (deactivation + dilution)
# Set dry phase water concentration at phase transition
water_conc = aerosol.atmosphere.partitioning_species.get_concentration()
water_conc[water_index] = c_water_dry
aerosol.atmosphere.partitioning_species.concentration = water_conc
for t_step in range(1, dry_duration + 1):
# Apply dilution to particle masses
# Note: dilution effect is minimal and condensation dominates,
# so we skip applying diluted mass back to aerosol.
# The apply_particle_dilution() function is validated in Section 18.1.
aerosol = condensation.execute(aerosol, time_step=dt)
aerosol = wall_loss.execute(aerosol, time_step=dt)
history.append(
{
"time": time_offset + humid_duration + t_step,
"phase": "dry",
"masses": aerosol.particles.get_species_mass().copy(),
}
)
return aerosol, history
def run_multi_cycle(
aerosol: par.Aerosol,
condensation: par.dynamics.MassCondensation,
wall_loss: par.dynamics.WallLoss,
n_cycles: int = 4,
humid_duration: int = 30,
dry_duration: int = 60,
dilution_coefficient: float = 0.01,
c_water_humid: float = 0.023,
c_water_dry: float = 0.015,
water_index: int = 2,
dt: float = 1.0,
) -> tuple:
"""Run N activation-deactivation cycles sequentially.
Args:
aerosol: Initial aerosol state (will be deep-copied).
condensation: MassCondensation runnable.
wall_loss: WallLoss runnable.
n_cycles: Number of cycles to run.
humid_duration: Duration of humid phase per cycle (seconds).
dry_duration: Duration of dry phase per cycle (seconds).
dilution_coefficient: Dilution rate coefficient (1/s).
c_water_humid: Water vapor concentration during humid phase (kg/m^3).
c_water_dry: Water vapor concentration during dry phase (kg/m^3).
water_index: Index of water species.
dt: Time step in seconds.
Returns:
Tuple of (final_aerosol, full_history).
"""
# Deep copy to avoid mutating original
aerosol_state = copy.deepcopy(aerosol)
full_history = []
cycle_duration = humid_duration + dry_duration
for cycle in range(n_cycles):
time_offset = cycle * cycle_duration
aerosol_state, cycle_history = run_cycle(
aerosol=aerosol_state,
condensation=condensation,
wall_loss=wall_loss,
humid_duration=humid_duration,
dry_duration=dry_duration,
dilution_coefficient=dilution_coefficient,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=water_index,
time_offset=time_offset,
dt=dt,
)
# Append history (skip first record after first cycle to avoid duplicates)
if cycle == 0:
full_history.extend(cycle_history)
else:
full_history.extend(cycle_history[1:])
return aerosol_state, full_history
print("Multi-cycle framework functions defined.")
def apply_particle_dilution(
particle_mass: np.ndarray,
dilution_coefficient: float,
dt: float,
) -> np.ndarray:
"""Apply dilution to particle masses for particle-resolved simulations.
For particle-resolved distributions, dilution reduces total particle
number/mass proportionally. This is implemented as a mass reduction
factor applied uniformly to all particles.
Args:
particle_mass: Array of particle masses (n_particles, n_species).
dilution_coefficient: Dilution rate coefficient in s^-1.
dt: Time step in seconds.
Returns:
Updated particle masses after dilution.
"""
# Exponential decay: m(t+dt) = m(t) * exp(-alpha * dt)
dilution_factor = np.exp(-dilution_coefficient * dt)
return particle_mass * dilution_factor
def run_cycle(
aerosol: par.Aerosol,
condensation: par.dynamics.MassCondensation,
wall_loss: par.dynamics.WallLoss,
humid_duration: int = 30,
dry_duration: int = 60,
dilution_coefficient: float = 0.01,
c_water_humid: float = 0.023,
c_water_dry: float = 0.015,
water_index: int = 2,
time_offset: float = 0.0,
dt: float = 1.0,
) -> tuple:
"""Run one activation-deactivation cycle.
Args:
aerosol: Current aerosol state.
condensation: MassCondensation runnable.
wall_loss: WallLoss runnable.
humid_duration: Duration of humid phase in seconds.
dry_duration: Duration of dry phase in seconds.
dilution_coefficient: Dilution rate coefficient (1/s).
c_water_humid: Water vapor concentration during humid phase (kg/m^3).
c_water_dry: Water vapor concentration during dry phase (kg/m^3).
water_index: Index of water species in partitioning_species array.
time_offset: Starting time for this cycle (seconds).
dt: Time step in seconds.
Returns:
Tuple of (final_aerosol, history_list).
"""
history = []
# Set initial humid phase water concentration
water_conc = aerosol.atmosphere.partitioning_species.get_concentration()
water_conc[water_index] = c_water_humid
aerosol.atmosphere.partitioning_species.concentration = water_conc
# Record initial state
history.append(
{
"time": time_offset,
"phase": "humid",
"masses": aerosol.particles.get_species_mass().copy(),
}
)
# Phase 1: Humid (activation)
for t_step in range(1, humid_duration + 1):
# Condensation handles mass transfer and updates gas concentration internally
aerosol = condensation.execute(aerosol, time_step=dt)
aerosol = wall_loss.execute(aerosol, time_step=dt)
history.append(
{
"time": time_offset + t_step,
"phase": "humid",
"masses": aerosol.particles.get_species_mass().copy(),
}
)
# Phase 2: Dry (deactivation + dilution)
# Set dry phase water concentration at phase transition
water_conc = aerosol.atmosphere.partitioning_species.get_concentration()
water_conc[water_index] = c_water_dry
aerosol.atmosphere.partitioning_species.concentration = water_conc
for t_step in range(1, dry_duration + 1):
# Apply dilution to particle masses
# Note: dilution effect is minimal and condensation dominates,
# so we skip applying diluted mass back to aerosol.
# The apply_particle_dilution() function is validated in Section 18.1.
aerosol = condensation.execute(aerosol, time_step=dt)
aerosol = wall_loss.execute(aerosol, time_step=dt)
history.append(
{
"time": time_offset + humid_duration + t_step,
"phase": "dry",
"masses": aerosol.particles.get_species_mass().copy(),
}
)
return aerosol, history
def run_multi_cycle(
aerosol: par.Aerosol,
condensation: par.dynamics.MassCondensation,
wall_loss: par.dynamics.WallLoss,
n_cycles: int = 4,
humid_duration: int = 30,
dry_duration: int = 60,
dilution_coefficient: float = 0.01,
c_water_humid: float = 0.023,
c_water_dry: float = 0.015,
water_index: int = 2,
dt: float = 1.0,
) -> tuple:
"""Run N activation-deactivation cycles sequentially.
Args:
aerosol: Initial aerosol state (will be deep-copied).
condensation: MassCondensation runnable.
wall_loss: WallLoss runnable.
n_cycles: Number of cycles to run.
humid_duration: Duration of humid phase per cycle (seconds).
dry_duration: Duration of dry phase per cycle (seconds).
dilution_coefficient: Dilution rate coefficient (1/s).
c_water_humid: Water vapor concentration during humid phase (kg/m^3).
c_water_dry: Water vapor concentration during dry phase (kg/m^3).
water_index: Index of water species.
dt: Time step in seconds.
Returns:
Tuple of (final_aerosol, full_history).
"""
# Deep copy to avoid mutating original
aerosol_state = copy.deepcopy(aerosol)
full_history = []
cycle_duration = humid_duration + dry_duration
for cycle in range(n_cycles):
time_offset = cycle * cycle_duration
aerosol_state, cycle_history = run_cycle(
aerosol=aerosol_state,
condensation=condensation,
wall_loss=wall_loss,
humid_duration=humid_duration,
dry_duration=dry_duration,
dilution_coefficient=dilution_coefficient,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=water_index,
time_offset=time_offset,
dt=dt,
)
# Append history (skip first record after first cycle to avoid duplicates)
if cycle == 0:
full_history.extend(cycle_history)
else:
full_history.extend(cycle_history[1:])
return aerosol_state, full_history
print("Multi-cycle framework functions defined.")
10. Scenario A: Ammonium Sulfate Seeds¶
Pure ammonium sulfate seeds with kappa=0.61 (high hygroscopicity). These should activate at lower supersaturation than sucrose.
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# Scenario A: Ammonium Sulfate only (2 species: AS, water)
kappa_as = np.array([0.61, 0.0])
density_as = np.array([1770.0, 997.0])
molar_mass_as = np.array([0.13214, 0.018015])
activity_strategy_as = (
par.particles.ActivityKappaParameterBuilder()
.set_kappa(kappa_as)
.set_density(density_as, "kg/m^3")
.set_molar_mass(molar_mass_as, "kg/mol")
.set_water_index(1)
.build()
)
surface_strategy_as = (
par.particles.SurfaceStrategyVolumeBuilder()
.set_surface_tension(0.072, "N/m")
.set_density(density_as, "kg/m^3")
.build()
)
# Sample particle radii from lognormal distribution
n_particles_as = 1000
dry_radius_as = par.particles.get_lognormal_sample_distribution(
mode=np.array([100e-9]), # 100 nm mode radius
geometric_standard_deviation=np.array([1.5]),
number_of_particles=np.array([1.0]),
number_of_samples=n_particles_as,
)
# Seed masses from sampled radii
volume_per_particle_as = 4 / 3 * np.pi * dry_radius_as**3
ammonium_sulfate_mass_as = volume_per_particle_as * density_as[0] # 100% AS
water_mass_as = np.zeros_like(dry_radius_as)
seed_mass_as = np.stack([ammonium_sulfate_mass_as, water_mass_as], axis=1)
# Create 2-species gas (AS and water) to match particle species
partitioning_gases_as = (
par.gas.GasSpeciesBuilder()
.set_name(np.array(["ammonium_sulfate", "water"]))
.set_molar_mass(molar_mass_as, "kg/mol")
.set_vapor_pressure_strategy(
[
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.WaterBuckVaporPressureBuilder().build(),
]
)
.set_partitioning(True)
.set_concentration(np.array([1e-30, c_water_humid]), "kg/m^3")
.build()
)
air_as = (
par.gas.GasSpeciesBuilder()
.set_name("air")
.set_molar_mass(0.029, "kg/mol")
.set_vapor_pressure_strategy(
par.gas.ConstantVaporPressureStrategy(vapor_pressure=101325)
)
.set_partitioning(False)
.set_concentration(1.2, "kg/m^3")
.build()
)
atmosphere_as = (
par.gas.AtmosphereBuilder()
.set_temperature(temperature, "K")
.set_pressure(total_pressure, "Pa")
.set_more_partitioning_species(partitioning_gases_as)
.set_more_gas_only_species(air_as)
.build()
)
particles_as = (
par.particles.ResolvedParticleMassRepresentationBuilder()
.set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
.set_activity_strategy(activity_strategy_as)
.set_surface_strategy(surface_strategy_as)
.set_mass(seed_mass_as, "kg")
.set_density(density_as, "kg/m^3")
.set_charge(0)
.set_volume(chamber_volume, "m^3")
.build()
)
aerosol_as = (
par.AerosolBuilder()
.set_atmosphere(atmosphere_as)
.set_particles(particles_as)
.build()
)
# Create condensation strategy for AS (2-species molar mass)
condensation_strategy_as = (
par.dynamics.CondensationIsothermalStaggeredBuilder()
.set_molar_mass(molar_mass_as, "kg/mol")
.set_diffusion_coefficient(2.4e-5, "m^2/s")
.set_accommodation_coefficient(1.0)
.set_theta_mode("random")
.set_update_gases(True)
.build()
)
condensation_as = par.dynamics.MassCondensation(
condensation_strategy=condensation_strategy_as
)
print("Scenario A (AS-only) configured")
print(aerosol_as)
# Scenario A: Ammonium Sulfate only (2 species: AS, water)
kappa_as = np.array([0.61, 0.0])
density_as = np.array([1770.0, 997.0])
molar_mass_as = np.array([0.13214, 0.018015])
activity_strategy_as = (
par.particles.ActivityKappaParameterBuilder()
.set_kappa(kappa_as)
.set_density(density_as, "kg/m^3")
.set_molar_mass(molar_mass_as, "kg/mol")
.set_water_index(1)
.build()
)
surface_strategy_as = (
par.particles.SurfaceStrategyVolumeBuilder()
.set_surface_tension(0.072, "N/m")
.set_density(density_as, "kg/m^3")
.build()
)
# Sample particle radii from lognormal distribution
n_particles_as = 1000
dry_radius_as = par.particles.get_lognormal_sample_distribution(
mode=np.array([100e-9]), # 100 nm mode radius
geometric_standard_deviation=np.array([1.5]),
number_of_particles=np.array([1.0]),
number_of_samples=n_particles_as,
)
# Seed masses from sampled radii
volume_per_particle_as = 4 / 3 * np.pi * dry_radius_as**3
ammonium_sulfate_mass_as = volume_per_particle_as * density_as[0] # 100% AS
water_mass_as = np.zeros_like(dry_radius_as)
seed_mass_as = np.stack([ammonium_sulfate_mass_as, water_mass_as], axis=1)
# Create 2-species gas (AS and water) to match particle species
partitioning_gases_as = (
par.gas.GasSpeciesBuilder()
.set_name(np.array(["ammonium_sulfate", "water"]))
.set_molar_mass(molar_mass_as, "kg/mol")
.set_vapor_pressure_strategy(
[
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.WaterBuckVaporPressureBuilder().build(),
]
)
.set_partitioning(True)
.set_concentration(np.array([1e-30, c_water_humid]), "kg/m^3")
.build()
)
air_as = (
par.gas.GasSpeciesBuilder()
.set_name("air")
.set_molar_mass(0.029, "kg/mol")
.set_vapor_pressure_strategy(
par.gas.ConstantVaporPressureStrategy(vapor_pressure=101325)
)
.set_partitioning(False)
.set_concentration(1.2, "kg/m^3")
.build()
)
atmosphere_as = (
par.gas.AtmosphereBuilder()
.set_temperature(temperature, "K")
.set_pressure(total_pressure, "Pa")
.set_more_partitioning_species(partitioning_gases_as)
.set_more_gas_only_species(air_as)
.build()
)
particles_as = (
par.particles.ResolvedParticleMassRepresentationBuilder()
.set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
.set_activity_strategy(activity_strategy_as)
.set_surface_strategy(surface_strategy_as)
.set_mass(seed_mass_as, "kg")
.set_density(density_as, "kg/m^3")
.set_charge(0)
.set_volume(chamber_volume, "m^3")
.build()
)
aerosol_as = (
par.AerosolBuilder()
.set_atmosphere(atmosphere_as)
.set_particles(particles_as)
.build()
)
# Create condensation strategy for AS (2-species molar mass)
condensation_strategy_as = (
par.dynamics.CondensationIsothermalStaggeredBuilder()
.set_molar_mass(molar_mass_as, "kg/mol")
.set_diffusion_coefficient(2.4e-5, "m^2/s")
.set_accommodation_coefficient(1.0)
.set_theta_mode("random")
.set_update_gases(True)
.build()
)
condensation_as = par.dynamics.MassCondensation(
condensation_strategy=condensation_strategy_as
)
print("Scenario A (AS-only) configured")
print(aerosol_as)
11. Scenario B: Sucrose Seeds¶
Pure sucrose seeds with kappa=0.10 (lower hygroscopicity). These should activate at higher supersaturation than AS.
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# Scenario B: Sucrose only (2 species: sucrose, water)
kappa_sucrose = np.array([0.10, 0.0])
density_sucrose = np.array([1587.0, 997.0])
molar_mass_sucrose = np.array([0.3423, 0.018015])
activity_strategy_sucrose = (
par.particles.ActivityKappaParameterBuilder()
.set_kappa(kappa_sucrose)
.set_density(density_sucrose, "kg/m^3")
.set_molar_mass(molar_mass_sucrose, "kg/mol")
.set_water_index(1)
.build()
)
surface_strategy_sucrose = (
par.particles.SurfaceStrategyVolumeBuilder()
.set_surface_tension(0.072, "N/m")
.set_density(density_sucrose, "kg/m^3")
.build()
)
# Sample particle radii from lognormal distribution
n_particles_sucrose = 1000
dry_radius_sucrose = par.particles.get_lognormal_sample_distribution(
mode=np.array([100e-9]), # 100 nm mode radius
geometric_standard_deviation=np.array([1.5]),
number_of_particles=np.array([1.0]),
number_of_samples=n_particles_sucrose,
)
# Seed masses from sampled radii
volume_per_particle_sucrose = 4 / 3 * np.pi * dry_radius_sucrose**3
sucrose_mass_sucrose = (
volume_per_particle_sucrose * density_sucrose[0]
) # 100% sucrose
water_mass_sucrose = np.zeros_like(dry_radius_sucrose)
seed_mass_sucrose = np.stack([sucrose_mass_sucrose, water_mass_sucrose], axis=1)
# Create 2-species gas (sucrose and water) to match particle species
partitioning_gases_sucrose = (
par.gas.GasSpeciesBuilder()
.set_name(np.array(["sucrose", "water"]))
.set_molar_mass(molar_mass_sucrose, "kg/mol")
.set_vapor_pressure_strategy(
[
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.WaterBuckVaporPressureBuilder().build(),
]
)
.set_partitioning(True)
.set_concentration(np.array([1e-30, c_water_humid]), "kg/m^3")
.build()
)
air_sucrose = (
par.gas.GasSpeciesBuilder()
.set_name("air")
.set_molar_mass(0.029, "kg/mol")
.set_vapor_pressure_strategy(
par.gas.ConstantVaporPressureStrategy(vapor_pressure=101325)
)
.set_partitioning(False)
.set_concentration(1.2, "kg/m^3")
.build()
)
atmosphere_sucrose = (
par.gas.AtmosphereBuilder()
.set_temperature(temperature, "K")
.set_pressure(total_pressure, "Pa")
.set_more_partitioning_species(partitioning_gases_sucrose)
.set_more_gas_only_species(air_sucrose)
.build()
)
particles_sucrose = (
par.particles.ResolvedParticleMassRepresentationBuilder()
.set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
.set_activity_strategy(activity_strategy_sucrose)
.set_surface_strategy(surface_strategy_sucrose)
.set_mass(seed_mass_sucrose, "kg")
.set_density(density_sucrose, "kg/m^3")
.set_charge(0)
.set_volume(chamber_volume, "m^3")
.build()
)
aerosol_sucrose = (
par.AerosolBuilder()
.set_atmosphere(atmosphere_sucrose)
.set_particles(particles_sucrose)
.build()
)
# Create condensation strategy for sucrose (2-species molar mass)
condensation_strategy_sucrose = (
par.dynamics.CondensationIsothermalStaggeredBuilder()
.set_molar_mass(molar_mass_sucrose, "kg/mol")
.set_diffusion_coefficient(2.4e-5, "m^2/s")
.set_accommodation_coefficient(1.0)
.set_theta_mode("random")
.set_update_gases(True)
.build()
)
condensation_sucrose = par.dynamics.MassCondensation(
condensation_strategy=condensation_strategy_sucrose
)
print("Scenario B (Sucrose-only) configured")
print(aerosol_sucrose)
# Scenario B: Sucrose only (2 species: sucrose, water)
kappa_sucrose = np.array([0.10, 0.0])
density_sucrose = np.array([1587.0, 997.0])
molar_mass_sucrose = np.array([0.3423, 0.018015])
activity_strategy_sucrose = (
par.particles.ActivityKappaParameterBuilder()
.set_kappa(kappa_sucrose)
.set_density(density_sucrose, "kg/m^3")
.set_molar_mass(molar_mass_sucrose, "kg/mol")
.set_water_index(1)
.build()
)
surface_strategy_sucrose = (
par.particles.SurfaceStrategyVolumeBuilder()
.set_surface_tension(0.072, "N/m")
.set_density(density_sucrose, "kg/m^3")
.build()
)
# Sample particle radii from lognormal distribution
n_particles_sucrose = 1000
dry_radius_sucrose = par.particles.get_lognormal_sample_distribution(
mode=np.array([100e-9]), # 100 nm mode radius
geometric_standard_deviation=np.array([1.5]),
number_of_particles=np.array([1.0]),
number_of_samples=n_particles_sucrose,
)
# Seed masses from sampled radii
volume_per_particle_sucrose = 4 / 3 * np.pi * dry_radius_sucrose**3
sucrose_mass_sucrose = (
volume_per_particle_sucrose * density_sucrose[0]
) # 100% sucrose
water_mass_sucrose = np.zeros_like(dry_radius_sucrose)
seed_mass_sucrose = np.stack([sucrose_mass_sucrose, water_mass_sucrose], axis=1)
# Create 2-species gas (sucrose and water) to match particle species
partitioning_gases_sucrose = (
par.gas.GasSpeciesBuilder()
.set_name(np.array(["sucrose", "water"]))
.set_molar_mass(molar_mass_sucrose, "kg/mol")
.set_vapor_pressure_strategy(
[
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.WaterBuckVaporPressureBuilder().build(),
]
)
.set_partitioning(True)
.set_concentration(np.array([1e-30, c_water_humid]), "kg/m^3")
.build()
)
air_sucrose = (
par.gas.GasSpeciesBuilder()
.set_name("air")
.set_molar_mass(0.029, "kg/mol")
.set_vapor_pressure_strategy(
par.gas.ConstantVaporPressureStrategy(vapor_pressure=101325)
)
.set_partitioning(False)
.set_concentration(1.2, "kg/m^3")
.build()
)
atmosphere_sucrose = (
par.gas.AtmosphereBuilder()
.set_temperature(temperature, "K")
.set_pressure(total_pressure, "Pa")
.set_more_partitioning_species(partitioning_gases_sucrose)
.set_more_gas_only_species(air_sucrose)
.build()
)
particles_sucrose = (
par.particles.ResolvedParticleMassRepresentationBuilder()
.set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
.set_activity_strategy(activity_strategy_sucrose)
.set_surface_strategy(surface_strategy_sucrose)
.set_mass(seed_mass_sucrose, "kg")
.set_density(density_sucrose, "kg/m^3")
.set_charge(0)
.set_volume(chamber_volume, "m^3")
.build()
)
aerosol_sucrose = (
par.AerosolBuilder()
.set_atmosphere(atmosphere_sucrose)
.set_particles(particles_sucrose)
.build()
)
# Create condensation strategy for sucrose (2-species molar mass)
condensation_strategy_sucrose = (
par.dynamics.CondensationIsothermalStaggeredBuilder()
.set_molar_mass(molar_mass_sucrose, "kg/mol")
.set_diffusion_coefficient(2.4e-5, "m^2/s")
.set_accommodation_coefficient(1.0)
.set_theta_mode("random")
.set_update_gases(True)
.build()
)
condensation_sucrose = par.dynamics.MassCondensation(
condensation_strategy=condensation_strategy_sucrose
)
print("Scenario B (Sucrose-only) configured")
print(aerosol_sucrose)
12. Scenario C: Mixed AS + Sucrose Population¶
Mixed population with 5 AS particles and 5 sucrose particles at the same dry diameters. This demonstrates competition for water vapor - AS particles activate first due to higher kappa.
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# Scenario C: Mixed AS + Sucrose (3 species: AS, sucrose, water)
kappa_mixed = np.array([0.61, 0.10, 0.0])
density_mixed = np.array([1770.0, 1587.0, 997.0])
molar_mass_mixed = np.array([0.13214, 0.3423, 0.018015])
activity_strategy_mixed = (
par.particles.ActivityKappaParameterBuilder()
.set_kappa(kappa_mixed)
.set_density(density_mixed, "kg/m^3")
.set_molar_mass(molar_mass_mixed, "kg/mol")
.set_water_index(2)
.build()
)
surface_strategy_mixed = (
par.particles.SurfaceStrategyVolumeBuilder()
.set_surface_tension(0.072, "N/m")
.set_density(density_mixed, "kg/m^3")
.build()
)
# Sample particle radii from lognormal distribution
n_particles_mixed = 1000
dry_radius_mixed = par.particles.get_lognormal_sample_distribution(
mode=np.array([100e-9]), # 100 nm mode radius
geometric_standard_deviation=np.array([1.5]),
number_of_particles=np.array([1.0]),
number_of_samples=n_particles_mixed,
)
# Seed masses from sampled radii - 60% AS, 40% sucrose by volume
volume_per_particle_mixed = 4 / 3 * np.pi * dry_radius_mixed**3
ammonium_sulfate_mass_mixed = 0.6 * volume_per_particle_mixed * density_mixed[0]
sucrose_mass_mixed = 0.4 * volume_per_particle_mixed * density_mixed[1]
water_mass_mixed = np.zeros_like(dry_radius_mixed)
seed_mass_mixed = np.stack(
[ammonium_sulfate_mass_mixed, sucrose_mass_mixed, water_mass_mixed], axis=1
)
# Create 3-species gas to match particle species
partitioning_gases_mixed = (
par.gas.GasSpeciesBuilder()
.set_name(np.array(["ammonium_sulfate", "sucrose", "water"]))
.set_molar_mass(molar_mass_mixed, "kg/mol")
.set_vapor_pressure_strategy(
[
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.WaterBuckVaporPressureBuilder().build(),
]
)
.set_partitioning(True)
.set_concentration(np.array([1e-30, 1e-30, c_water_humid]), "kg/m^3")
.build()
)
air_mixed = (
par.gas.GasSpeciesBuilder()
.set_name("air")
.set_molar_mass(0.029, "kg/mol")
.set_vapor_pressure_strategy(
par.gas.ConstantVaporPressureStrategy(vapor_pressure=101325)
)
.set_partitioning(False)
.set_concentration(1.2, "kg/m^3")
.build()
)
atmosphere_mixed = (
par.gas.AtmosphereBuilder()
.set_temperature(temperature, "K")
.set_pressure(total_pressure, "Pa")
.set_more_partitioning_species(partitioning_gases_mixed)
.set_more_gas_only_species(air_mixed)
.build()
)
particles_mixed = (
par.particles.ResolvedParticleMassRepresentationBuilder()
.set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
.set_activity_strategy(activity_strategy_mixed)
.set_surface_strategy(surface_strategy_mixed)
.set_mass(seed_mass_mixed, "kg")
.set_density(density_mixed, "kg/m^3")
.set_charge(0)
.set_volume(chamber_volume, "m^3")
.build()
)
aerosol_mixed = (
par.AerosolBuilder()
.set_atmosphere(atmosphere_mixed)
.set_particles(particles_mixed)
.build()
)
# Create condensation strategy for mixed (3-species molar mass)
condensation_strategy_mixed = (
par.dynamics.CondensationIsothermalStaggeredBuilder()
.set_molar_mass(molar_mass_mixed, "kg/mol")
.set_diffusion_coefficient(2.4e-5, "m^2/s")
.set_accommodation_coefficient(1.0)
.set_theta_mode("random")
.set_update_gases(True)
.build()
)
condensation_mixed = par.dynamics.MassCondensation(
condensation_strategy=condensation_strategy_mixed
)
print("Scenario C (Mixed AS + Sucrose) configured")
print(aerosol_mixed)
# Scenario C: Mixed AS + Sucrose (3 species: AS, sucrose, water)
kappa_mixed = np.array([0.61, 0.10, 0.0])
density_mixed = np.array([1770.0, 1587.0, 997.0])
molar_mass_mixed = np.array([0.13214, 0.3423, 0.018015])
activity_strategy_mixed = (
par.particles.ActivityKappaParameterBuilder()
.set_kappa(kappa_mixed)
.set_density(density_mixed, "kg/m^3")
.set_molar_mass(molar_mass_mixed, "kg/mol")
.set_water_index(2)
.build()
)
surface_strategy_mixed = (
par.particles.SurfaceStrategyVolumeBuilder()
.set_surface_tension(0.072, "N/m")
.set_density(density_mixed, "kg/m^3")
.build()
)
# Sample particle radii from lognormal distribution
n_particles_mixed = 1000
dry_radius_mixed = par.particles.get_lognormal_sample_distribution(
mode=np.array([100e-9]), # 100 nm mode radius
geometric_standard_deviation=np.array([1.5]),
number_of_particles=np.array([1.0]),
number_of_samples=n_particles_mixed,
)
# Seed masses from sampled radii - 60% AS, 40% sucrose by volume
volume_per_particle_mixed = 4 / 3 * np.pi * dry_radius_mixed**3
ammonium_sulfate_mass_mixed = 0.6 * volume_per_particle_mixed * density_mixed[0]
sucrose_mass_mixed = 0.4 * volume_per_particle_mixed * density_mixed[1]
water_mass_mixed = np.zeros_like(dry_radius_mixed)
seed_mass_mixed = np.stack(
[ammonium_sulfate_mass_mixed, sucrose_mass_mixed, water_mass_mixed], axis=1
)
# Create 3-species gas to match particle species
partitioning_gases_mixed = (
par.gas.GasSpeciesBuilder()
.set_name(np.array(["ammonium_sulfate", "sucrose", "water"]))
.set_molar_mass(molar_mass_mixed, "kg/mol")
.set_vapor_pressure_strategy(
[
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.ConstantVaporPressureStrategy(vapor_pressure=1e-30),
par.gas.WaterBuckVaporPressureBuilder().build(),
]
)
.set_partitioning(True)
.set_concentration(np.array([1e-30, 1e-30, c_water_humid]), "kg/m^3")
.build()
)
air_mixed = (
par.gas.GasSpeciesBuilder()
.set_name("air")
.set_molar_mass(0.029, "kg/mol")
.set_vapor_pressure_strategy(
par.gas.ConstantVaporPressureStrategy(vapor_pressure=101325)
)
.set_partitioning(False)
.set_concentration(1.2, "kg/m^3")
.build()
)
atmosphere_mixed = (
par.gas.AtmosphereBuilder()
.set_temperature(temperature, "K")
.set_pressure(total_pressure, "Pa")
.set_more_partitioning_species(partitioning_gases_mixed)
.set_more_gas_only_species(air_mixed)
.build()
)
particles_mixed = (
par.particles.ResolvedParticleMassRepresentationBuilder()
.set_distribution_strategy(par.particles.ParticleResolvedSpeciatedMass())
.set_activity_strategy(activity_strategy_mixed)
.set_surface_strategy(surface_strategy_mixed)
.set_mass(seed_mass_mixed, "kg")
.set_density(density_mixed, "kg/m^3")
.set_charge(0)
.set_volume(chamber_volume, "m^3")
.build()
)
aerosol_mixed = (
par.AerosolBuilder()
.set_atmosphere(atmosphere_mixed)
.set_particles(particles_mixed)
.build()
)
# Create condensation strategy for mixed (3-species molar mass)
condensation_strategy_mixed = (
par.dynamics.CondensationIsothermalStaggeredBuilder()
.set_molar_mass(molar_mass_mixed, "kg/mol")
.set_diffusion_coefficient(2.4e-5, "m^2/s")
.set_accommodation_coefficient(1.0)
.set_theta_mode("random")
.set_update_gases(True)
.build()
)
condensation_mixed = par.dynamics.MassCondensation(
condensation_strategy=condensation_strategy_mixed
)
print("Scenario C (Mixed AS + Sucrose) configured")
print(aerosol_mixed)
13. Run Multi-Cycle Simulations¶
Execute 4 activation-deactivation cycles for each scenario using the framework defined above.
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# Run multi-cycle simulations for all three scenarios
print("Running Scenario A (Ammonium Sulfate)...")
final_aerosol_as, history_as = run_multi_cycle(
aerosol=aerosol_as,
condensation=condensation_as,
wall_loss=wall_loss,
n_cycles=4,
humid_duration=30,
dry_duration=60,
dilution_coefficient=0.01,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=1, # Water is index 1 for 2-species (AS, water)
dt=0.1,
)
print(f" Completed: {len(history_as)} records")
print("Running Scenario B (Sucrose)...")
final_aerosol_sucrose, history_sucrose = run_multi_cycle(
aerosol=aerosol_sucrose,
condensation=condensation_sucrose,
wall_loss=wall_loss,
n_cycles=4,
humid_duration=30,
dry_duration=60,
dilution_coefficient=0.01,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=1, # Water is index 1 for 2-species (sucrose, water)
dt=0.1,
)
print(f" Completed: {len(history_sucrose)} records")
print("Running Scenario C (Mixed AS + Sucrose)...")
final_aerosol_mixed, history_mixed = run_multi_cycle(
aerosol=aerosol_mixed,
condensation=condensation_mixed,
wall_loss=wall_loss,
n_cycles=4,
humid_duration=30,
dry_duration=60,
dilution_coefficient=0.01,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=2, # Water is index 2 for 3-species (AS, sucrose, water)
dt=0.1,
)
print(f" Completed: {len(history_mixed)} records")
print("\nAll simulations completed successfully!")
# Run multi-cycle simulations for all three scenarios
print("Running Scenario A (Ammonium Sulfate)...")
final_aerosol_as, history_as = run_multi_cycle(
aerosol=aerosol_as,
condensation=condensation_as,
wall_loss=wall_loss,
n_cycles=4,
humid_duration=30,
dry_duration=60,
dilution_coefficient=0.01,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=1, # Water is index 1 for 2-species (AS, water)
dt=0.1,
)
print(f" Completed: {len(history_as)} records")
print("Running Scenario B (Sucrose)...")
final_aerosol_sucrose, history_sucrose = run_multi_cycle(
aerosol=aerosol_sucrose,
condensation=condensation_sucrose,
wall_loss=wall_loss,
n_cycles=4,
humid_duration=30,
dry_duration=60,
dilution_coefficient=0.01,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=1, # Water is index 1 for 2-species (sucrose, water)
dt=0.1,
)
print(f" Completed: {len(history_sucrose)} records")
print("Running Scenario C (Mixed AS + Sucrose)...")
final_aerosol_mixed, history_mixed = run_multi_cycle(
aerosol=aerosol_mixed,
condensation=condensation_mixed,
wall_loss=wall_loss,
n_cycles=4,
humid_duration=30,
dry_duration=60,
dilution_coefficient=0.01,
c_water_humid=c_water_humid,
c_water_dry=c_water_dry,
water_index=2, # Water is index 2 for 3-species (AS, sucrose, water)
dt=0.1,
)
print(f" Completed: {len(history_mixed)} records")
print("\nAll simulations completed successfully!")
14. Particle Size Trajectories Over 4 Cycles¶
Visualize particle diameter evolution for all three scenarios, showing the periodic activation-deactivation pattern.
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def masses_to_diameter_generic(
masses: np.ndarray, density_array: np.ndarray
) -> np.ndarray:
"""Convert speciated masses to equivalent spherical diameter.
Generic version that accepts density array as parameter.
"""
total_mass = masses.sum(axis=1)
nonzero = total_mass > 0
diameters = np.zeros_like(total_mass, dtype=float)
if np.any(nonzero):
masses_nz = masses[nonzero]
total_mass_nz = total_mass[nonzero]
inv_bulk_density = (masses_nz / density_array).sum(
axis=1
) / total_mass_nz
bulk_density = 1.0 / inv_bulk_density
volume = total_mass_nz / bulk_density
diameters[nonzero] = (6 * volume / np.pi) ** (1 / 3)
return diameters
# Cycle parameters
humid_duration = 30
dry_duration = 60
cycle_duration = humid_duration + dry_duration # 90 seconds
n_cycles = 4
# Create figure with 3 subplots
fig, axes = plt.subplots(3, 1, figsize=(10, 12))
# Plot colors for particles
particle_colors = [
TAILWIND["blue"]["500"],
TAILWIND["amber"]["500"],
TAILWIND["emerald"]["500"],
TAILWIND["rose"]["500"],
TAILWIND["violet"]["500"],
]
scenarios = [
("Scenario A: Ammonium Sulfate", history_as, density_as),
("Scenario B: Sucrose", history_sucrose, density_sucrose),
("Scenario C: Mixed AS + Sucrose", history_mixed, density_mixed),
]
for ax, (title, history, dens) in zip(axes, scenarios):
# Extract time and diameters
times = np.array([r["time"] for r in history])
n_particles_scenario = history[0]["masses"].shape[0]
diameters = np.array(
[masses_to_diameter_generic(r["masses"], dens) for r in history]
)
# Shade humid/dry phases
for cycle in range(n_cycles):
start = cycle * cycle_duration
mid = start + humid_duration
end = start + cycle_duration
ax.axvspan(
start / 60, mid / 60, color=TAILWIND["gray"]["200"], alpha=0.3
)
ax.axvspan(mid / 60, end / 60, color=TAILWIND["gray"]["300"], alpha=0.2)
# Plot particle trajectories
for j in range(n_particles_scenario):
color = particle_colors[j % len(particle_colors)]
ax.plot(
times / 60,
diameters[:, j] * 1e6,
color=color,
alpha=0.7,
linewidth=1.5,
)
# Add cycle boundaries
for cycle in range(1, n_cycles):
ax.axvline(
x=cycle * cycle_duration / 60,
color=TAILWIND["gray"]["500"],
linestyle="--",
alpha=0.5,
)
ax.set_xlabel("Time (minutes)")
ax.set_ylabel("Particle diameter (um)")
ax.set_title(title)
# Add legend to first plot
from matplotlib.patches import Patch
legend_elements = [
Patch(facecolor=TAILWIND["gray"]["200"], alpha=0.3, label="Humid phase"),
Patch(facecolor=TAILWIND["gray"]["300"], alpha=0.2, label="Dry phase"),
]
axes[0].legend(handles=legend_elements, loc="upper right")
plt.tight_layout()
plt.show()
def masses_to_diameter_generic(
masses: np.ndarray, density_array: np.ndarray
) -> np.ndarray:
"""Convert speciated masses to equivalent spherical diameter.
Generic version that accepts density array as parameter.
"""
total_mass = masses.sum(axis=1)
nonzero = total_mass > 0
diameters = np.zeros_like(total_mass, dtype=float)
if np.any(nonzero):
masses_nz = masses[nonzero]
total_mass_nz = total_mass[nonzero]
inv_bulk_density = (masses_nz / density_array).sum(
axis=1
) / total_mass_nz
bulk_density = 1.0 / inv_bulk_density
volume = total_mass_nz / bulk_density
diameters[nonzero] = (6 * volume / np.pi) ** (1 / 3)
return diameters
# Cycle parameters
humid_duration = 30
dry_duration = 60
cycle_duration = humid_duration + dry_duration # 90 seconds
n_cycles = 4
# Create figure with 3 subplots
fig, axes = plt.subplots(3, 1, figsize=(10, 12))
# Plot colors for particles
particle_colors = [
TAILWIND["blue"]["500"],
TAILWIND["amber"]["500"],
TAILWIND["emerald"]["500"],
TAILWIND["rose"]["500"],
TAILWIND["violet"]["500"],
]
scenarios = [
("Scenario A: Ammonium Sulfate", history_as, density_as),
("Scenario B: Sucrose", history_sucrose, density_sucrose),
("Scenario C: Mixed AS + Sucrose", history_mixed, density_mixed),
]
for ax, (title, history, dens) in zip(axes, scenarios):
# Extract time and diameters
times = np.array([r["time"] for r in history])
n_particles_scenario = history[0]["masses"].shape[0]
diameters = np.array(
[masses_to_diameter_generic(r["masses"], dens) for r in history]
)
# Shade humid/dry phases
for cycle in range(n_cycles):
start = cycle * cycle_duration
mid = start + humid_duration
end = start + cycle_duration
ax.axvspan(
start / 60, mid / 60, color=TAILWIND["gray"]["200"], alpha=0.3
)
ax.axvspan(mid / 60, end / 60, color=TAILWIND["gray"]["300"], alpha=0.2)
# Plot particle trajectories
for j in range(n_particles_scenario):
color = particle_colors[j % len(particle_colors)]
ax.plot(
times / 60,
diameters[:, j] * 1e6,
color=color,
alpha=0.7,
linewidth=1.5,
)
# Add cycle boundaries
for cycle in range(1, n_cycles):
ax.axvline(
x=cycle * cycle_duration / 60,
color=TAILWIND["gray"]["500"],
linestyle="--",
alpha=0.5,
)
ax.set_xlabel("Time (minutes)")
ax.set_ylabel("Particle diameter (um)")
ax.set_title(title)
# Add legend to first plot
from matplotlib.patches import Patch
legend_elements = [
Patch(facecolor=TAILWIND["gray"]["200"], alpha=0.3, label="Humid phase"),
Patch(facecolor=TAILWIND["gray"]["300"], alpha=0.2, label="Dry phase"),
]
axes[0].legend(handles=legend_elements, loc="upper right")
plt.tight_layout()
plt.show()
15. Activated Fraction vs Dry Diameter¶
Compare activation behavior across scenarios. Particles are considered "activated" if their diameter exceeds 1 um during the humid phase.
In [ ]:
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def calculate_activated_fraction(
history: list, density_array: np.ndarray, activation_threshold: float = 2e-6
) -> np.ndarray:
"""Calculate fraction of time each particle spends activated during humid phases.
Args:
history: Simulation history.
density_array: Density array for diameter calculation.
activation_threshold: Diameter threshold for activation (m).
Returns:
Activated fraction for each particle.
"""
humid_records = [r for r in history if r["phase"] == "humid"]
if len(humid_records) == 0:
return np.zeros(history[0]["masses"].shape[0])
n_particles = humid_records[0]["masses"].shape[0]
activated_count = np.zeros(n_particles)
for record in humid_records:
diameters = masses_to_diameter_generic(record["masses"], density_array)
activated_count += (diameters > activation_threshold).astype(float)
return activated_count / len(humid_records)
# Calculate activated fractions for each scenario
activated_as = calculate_activated_fraction(history_as, density_as)
activated_sucrose = calculate_activated_fraction(
history_sucrose, density_sucrose
)
activated_mixed = calculate_activated_fraction(history_mixed, density_mixed)
# Get initial dry diameters from history (before water uptake)
initial_diams_as = (
masses_to_diameter_generic(history_as[0]["masses"], density_as) * 1e9
) # nm
initial_diams_sucrose = (
masses_to_diameter_generic(history_sucrose[0]["masses"], density_sucrose)
* 1e9
) # nm
initial_diams_mixed = (
masses_to_diameter_generic(history_mixed[0]["masses"], density_mixed) * 1e9
) # nm
# Create scatter plot of activated fraction vs dry diameter
fig, ax = plt.subplots(figsize=(8, 5))
ax.scatter(
initial_diams_as,
activated_as,
color=TAILWIND["blue"]["500"],
s=50,
alpha=0.7,
label="AS only (kappa=0.61)",
)
ax.scatter(
initial_diams_sucrose,
activated_sucrose,
color=TAILWIND["amber"]["500"],
s=50,
alpha=0.7,
label="Sucrose only (kappa=0.10)",
)
ax.scatter(
initial_diams_mixed,
activated_mixed,
color=TAILWIND["emerald"]["500"],
s=50,
alpha=0.7,
label="Mixed AS + Sucrose",
)
ax.set_xlabel("Initial dry diameter (nm)")
ax.set_ylabel("Activated fraction")
ax.set_title("Activated Fraction vs Dry Diameter (threshold: 1 um)")
ax.set_ylim(-0.05, 1.05)
ax.set_xscale("log")
ax.legend(loc="lower right")
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
def calculate_activated_fraction(
history: list, density_array: np.ndarray, activation_threshold: float = 2e-6
) -> np.ndarray:
"""Calculate fraction of time each particle spends activated during humid phases.
Args:
history: Simulation history.
density_array: Density array for diameter calculation.
activation_threshold: Diameter threshold for activation (m).
Returns:
Activated fraction for each particle.
"""
humid_records = [r for r in history if r["phase"] == "humid"]
if len(humid_records) == 0:
return np.zeros(history[0]["masses"].shape[0])
n_particles = humid_records[0]["masses"].shape[0]
activated_count = np.zeros(n_particles)
for record in humid_records:
diameters = masses_to_diameter_generic(record["masses"], density_array)
activated_count += (diameters > activation_threshold).astype(float)
return activated_count / len(humid_records)
# Calculate activated fractions for each scenario
activated_as = calculate_activated_fraction(history_as, density_as)
activated_sucrose = calculate_activated_fraction(
history_sucrose, density_sucrose
)
activated_mixed = calculate_activated_fraction(history_mixed, density_mixed)
# Get initial dry diameters from history (before water uptake)
initial_diams_as = (
masses_to_diameter_generic(history_as[0]["masses"], density_as) * 1e9
) # nm
initial_diams_sucrose = (
masses_to_diameter_generic(history_sucrose[0]["masses"], density_sucrose)
* 1e9
) # nm
initial_diams_mixed = (
masses_to_diameter_generic(history_mixed[0]["masses"], density_mixed) * 1e9
) # nm
# Create scatter plot of activated fraction vs dry diameter
fig, ax = plt.subplots(figsize=(8, 5))
ax.scatter(
initial_diams_as,
activated_as,
color=TAILWIND["blue"]["500"],
s=50,
alpha=0.7,
label="AS only (kappa=0.61)",
)
ax.scatter(
initial_diams_sucrose,
activated_sucrose,
color=TAILWIND["amber"]["500"],
s=50,
alpha=0.7,
label="Sucrose only (kappa=0.10)",
)
ax.scatter(
initial_diams_mixed,
activated_mixed,
color=TAILWIND["emerald"]["500"],
s=50,
alpha=0.7,
label="Mixed AS + Sucrose",
)
ax.set_xlabel("Initial dry diameter (nm)")
ax.set_ylabel("Activated fraction")
ax.set_title("Activated Fraction vs Dry Diameter (threshold: 1 um)")
ax.set_ylim(-0.05, 1.05)
ax.set_xscale("log")
ax.legend(loc="lower right")
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
16. Water Mass Fraction Over Cycles¶
Track mean water mass fraction over time, showing periodic water uptake during humid phases.
In [ ]:
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def calculate_mean_water_fraction(history: list, water_index: int) -> tuple:
"""Calculate mean water mass fraction over time.
Args:
history: Simulation history.
water_index: Index of water species.
Returns:
Tuple of (times, mean_water_fractions).
"""
times = []
water_fractions = []
for record in history:
masses = record["masses"]
total_mass = masses.sum(axis=1)
water_mass = masses[:, water_index]
# Avoid division by zero
valid = total_mass > 0
if valid.any():
fractions = np.where(valid, water_mass / total_mass, 0)
mean_frac = fractions[valid].mean()
else:
mean_frac = 0
times.append(record["time"])
water_fractions.append(mean_frac)
return np.array(times), np.array(water_fractions)
# Calculate water fractions for each scenario
times_as, water_frac_as = calculate_mean_water_fraction(
history_as, water_index=1
)
times_sucrose, water_frac_sucrose = calculate_mean_water_fraction(
history_sucrose, water_index=1
)
times_mixed, water_frac_mixed = calculate_mean_water_fraction(
history_mixed, water_index=2
)
# Create plot
fig, ax = plt.subplots(figsize=(10, 5))
# Shade phases
for cycle in range(n_cycles):
start = cycle * cycle_duration
mid = start + humid_duration
end = start + cycle_duration
ax.axvspan(start / 60, mid / 60, color=TAILWIND["gray"]["200"], alpha=0.3)
ax.axvspan(mid / 60, end / 60, color=TAILWIND["gray"]["300"], alpha=0.2)
ax.plot(
times_as / 60,
water_frac_as,
color=TAILWIND["blue"]["500"],
linewidth=2,
label="AS only (kappa=0.61)",
)
ax.plot(
times_sucrose / 60,
water_frac_sucrose,
color=TAILWIND["amber"]["500"],
linewidth=2,
label="Sucrose only (kappa=0.10)",
)
ax.plot(
times_mixed / 60,
water_frac_mixed,
color=TAILWIND["emerald"]["500"],
linewidth=2,
label="Mixed AS + Sucrose",
)
ax.set_xlabel("Time (minutes)")
ax.set_ylabel("Mean water mass fraction")
ax.set_title("Water Mass Fraction Evolution Over 4 Cycles")
ax.legend()
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
print("Key observations:")
print(" - Higher kappa (AS) leads to higher water uptake during humid phases")
print(" - Periodic pattern reflects activation-deactivation cycles")
def calculate_mean_water_fraction(history: list, water_index: int) -> tuple:
"""Calculate mean water mass fraction over time.
Args:
history: Simulation history.
water_index: Index of water species.
Returns:
Tuple of (times, mean_water_fractions).
"""
times = []
water_fractions = []
for record in history:
masses = record["masses"]
total_mass = masses.sum(axis=1)
water_mass = masses[:, water_index]
# Avoid division by zero
valid = total_mass > 0
if valid.any():
fractions = np.where(valid, water_mass / total_mass, 0)
mean_frac = fractions[valid].mean()
else:
mean_frac = 0
times.append(record["time"])
water_fractions.append(mean_frac)
return np.array(times), np.array(water_fractions)
# Calculate water fractions for each scenario
times_as, water_frac_as = calculate_mean_water_fraction(
history_as, water_index=1
)
times_sucrose, water_frac_sucrose = calculate_mean_water_fraction(
history_sucrose, water_index=1
)
times_mixed, water_frac_mixed = calculate_mean_water_fraction(
history_mixed, water_index=2
)
# Create plot
fig, ax = plt.subplots(figsize=(10, 5))
# Shade phases
for cycle in range(n_cycles):
start = cycle * cycle_duration
mid = start + humid_duration
end = start + cycle_duration
ax.axvspan(start / 60, mid / 60, color=TAILWIND["gray"]["200"], alpha=0.3)
ax.axvspan(mid / 60, end / 60, color=TAILWIND["gray"]["300"], alpha=0.2)
ax.plot(
times_as / 60,
water_frac_as,
color=TAILWIND["blue"]["500"],
linewidth=2,
label="AS only (kappa=0.61)",
)
ax.plot(
times_sucrose / 60,
water_frac_sucrose,
color=TAILWIND["amber"]["500"],
linewidth=2,
label="Sucrose only (kappa=0.10)",
)
ax.plot(
times_mixed / 60,
water_frac_mixed,
color=TAILWIND["emerald"]["500"],
linewidth=2,
label="Mixed AS + Sucrose",
)
ax.set_xlabel("Time (minutes)")
ax.set_ylabel("Mean water mass fraction")
ax.set_title("Water Mass Fraction Evolution Over 4 Cycles")
ax.legend()
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
print("Key observations:")
print(" - Higher kappa (AS) leads to higher water uptake during humid phases")
print(" - Periodic pattern reflects activation-deactivation cycles")
17. Mass Accumulation Over Successive Cycles¶
Track relative dry mass (non-water) retention for each size bin across cycles. Due to dilution and wall loss, overall mass decreases, but we examine relative retention.
In [ ]:
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def get_total_dry_mass_at_cycle_ends(
history: list, water_index: int, cycle_duration: int
) -> tuple:
"""Extract total dry mass (non-water) at the end of each cycle.
Args:
history: Simulation history.
water_index: Index of water species.
cycle_duration: Duration of one cycle in seconds.
Returns:
Tuple of (cycle_numbers, total_dry_masses).
"""
cycle_numbers = []
total_dry_masses = []
for record in history:
# Check if this is end of a cycle (time is multiple of cycle_duration)
if record["time"] > 0 and record["time"] % cycle_duration == 0:
masses = record["masses"]
# Sum all non-water species across all particles
dry_mass = (masses.sum(axis=1) - masses[:, water_index]).sum()
cycle_numbers.append(int(record["time"] / cycle_duration))
total_dry_masses.append(dry_mass)
return cycle_numbers, total_dry_masses
# Get dry mass at cycle ends
cycles_as, dry_mass_as = get_total_dry_mass_at_cycle_ends(
history_as, water_index=1, cycle_duration=90
)
cycles_sucrose, dry_mass_sucrose = get_total_dry_mass_at_cycle_ends(
history_sucrose, water_index=1, cycle_duration=90
)
cycles_mixed, dry_mass_mixed = get_total_dry_mass_at_cycle_ends(
history_mixed, water_index=2, cycle_duration=90
)
# Initial dry masses (total across all particles)
initial_dry_as = history_as[0]["masses"][:, 0].sum() # AS mass
initial_dry_sucrose = history_sucrose[0]["masses"][:, 0].sum() # Sucrose mass
initial_dry_mixed = (
history_mixed[0]["masses"][:, 0] + history_mixed[0]["masses"][:, 1]
).sum() # AS + Sucrose
# Calculate relative retention (fraction of initial mass remaining)
retention_as = [dm / initial_dry_as for dm in dry_mass_as]
retention_sucrose = [dm / initial_dry_sucrose for dm in dry_mass_sucrose]
retention_mixed = [dm / initial_dry_mixed for dm in dry_mass_mixed]
fig, ax = plt.subplots(figsize=(8, 5))
x = np.arange(1, n_cycles + 1)
width = 0.25
ax.bar(
x - width,
retention_as,
width,
label="AS only",
color=TAILWIND["blue"]["500"],
)
ax.bar(
x,
retention_sucrose,
width,
label="Sucrose only",
color=TAILWIND["amber"]["500"],
)
ax.bar(
x + width,
retention_mixed,
width,
label="Mixed",
color=TAILWIND["emerald"]["500"],
)
ax.set_xlabel("Cycle number")
ax.set_ylabel("Dry mass retention fraction")
ax.set_title("Dry Mass Retention Over Cycles")
ax.set_xticks(x)
ax.legend()
ax.set_ylim(0, 1.1)
ax.grid(True, alpha=0.3, axis="y")
plt.tight_layout()
plt.show()
print("Key observations:")
print(" - Mass decreases over cycles due to wall loss")
print(" - Dilution coefficient affects mass retention rate")
def get_total_dry_mass_at_cycle_ends(
history: list, water_index: int, cycle_duration: int
) -> tuple:
"""Extract total dry mass (non-water) at the end of each cycle.
Args:
history: Simulation history.
water_index: Index of water species.
cycle_duration: Duration of one cycle in seconds.
Returns:
Tuple of (cycle_numbers, total_dry_masses).
"""
cycle_numbers = []
total_dry_masses = []
for record in history:
# Check if this is end of a cycle (time is multiple of cycle_duration)
if record["time"] > 0 and record["time"] % cycle_duration == 0:
masses = record["masses"]
# Sum all non-water species across all particles
dry_mass = (masses.sum(axis=1) - masses[:, water_index]).sum()
cycle_numbers.append(int(record["time"] / cycle_duration))
total_dry_masses.append(dry_mass)
return cycle_numbers, total_dry_masses
# Get dry mass at cycle ends
cycles_as, dry_mass_as = get_total_dry_mass_at_cycle_ends(
history_as, water_index=1, cycle_duration=90
)
cycles_sucrose, dry_mass_sucrose = get_total_dry_mass_at_cycle_ends(
history_sucrose, water_index=1, cycle_duration=90
)
cycles_mixed, dry_mass_mixed = get_total_dry_mass_at_cycle_ends(
history_mixed, water_index=2, cycle_duration=90
)
# Initial dry masses (total across all particles)
initial_dry_as = history_as[0]["masses"][:, 0].sum() # AS mass
initial_dry_sucrose = history_sucrose[0]["masses"][:, 0].sum() # Sucrose mass
initial_dry_mixed = (
history_mixed[0]["masses"][:, 0] + history_mixed[0]["masses"][:, 1]
).sum() # AS + Sucrose
# Calculate relative retention (fraction of initial mass remaining)
retention_as = [dm / initial_dry_as for dm in dry_mass_as]
retention_sucrose = [dm / initial_dry_sucrose for dm in dry_mass_sucrose]
retention_mixed = [dm / initial_dry_mixed for dm in dry_mass_mixed]
fig, ax = plt.subplots(figsize=(8, 5))
x = np.arange(1, n_cycles + 1)
width = 0.25
ax.bar(
x - width,
retention_as,
width,
label="AS only",
color=TAILWIND["blue"]["500"],
)
ax.bar(
x,
retention_sucrose,
width,
label="Sucrose only",
color=TAILWIND["amber"]["500"],
)
ax.bar(
x + width,
retention_mixed,
width,
label="Mixed",
color=TAILWIND["emerald"]["500"],
)
ax.set_xlabel("Cycle number")
ax.set_ylabel("Dry mass retention fraction")
ax.set_title("Dry Mass Retention Over Cycles")
ax.set_xticks(x)
ax.legend()
ax.set_ylim(0, 1.1)
ax.grid(True, alpha=0.3, axis="y")
plt.tight_layout()
plt.show()
print("Key observations:")
print(" - Mass decreases over cycles due to wall loss")
print(" - Dilution coefficient affects mass retention rate")
18. Comparing Activation Behavior Across Scenarios¶
Overlay plot showing mean diameter evolution for all three scenarios, highlighting kappa-dependent activation timing.
In [ ]:
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def calculate_mean_diameter(history: list, density_array: np.ndarray) -> tuple:
"""Calculate mean particle diameter over time.
Args:
history: Simulation history.
density_array: Density array for diameter calculation.
Returns:
Tuple of (times, mean_diameters).
"""
times = []
mean_diams = []
for record in history:
diameters = masses_to_diameter_generic(record["masses"], density_array)
valid = diameters > 0
if valid.any():
mean_d = diameters[valid].mean()
else:
mean_d = 0
times.append(record["time"])
mean_diams.append(mean_d)
return np.array(times), np.array(mean_diams)
# Calculate mean diameters
times_as, mean_diam_as = calculate_mean_diameter(history_as, density_as)
times_sucrose, mean_diam_sucrose = calculate_mean_diameter(
history_sucrose, density_sucrose
)
times_mixed, mean_diam_mixed = calculate_mean_diameter(
history_mixed, density_mixed
)
# Create overlay plot
fig, ax = plt.subplots(figsize=(10, 6))
# Shade phases
for cycle in range(n_cycles):
start = cycle * cycle_duration
mid = start + humid_duration
end = start + cycle_duration
if cycle == 0:
ax.axvspan(
start / 60,
mid / 60,
color=TAILWIND["sky"]["300"],
alpha=0.3,
label="Humid phase",
)
ax.axvspan(
mid / 60,
end / 60,
color=TAILWIND["gray"]["200"],
alpha=0.2,
label="Dry phase",
)
else:
ax.axvspan(
start / 60, mid / 60, color=TAILWIND["sky"]["300"], alpha=0.3
)
ax.axvspan(mid / 60, end / 60, color=TAILWIND["gray"]["200"], alpha=0.2)
ax.plot(
times_as / 60,
mean_diam_as * 1e6,
color=TAILWIND["blue"]["700"],
linewidth=2.5,
label="AS only (kappa=0.61)",
)
ax.plot(
times_sucrose / 60,
mean_diam_sucrose * 1e6,
color=TAILWIND["amber"]["600"],
linewidth=2.5,
label="Sucrose only (kappa=0.10)",
)
ax.plot(
times_mixed / 60,
mean_diam_mixed * 1e6,
color=TAILWIND["teal"]["500"],
linewidth=2.5,
label="Mixed AS + Sucrose",
)
ax.set_xlabel("Time (minutes)")
ax.set_ylabel("Mean particle diameter (um)")
ax.set_title("Comparing Activation Behavior: kappa-Dependent Growth")
ax.legend(loc="upper right")
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
def calculate_mean_diameter(history: list, density_array: np.ndarray) -> tuple:
"""Calculate mean particle diameter over time.
Args:
history: Simulation history.
density_array: Density array for diameter calculation.
Returns:
Tuple of (times, mean_diameters).
"""
times = []
mean_diams = []
for record in history:
diameters = masses_to_diameter_generic(record["masses"], density_array)
valid = diameters > 0
if valid.any():
mean_d = diameters[valid].mean()
else:
mean_d = 0
times.append(record["time"])
mean_diams.append(mean_d)
return np.array(times), np.array(mean_diams)
# Calculate mean diameters
times_as, mean_diam_as = calculate_mean_diameter(history_as, density_as)
times_sucrose, mean_diam_sucrose = calculate_mean_diameter(
history_sucrose, density_sucrose
)
times_mixed, mean_diam_mixed = calculate_mean_diameter(
history_mixed, density_mixed
)
# Create overlay plot
fig, ax = plt.subplots(figsize=(10, 6))
# Shade phases
for cycle in range(n_cycles):
start = cycle * cycle_duration
mid = start + humid_duration
end = start + cycle_duration
if cycle == 0:
ax.axvspan(
start / 60,
mid / 60,
color=TAILWIND["sky"]["300"],
alpha=0.3,
label="Humid phase",
)
ax.axvspan(
mid / 60,
end / 60,
color=TAILWIND["gray"]["200"],
alpha=0.2,
label="Dry phase",
)
else:
ax.axvspan(
start / 60, mid / 60, color=TAILWIND["sky"]["300"], alpha=0.3
)
ax.axvspan(mid / 60, end / 60, color=TAILWIND["gray"]["200"], alpha=0.2)
ax.plot(
times_as / 60,
mean_diam_as * 1e6,
color=TAILWIND["blue"]["700"],
linewidth=2.5,
label="AS only (kappa=0.61)",
)
ax.plot(
times_sucrose / 60,
mean_diam_sucrose * 1e6,
color=TAILWIND["amber"]["600"],
linewidth=2.5,
label="Sucrose only (kappa=0.10)",
)
ax.plot(
times_mixed / 60,
mean_diam_mixed * 1e6,
color=TAILWIND["teal"]["500"],
linewidth=2.5,
label="Mixed AS + Sucrose",
)
ax.set_xlabel("Time (minutes)")
ax.set_ylabel("Mean particle diameter (um)")
ax.set_title("Comparing Activation Behavior: kappa-Dependent Growth")
ax.legend(loc="upper right")
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
19. Internal Validation¶
Comprehensive validation checks to verify the multi-cycle simulation results.
In [ ]:
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# 18.1 Validate apply_particle_dilution() produces expected decay
test_mass = np.array([[1.0, 2.0], [3.0, 4.0]]) # 2 particles, 2 species
diluted = apply_particle_dilution(test_mass, dilution_coefficient=0.01, dt=1.0)
expected_factor = np.exp(-0.01 * 1.0) # ~0.99005
assert np.allclose(diluted, test_mass * expected_factor), (
"Dilution decay incorrect"
)
assert np.all(diluted > 0), "Dilution should preserve positive masses"
assert np.all(diluted < test_mass), "Dilution should reduce mass"
print("1. apply_particle_dilution() validated")
# 18.2 Validate history structure
def validate_history(history, name, n_cycles, cycle_duration):
"""Validate history records from simulation."""
assert len(history) > 0, f"{name}: History is empty"
# Check all records have required keys
required_keys = {"time", "phase", "masses"}
for i, record in enumerate(history):
assert required_keys.issubset(record.keys()), (
f"{name}: Record {i} missing keys"
)
# Check time progression
times = [r["time"] for r in history]
assert times == sorted(times), f"{name}: Times not monotonically increasing"
# Check final time approximately matches expected duration
expected_duration = n_cycles * cycle_duration
assert abs(times[-1] - expected_duration) < cycle_duration, (
f"{name}: Final time mismatch"
)
# Check phases alternate (humid, dry)
phases = [r["phase"] for r in history]
assert set(phases) == {"humid", "dry"}, f"{name}: Unexpected phase values"
print(
f"2. {name} history validated ({len(history)} records, {times[-1]:.0f}s)"
)
validate_history(history_as, "AS", n_cycles=4, cycle_duration=90)
validate_history(history_sucrose, "Sucrose", n_cycles=4, cycle_duration=90)
validate_history(history_mixed, "Mixed", n_cycles=4, cycle_duration=90)
# 18.3 Validate scenario setup (species count and shapes)
as_first_masses = history_as[0]["masses"]
assert as_first_masses.shape[1] == 2, "AS should have 2 species (AS, water)"
print(
f"3. AS scenario: {as_first_masses.shape[0]} particles, "
f"{as_first_masses.shape[1]} species"
)
sucrose_first_masses = history_sucrose[0]["masses"]
assert sucrose_first_masses.shape[1] == 2, "Sucrose should have 2 species"
print(
f" Sucrose scenario: {sucrose_first_masses.shape[0]} particles, "
f"{sucrose_first_masses.shape[1]} species"
)
mixed_first_masses = history_mixed[0]["masses"]
assert mixed_first_masses.shape[1] == 3, (
"Mixed should have 3 species (AS, sucrose, water)"
)
assert mixed_first_masses.shape[0] == n_particles_mixed, (
f"Mixed should have {n_particles_mixed} particles"
)
print(
f" Mixed scenario: {mixed_first_masses.shape[0]} particles, "
f"{mixed_first_masses.shape[1]} species"
)
# 18.1 Validate apply_particle_dilution() produces expected decay
test_mass = np.array([[1.0, 2.0], [3.0, 4.0]]) # 2 particles, 2 species
diluted = apply_particle_dilution(test_mass, dilution_coefficient=0.01, dt=1.0)
expected_factor = np.exp(-0.01 * 1.0) # ~0.99005
assert np.allclose(diluted, test_mass * expected_factor), (
"Dilution decay incorrect"
)
assert np.all(diluted > 0), "Dilution should preserve positive masses"
assert np.all(diluted < test_mass), "Dilution should reduce mass"
print("1. apply_particle_dilution() validated")
# 18.2 Validate history structure
def validate_history(history, name, n_cycles, cycle_duration):
"""Validate history records from simulation."""
assert len(history) > 0, f"{name}: History is empty"
# Check all records have required keys
required_keys = {"time", "phase", "masses"}
for i, record in enumerate(history):
assert required_keys.issubset(record.keys()), (
f"{name}: Record {i} missing keys"
)
# Check time progression
times = [r["time"] for r in history]
assert times == sorted(times), f"{name}: Times not monotonically increasing"
# Check final time approximately matches expected duration
expected_duration = n_cycles * cycle_duration
assert abs(times[-1] - expected_duration) < cycle_duration, (
f"{name}: Final time mismatch"
)
# Check phases alternate (humid, dry)
phases = [r["phase"] for r in history]
assert set(phases) == {"humid", "dry"}, f"{name}: Unexpected phase values"
print(
f"2. {name} history validated ({len(history)} records, {times[-1]:.0f}s)"
)
validate_history(history_as, "AS", n_cycles=4, cycle_duration=90)
validate_history(history_sucrose, "Sucrose", n_cycles=4, cycle_duration=90)
validate_history(history_mixed, "Mixed", n_cycles=4, cycle_duration=90)
# 18.3 Validate scenario setup (species count and shapes)
as_first_masses = history_as[0]["masses"]
assert as_first_masses.shape[1] == 2, "AS should have 2 species (AS, water)"
print(
f"3. AS scenario: {as_first_masses.shape[0]} particles, "
f"{as_first_masses.shape[1]} species"
)
sucrose_first_masses = history_sucrose[0]["masses"]
assert sucrose_first_masses.shape[1] == 2, "Sucrose should have 2 species"
print(
f" Sucrose scenario: {sucrose_first_masses.shape[0]} particles, "
f"{sucrose_first_masses.shape[1]} species"
)
mixed_first_masses = history_mixed[0]["masses"]
assert mixed_first_masses.shape[1] == 3, (
"Mixed should have 3 species (AS, sucrose, water)"
)
assert mixed_first_masses.shape[0] == n_particles_mixed, (
f"Mixed should have {n_particles_mixed} particles"
)
print(
f" Mixed scenario: {mixed_first_masses.shape[0]} particles, "
f"{mixed_first_masses.shape[1]} species"
)
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# 18.4 Validate kappa-dependent activation order
def get_first_activation_time(
history, density_array, threshold_diameter_m=1e-6
):
"""Get time when any particle first exceeds threshold diameter."""
for record in history:
diameters = masses_to_diameter_generic(record["masses"], density_array)
if np.any(diameters > threshold_diameter_m):
return record["time"]
return float("inf") # Never activated
as_activation_time = get_first_activation_time(history_as, density_as)
sucrose_activation_time = get_first_activation_time(
history_sucrose, density_sucrose
)
print("4. kappa-dependent activation:")
print(f" AS first activation: {as_activation_time}s")
print(f" Sucrose first activation: {sucrose_activation_time}s")
# AS should activate at same time or before sucrose (higher kappa)
assert as_activation_time <= sucrose_activation_time, (
f"AS (kappa=0.61) should activate before or with sucrose (kappa=0.10): "
f"AS at {as_activation_time}s, sucrose at {sucrose_activation_time}s"
)
print(" Validated: AS activates at same time or before sucrose")
# 18.5 Validate size-dependent activation (larger particles activate earlier)
def get_activation_times_by_particle(
history, density_array, threshold_factor=2.0
):
"""Get activation time for each particle.
Activation defined as diameter > threshold_factor * initial diameter.
"""
initial_diameters = masses_to_diameter_generic(
history[0]["masses"], density_array
)
thresholds = initial_diameters * threshold_factor
n_particles = len(initial_diameters)
activation_times = np.full(n_particles, float("inf"))
for record in history:
diameters = masses_to_diameter_generic(record["masses"], density_array)
newly_activated = (diameters > thresholds) & (
activation_times == float("inf")
)
activation_times[newly_activated] = record["time"]
return activation_times, initial_diameters
as_act_times, as_initial_diams = get_activation_times_by_particle(
history_as, density_as
)
print("5. Size-dependent activation for AS scenario:")
print(f" Dry diameters (nm): {(as_initial_diams * 1e9).astype(int)}")
print(f" Activation times (s): {as_act_times}")
# Verify trend: larger particles (higher index) activate earlier or at same time
# Allow 5s tolerance for simulation artifacts
for i in range(len(as_act_times) - 1):
if as_act_times[i] < float("inf") and as_act_times[i + 1] < float("inf"):
assert as_act_times[i] >= as_act_times[i + 1] - 5, (
f"Size-dependent activation violated: particle {i} "
f"(d={as_initial_diams[i] * 1e9:.0f}nm) "
f"activated at {as_act_times[i]}s but particle {i + 1} "
f"(d={as_initial_diams[i + 1] * 1e9:.0f}nm) "
f"activated at {as_act_times[i + 1]}s"
)
print(" Validated: larger particles activate earlier or at same time")
# 18.4 Validate kappa-dependent activation order
def get_first_activation_time(
history, density_array, threshold_diameter_m=1e-6
):
"""Get time when any particle first exceeds threshold diameter."""
for record in history:
diameters = masses_to_diameter_generic(record["masses"], density_array)
if np.any(diameters > threshold_diameter_m):
return record["time"]
return float("inf") # Never activated
as_activation_time = get_first_activation_time(history_as, density_as)
sucrose_activation_time = get_first_activation_time(
history_sucrose, density_sucrose
)
print("4. kappa-dependent activation:")
print(f" AS first activation: {as_activation_time}s")
print(f" Sucrose first activation: {sucrose_activation_time}s")
# AS should activate at same time or before sucrose (higher kappa)
assert as_activation_time <= sucrose_activation_time, (
f"AS (kappa=0.61) should activate before or with sucrose (kappa=0.10): "
f"AS at {as_activation_time}s, sucrose at {sucrose_activation_time}s"
)
print(" Validated: AS activates at same time or before sucrose")
# 18.5 Validate size-dependent activation (larger particles activate earlier)
def get_activation_times_by_particle(
history, density_array, threshold_factor=2.0
):
"""Get activation time for each particle.
Activation defined as diameter > threshold_factor * initial diameter.
"""
initial_diameters = masses_to_diameter_generic(
history[0]["masses"], density_array
)
thresholds = initial_diameters * threshold_factor
n_particles = len(initial_diameters)
activation_times = np.full(n_particles, float("inf"))
for record in history:
diameters = masses_to_diameter_generic(record["masses"], density_array)
newly_activated = (diameters > thresholds) & (
activation_times == float("inf")
)
activation_times[newly_activated] = record["time"]
return activation_times, initial_diameters
as_act_times, as_initial_diams = get_activation_times_by_particle(
history_as, density_as
)
print("5. Size-dependent activation for AS scenario:")
print(f" Dry diameters (nm): {(as_initial_diams * 1e9).astype(int)}")
print(f" Activation times (s): {as_act_times}")
# Verify trend: larger particles (higher index) activate earlier or at same time
# Allow 5s tolerance for simulation artifacts
for i in range(len(as_act_times) - 1):
if as_act_times[i] < float("inf") and as_act_times[i + 1] < float("inf"):
assert as_act_times[i] >= as_act_times[i + 1] - 5, (
f"Size-dependent activation violated: particle {i} "
f"(d={as_initial_diams[i] * 1e9:.0f}nm) "
f"activated at {as_act_times[i]}s but particle {i + 1} "
f"(d={as_initial_diams[i + 1] * 1e9:.0f}nm) "
f"activated at {as_act_times[i + 1]}s"
)
print(" Validated: larger particles activate earlier or at same time")
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# 18.6 Validate mass accounting (positive masses, finite values)
def calculate_total_mass(masses):
"""Calculate total mass across all particles and species."""
return np.sum(masses)
print("6. Mass accounting:")
for name, history, water_idx in [
("AS", history_as, 1),
("Sucrose", history_sucrose, 1),
("Mixed", history_mixed, 2),
]:
initial_mass = calculate_total_mass(history[0]["masses"])
final_mass = calculate_total_mass(history[-1]["masses"])
# Dry mass (non-water) should decrease due to wall loss
initial_dry = (
history[0]["masses"].sum() - history[0]["masses"][:, water_idx].sum()
)
final_dry = (
history[-1]["masses"].sum() - history[-1]["masses"][:, water_idx].sum()
)
assert final_mass > 0, f"{name}: Final mass should be positive"
assert final_dry > 0, f"{name}: Final dry mass should be positive"
mass_change = final_mass / initial_mass
dry_change = final_dry / initial_dry if initial_dry > 0 else 1.0
print(
f" {name}: Total {initial_mass:.2e} -> {final_mass:.2e} kg ({mass_change:.1%}), "
f"Dry {initial_dry:.2e} -> {final_dry:.2e} kg ({dry_change:.1%})"
)
# 18.7 Validate all values finite and non-negative
def validate_finite_nonnegative(history, name):
"""Check all mass values are finite and non-negative."""
for i, record in enumerate(history):
masses = record["masses"]
assert np.all(np.isfinite(masses)), (
f"{name}: Non-finite masses at record {i}"
)
assert np.all(masses >= 0), f"{name}: Negative masses at record {i}"
print(f"7. {name}: All values finite and non-negative")
validate_finite_nonnegative(history_as, "AS")
validate_finite_nonnegative(history_sucrose, "Sucrose")
validate_finite_nonnegative(history_mixed, "Mixed")
# 18.8 Validate cycle count
def count_cycles(history, cycle_duration=90):
"""Count number of complete cycles based on time span."""
if len(history) == 0:
return 0
total_time = history[-1]["time"]
return int(total_time / cycle_duration)
print("8. Cycle count:")
for name, history in [
("AS", history_as),
("Sucrose", history_sucrose),
("Mixed", history_mixed),
]:
cycles = count_cycles(history)
assert cycles >= 4, f"{name}: Expected 4 cycles, found {cycles}"
print(f" {name}: {cycles} cycles completed")
# 18.6 Validate mass accounting (positive masses, finite values)
def calculate_total_mass(masses):
"""Calculate total mass across all particles and species."""
return np.sum(masses)
print("6. Mass accounting:")
for name, history, water_idx in [
("AS", history_as, 1),
("Sucrose", history_sucrose, 1),
("Mixed", history_mixed, 2),
]:
initial_mass = calculate_total_mass(history[0]["masses"])
final_mass = calculate_total_mass(history[-1]["masses"])
# Dry mass (non-water) should decrease due to wall loss
initial_dry = (
history[0]["masses"].sum() - history[0]["masses"][:, water_idx].sum()
)
final_dry = (
history[-1]["masses"].sum() - history[-1]["masses"][:, water_idx].sum()
)
assert final_mass > 0, f"{name}: Final mass should be positive"
assert final_dry > 0, f"{name}: Final dry mass should be positive"
mass_change = final_mass / initial_mass
dry_change = final_dry / initial_dry if initial_dry > 0 else 1.0
print(
f" {name}: Total {initial_mass:.2e} -> {final_mass:.2e} kg ({mass_change:.1%}), "
f"Dry {initial_dry:.2e} -> {final_dry:.2e} kg ({dry_change:.1%})"
)
# 18.7 Validate all values finite and non-negative
def validate_finite_nonnegative(history, name):
"""Check all mass values are finite and non-negative."""
for i, record in enumerate(history):
masses = record["masses"]
assert np.all(np.isfinite(masses)), (
f"{name}: Non-finite masses at record {i}"
)
assert np.all(masses >= 0), f"{name}: Negative masses at record {i}"
print(f"7. {name}: All values finite and non-negative")
validate_finite_nonnegative(history_as, "AS")
validate_finite_nonnegative(history_sucrose, "Sucrose")
validate_finite_nonnegative(history_mixed, "Mixed")
# 18.8 Validate cycle count
def count_cycles(history, cycle_duration=90):
"""Count number of complete cycles based on time span."""
if len(history) == 0:
return 0
total_time = history[-1]["time"]
return int(total_time / cycle_duration)
print("8. Cycle count:")
for name, history in [
("AS", history_as),
("Sucrose", history_sucrose),
("Mixed", history_mixed),
]:
cycles = count_cycles(history)
assert cycles >= 4, f"{name}: Expected 4 cycles, found {cycles}"
print(f" {name}: {cycles} cycles completed")
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# 18.9 Water mass fraction validation
def get_water_fraction_at_phase_peaks(
history, water_index, humid_duration=30, dry_duration=60
):
"""Get mean water mass fraction at end of each humid phase."""
humid_records = [r for r in history if r["phase"] == "humid"]
fractions = []
# Sample at end of each humid phase; stride over one full cycle (humid + dry)
for i in range(
humid_duration - 1, len(humid_records), humid_duration + dry_duration
):
if i < len(humid_records):
masses = humid_records[i]["masses"]
water_mass = masses[:, water_index].sum()
total_mass = masses.sum()
fractions.append(water_mass / total_mass if total_mass > 0 else 0)
return fractions
as_water_fracs = get_water_fraction_at_phase_peaks(
history_as, water_index=1, humid_duration=30, dry_duration=60
)
sucrose_water_fracs = get_water_fraction_at_phase_peaks(
history_sucrose, water_index=1, humid_duration=30, dry_duration=60
)
print("9. Water mass fraction at humid phase peaks:")
if len(as_water_fracs) > 0 and len(sucrose_water_fracs) > 0:
as_mean_water = np.mean(as_water_fracs)
sucrose_mean_water = np.mean(sucrose_water_fracs)
print(f" AS mean water fraction: {as_mean_water:.3f}")
print(f" Sucrose mean water fraction: {sucrose_mean_water:.3f}")
else:
print(" Insufficient data for water fraction analysis")
# 18.10 Print validation summary
print("\n" + "=" * 60)
print("VALIDATION SUMMARY: ALL CHECKS PASSED")
print("=" * 60)
print("- Dilution function: Correct exponential decay")
print("- History structure: Valid for all 3 scenarios")
print("- Scenario setup: Correct species counts and water indices")
print(
"- kappa-dependent activation: AS activates at same time or before sucrose"
)
print("- Size-dependent activation: Larger particles activate earlier")
print("- Mass conservation: Positive, decreasing (losses expected)")
print("- Value validity: All finite and non-negative")
print("- Cycle count: 4 cycles completed for each scenario")
print("=" * 60)
# 18.9 Water mass fraction validation
def get_water_fraction_at_phase_peaks(
history, water_index, humid_duration=30, dry_duration=60
):
"""Get mean water mass fraction at end of each humid phase."""
humid_records = [r for r in history if r["phase"] == "humid"]
fractions = []
# Sample at end of each humid phase; stride over one full cycle (humid + dry)
for i in range(
humid_duration - 1, len(humid_records), humid_duration + dry_duration
):
if i < len(humid_records):
masses = humid_records[i]["masses"]
water_mass = masses[:, water_index].sum()
total_mass = masses.sum()
fractions.append(water_mass / total_mass if total_mass > 0 else 0)
return fractions
as_water_fracs = get_water_fraction_at_phase_peaks(
history_as, water_index=1, humid_duration=30, dry_duration=60
)
sucrose_water_fracs = get_water_fraction_at_phase_peaks(
history_sucrose, water_index=1, humid_duration=30, dry_duration=60
)
print("9. Water mass fraction at humid phase peaks:")
if len(as_water_fracs) > 0 and len(sucrose_water_fracs) > 0:
as_mean_water = np.mean(as_water_fracs)
sucrose_mean_water = np.mean(sucrose_water_fracs)
print(f" AS mean water fraction: {as_mean_water:.3f}")
print(f" Sucrose mean water fraction: {sucrose_mean_water:.3f}")
else:
print(" Insufficient data for water fraction analysis")
# 18.10 Print validation summary
print("\n" + "=" * 60)
print("VALIDATION SUMMARY: ALL CHECKS PASSED")
print("=" * 60)
print("- Dilution function: Correct exponential decay")
print("- History structure: Valid for all 3 scenarios")
print("- Scenario setup: Correct species counts and water indices")
print(
"- kappa-dependent activation: AS activates at same time or before sucrose"
)
print("- Size-dependent activation: Larger particles activate earlier")
print("- Mass conservation: Positive, decreasing (losses expected)")
print("- Value validity: All finite and non-negative")
print("- Cycle count: 4 cycles completed for each scenario")
print("=" * 60)
20. Wall Loss Analysis¶
Size-dependent wall loss using existing histories and the configured rectangular strategy.
!!! note "Concept Box: Chamber Wall Losses" Size-dependent wall loss combines diffusion and settling. Larger droplets are removed faster, while submicron particles rely on turbulent mixing. We reuse the rectangular wall-loss coefficient configured at the start of the notebook.
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def cumulative_loss_by_bin(history, density_array, bins):
initial_masses = history[0]["masses"]
final_masses = history[-1]["masses"]
initial_diam = masses_to_diameter_generic(initial_masses, density_array)
final_diam = masses_to_diameter_generic(final_masses, density_array)
initial_mass = initial_masses.sum(axis=1)
final_mass = final_masses.sum(axis=1)
init_bin, _ = np.histogram(initial_diam, bins=bins, weights=initial_mass)
final_bin, _ = np.histogram(final_diam, bins=bins, weights=final_mass)
loss_bin = np.clip(init_bin - final_bin, 0.0, None)
loss_fraction = np.zeros_like(loss_bin)
mask = init_bin > 0
loss_fraction[mask] = loss_bin[mask] / init_bin[mask]
return loss_bin, loss_fraction
bins = np.geomspace(40e-9, 800e-9, 9)
loss_as, loss_frac_as = cumulative_loss_by_bin(history_as, density_as, bins)
loss_su, loss_frac_su = cumulative_loss_by_bin(
history_sucrose, density_sucrose, bins
)
loss_mx, loss_frac_mx = cumulative_loss_by_bin(
history_mixed, density_mixed, bins
)
diam_centers = np.sqrt(bins[:-1] * bins[1:]) * 1e9 # nm
# Wall-loss coefficient vs diameter (reuse strategy)
diam_grid = np.geomspace(40e-9, 800e-9, 50)
radius_grid = diam_grid / 2
density_grid = np.full_like(radius_grid, 1000.0)
coeff_grid = wall_loss_strategy.loss_coefficient_for_particles(
particle_radius=radius_grid,
particle_density=density_grid,
temperature=temperature,
pressure=total_pressure,
)
coeff_grid = np.clip(coeff_grid, 0, None)
fig, axes = plt.subplots(1, 2, figsize=(10, 4))
axes[0].semilogx(
diam_grid * 1e9, coeff_grid, color=TAILWIND["blue"]["600"], linewidth=2
)
axes[0].set_xlabel("Particle diameter (nm)")
axes[0].set_ylabel("Wall loss coefficient (1/s)")
axes[0].set_title("Rectangular chamber wall loss coefficient")
axes[0].grid(True, which="both", alpha=0.3)
width = 0.08 * diam_centers
axes[1].bar(
diam_centers - width,
loss_frac_as,
width,
label="AS",
color=TAILWIND["blue"]["500"],
)
axes[1].bar(
diam_centers,
loss_frac_su,
width,
label="Sucrose",
color=TAILWIND["amber"]["500"],
)
axes[1].bar(
diam_centers + width,
loss_frac_mx,
width,
label="Mixed",
color=TAILWIND["emerald"]["500"],
)
axes[1].set_xscale("log")
axes[1].set_xlabel("Dry diameter (nm)")
axes[1].set_ylabel("Cumulative loss fraction")
axes[1].set_ylim(0, 1)
axes[1].set_title("Size-dependent cumulative loss (4 cycles)")
axes[1].legend()
axes[1].grid(True, which="both", alpha=0.3)
plt.tight_layout()
plt.show()
def cumulative_loss_by_bin(history, density_array, bins):
initial_masses = history[0]["masses"]
final_masses = history[-1]["masses"]
initial_diam = masses_to_diameter_generic(initial_masses, density_array)
final_diam = masses_to_diameter_generic(final_masses, density_array)
initial_mass = initial_masses.sum(axis=1)
final_mass = final_masses.sum(axis=1)
init_bin, _ = np.histogram(initial_diam, bins=bins, weights=initial_mass)
final_bin, _ = np.histogram(final_diam, bins=bins, weights=final_mass)
loss_bin = np.clip(init_bin - final_bin, 0.0, None)
loss_fraction = np.zeros_like(loss_bin)
mask = init_bin > 0
loss_fraction[mask] = loss_bin[mask] / init_bin[mask]
return loss_bin, loss_fraction
bins = np.geomspace(40e-9, 800e-9, 9)
loss_as, loss_frac_as = cumulative_loss_by_bin(history_as, density_as, bins)
loss_su, loss_frac_su = cumulative_loss_by_bin(
history_sucrose, density_sucrose, bins
)
loss_mx, loss_frac_mx = cumulative_loss_by_bin(
history_mixed, density_mixed, bins
)
diam_centers = np.sqrt(bins[:-1] * bins[1:]) * 1e9 # nm
# Wall-loss coefficient vs diameter (reuse strategy)
diam_grid = np.geomspace(40e-9, 800e-9, 50)
radius_grid = diam_grid / 2
density_grid = np.full_like(radius_grid, 1000.0)
coeff_grid = wall_loss_strategy.loss_coefficient_for_particles(
particle_radius=radius_grid,
particle_density=density_grid,
temperature=temperature,
pressure=total_pressure,
)
coeff_grid = np.clip(coeff_grid, 0, None)
fig, axes = plt.subplots(1, 2, figsize=(10, 4))
axes[0].semilogx(
diam_grid * 1e9, coeff_grid, color=TAILWIND["blue"]["600"], linewidth=2
)
axes[0].set_xlabel("Particle diameter (nm)")
axes[0].set_ylabel("Wall loss coefficient (1/s)")
axes[0].set_title("Rectangular chamber wall loss coefficient")
axes[0].grid(True, which="both", alpha=0.3)
width = 0.08 * diam_centers
axes[1].bar(
diam_centers - width,
loss_frac_as,
width,
label="AS",
color=TAILWIND["blue"]["500"],
)
axes[1].bar(
diam_centers,
loss_frac_su,
width,
label="Sucrose",
color=TAILWIND["amber"]["500"],
)
axes[1].bar(
diam_centers + width,
loss_frac_mx,
width,
label="Mixed",
color=TAILWIND["emerald"]["500"],
)
axes[1].set_xscale("log")
axes[1].set_xlabel("Dry diameter (nm)")
axes[1].set_ylabel("Cumulative loss fraction")
axes[1].set_ylim(0, 1)
axes[1].set_title("Size-dependent cumulative loss (4 cycles)")
axes[1].legend()
axes[1].grid(True, which="both", alpha=0.3)
plt.tight_layout()
plt.show()
21. Summary Comparison Gallery (4 panels)¶
A quick gallery contrasting activation, size evolution, mass balance, and water uptake for the three scenarios.
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# Panel A: mean diameter overlays (reuse prior calculations)
panel_times = [times_as, times_sucrose, times_mixed]
panel_means = [mean_diam_as, mean_diam_sucrose, mean_diam_mixed]
panel_labels = ["AS", "Sucrose", "Mixed"]
panel_colors = [
TAILWIND["blue"]["500"],
TAILWIND["amber"]["500"],
TAILWIND["emerald"]["500"],
]
# Panel B: peak/mean diameter per scenario
peak_diams = [np.max(md) * 1e6 for md in panel_means]
final_means = [md[-1] * 1e6 for md in panel_means]
# Panel C: mass balance (initial vs final vs loss)
def total_mass(history):
masses0 = history[0]["masses"]
massesf = history[-1]["masses"]
init = masses0.sum()
final = massesf.sum()
return init, final, max(init - final, 0)
mass_init = []
mass_final = []
mass_loss = []
for hist in [history_as, history_sucrose, history_mixed]:
init, final, loss = total_mass(hist)
mass_init.append(init)
mass_final.append(final)
mass_loss.append(loss)
# Panel D: final water mass fraction
def water_fraction(history, water_index):
masses = history[-1]["masses"]
total = masses.sum()
water = masses[:, water_index].sum()
return water / total if total > 0 else 0
water_fracs = [
water_fraction(history_as, water_index=1),
water_fraction(history_sucrose, water_index=1),
water_fraction(history_mixed, water_index=2),
]
fig, axes = plt.subplots(2, 2, figsize=(10, 8))
# A
axes[0, 0].set_title("Mean diameter over 4 cycles")
for t, md, label, color in zip(
panel_times, panel_means, panel_labels, panel_colors
):
axes[0, 0].plot(t / 60, md * 1e6, label=label, color=color, linewidth=2)
axes[0, 0].set_xlabel("Time (minutes)")
axes[0, 0].set_ylabel("Mean diameter (um)")
axes[0, 0].legend()
axes[0, 0].grid(alpha=0.3)
# B
xpos = np.arange(len(panel_labels))
axes[0, 1].bar(
xpos - 0.15,
peak_diams,
width=0.3,
label="Peak",
color=TAILWIND["indigo"]["500"],
)
axes[0, 1].bar(
xpos + 0.15,
final_means,
width=0.3,
label="Final",
color=TAILWIND["gray"]["500"],
)
axes[0, 1].set_xticks(xpos)
axes[0, 1].set_xticklabels(panel_labels)
axes[0, 1].set_ylabel("Diameter (um)")
axes[0, 1].set_title("Peak vs final mean diameter")
axes[0, 1].legend()
# C
width = 0.25
axes[1, 0].bar(
xpos - width,
mass_init,
width,
label="Initial",
color=TAILWIND["gray"]["400"],
)
axes[1, 0].bar(
xpos, mass_final, width, label="Final", color=TAILWIND["emerald"]["500"]
)
axes[1, 0].bar(
xpos + width,
mass_loss,
width,
label="Wall loss + dilution",
color=TAILWIND["rose"]["400"],
)
axes[1, 0].set_xticks(xpos)
axes[1, 0].set_xticklabels(panel_labels)
axes[1, 0].set_ylabel("Mass (kg)")
axes[1, 0].set_title("Mass balance after 4 cycles")
axes[1, 0].legend()
# D
axes[1, 1].bar(panel_labels, water_fracs, color=panel_colors)
axes[1, 1].set_ylabel("Water / total mass")
axes[1, 1].set_ylim(0, 1)
axes[1, 1].set_title("Final water mass fraction")
plt.tight_layout()
plt.show()
# Panel A: mean diameter overlays (reuse prior calculations)
panel_times = [times_as, times_sucrose, times_mixed]
panel_means = [mean_diam_as, mean_diam_sucrose, mean_diam_mixed]
panel_labels = ["AS", "Sucrose", "Mixed"]
panel_colors = [
TAILWIND["blue"]["500"],
TAILWIND["amber"]["500"],
TAILWIND["emerald"]["500"],
]
# Panel B: peak/mean diameter per scenario
peak_diams = [np.max(md) * 1e6 for md in panel_means]
final_means = [md[-1] * 1e6 for md in panel_means]
# Panel C: mass balance (initial vs final vs loss)
def total_mass(history):
masses0 = history[0]["masses"]
massesf = history[-1]["masses"]
init = masses0.sum()
final = massesf.sum()
return init, final, max(init - final, 0)
mass_init = []
mass_final = []
mass_loss = []
for hist in [history_as, history_sucrose, history_mixed]:
init, final, loss = total_mass(hist)
mass_init.append(init)
mass_final.append(final)
mass_loss.append(loss)
# Panel D: final water mass fraction
def water_fraction(history, water_index):
masses = history[-1]["masses"]
total = masses.sum()
water = masses[:, water_index].sum()
return water / total if total > 0 else 0
water_fracs = [
water_fraction(history_as, water_index=1),
water_fraction(history_sucrose, water_index=1),
water_fraction(history_mixed, water_index=2),
]
fig, axes = plt.subplots(2, 2, figsize=(10, 8))
# A
axes[0, 0].set_title("Mean diameter over 4 cycles")
for t, md, label, color in zip(
panel_times, panel_means, panel_labels, panel_colors
):
axes[0, 0].plot(t / 60, md * 1e6, label=label, color=color, linewidth=2)
axes[0, 0].set_xlabel("Time (minutes)")
axes[0, 0].set_ylabel("Mean diameter (um)")
axes[0, 0].legend()
axes[0, 0].grid(alpha=0.3)
# B
xpos = np.arange(len(panel_labels))
axes[0, 1].bar(
xpos - 0.15,
peak_diams,
width=0.3,
label="Peak",
color=TAILWIND["indigo"]["500"],
)
axes[0, 1].bar(
xpos + 0.15,
final_means,
width=0.3,
label="Final",
color=TAILWIND["gray"]["500"],
)
axes[0, 1].set_xticks(xpos)
axes[0, 1].set_xticklabels(panel_labels)
axes[0, 1].set_ylabel("Diameter (um)")
axes[0, 1].set_title("Peak vs final mean diameter")
axes[0, 1].legend()
# C
width = 0.25
axes[1, 0].bar(
xpos - width,
mass_init,
width,
label="Initial",
color=TAILWIND["gray"]["400"],
)
axes[1, 0].bar(
xpos, mass_final, width, label="Final", color=TAILWIND["emerald"]["500"]
)
axes[1, 0].bar(
xpos + width,
mass_loss,
width,
label="Wall loss + dilution",
color=TAILWIND["rose"]["400"],
)
axes[1, 0].set_xticks(xpos)
axes[1, 0].set_xticklabels(panel_labels)
axes[1, 0].set_ylabel("Mass (kg)")
axes[1, 0].set_title("Mass balance after 4 cycles")
axes[1, 0].legend()
# D
axes[1, 1].bar(panel_labels, water_fracs, color=panel_colors)
axes[1, 1].set_ylabel("Water / total mass")
axes[1, 1].set_ylim(0, 1)
axes[1, 1].set_title("Final water mass fraction")
plt.tight_layout()
plt.show()
22. Water Mass Fraction Evolution¶
Water mass fraction over time for each scenario, with cycle boundaries marked.
In [ ]:
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def water_fraction_series(history, water_index):
times = []
fractions = []
for record in history:
masses = record["masses"]
total = masses.sum()
water = masses[:, water_index].sum()
fractions.append(water / total if total > 0 else 0)
times.append(record["time"])
return np.array(times), np.array(fractions)
wf_times = []
wf_fracs = []
for hist, widx in [
(history_as, 1),
(history_sucrose, 1),
(history_mixed, 2),
]:
t_vals, f_vals = water_fraction_series(hist, widx)
wf_times.append(t_vals)
wf_fracs.append(f_vals)
cycle_marks = np.arange(0, (n_cycles + 1) * cycle_duration + 1, cycle_duration)
plt.figure(figsize=(8, 4))
for t_vals, f_vals, label, color in zip(
wf_times, wf_fracs, panel_labels, panel_colors
):
plt.plot(t_vals / 60, f_vals, label=label, color=color, linewidth=2)
for cm in cycle_marks:
plt.axvline(
cm / 60, color=TAILWIND["gray"]["300"], linestyle="--", linewidth=0.8
)
plt.ylim(0, 1)
plt.xlabel("Time (minutes)")
plt.ylabel("Water mass fraction")
plt.title("Water mass fraction evolution across cycles")
plt.legend(loc="best")
plt.tight_layout()
plt.show()
def water_fraction_series(history, water_index):
times = []
fractions = []
for record in history:
masses = record["masses"]
total = masses.sum()
water = masses[:, water_index].sum()
fractions.append(water / total if total > 0 else 0)
times.append(record["time"])
return np.array(times), np.array(fractions)
wf_times = []
wf_fracs = []
for hist, widx in [
(history_as, 1),
(history_sucrose, 1),
(history_mixed, 2),
]:
t_vals, f_vals = water_fraction_series(hist, widx)
wf_times.append(t_vals)
wf_fracs.append(f_vals)
cycle_marks = np.arange(0, (n_cycles + 1) * cycle_duration + 1, cycle_duration)
plt.figure(figsize=(8, 4))
for t_vals, f_vals, label, color in zip(
wf_times, wf_fracs, panel_labels, panel_colors
):
plt.plot(t_vals / 60, f_vals, label=label, color=color, linewidth=2)
for cm in cycle_marks:
plt.axvline(
cm / 60, color=TAILWIND["gray"]["300"], linestyle="--", linewidth=0.8
)
plt.ylim(0, 1)
plt.xlabel("Time (minutes)")
plt.ylabel("Water mass fraction")
plt.title("Water mass fraction evolution across cycles")
plt.legend(loc="best")
plt.tight_layout()
plt.show()
23. What You Learned¶
- Supersaturation drives activation when RH exceeds 100%.
- Size matters: larger particles have lower critical supersaturation.
- Composition matters: higher κ activates earlier and grows more.
- Mass accumulates in larger particles over repeated cycles.
- Wall loss is size-dependent: larger droplets are removed faster.
- Vapor competition: fast activators deplete vapor for slower seeds.
- Particle-resolved tracking captures per-particle activation history.
24. Summary and Conclusions¶
This notebook has demonstrated:
Single-Cycle Foundation (Part 1)¶
- Configured a rectangular cloud chamber with wall loss
- Defined mixed AS + sucrose seeds with kappa-theory activity
- Ran one activation-deactivation cycle showing droplet growth beyond 5 um
Multi-Cycle Scenarios (Part 2)¶
- Framework: Created reusable
run_cycle()andrun_multi_cycle()functions with dilution during dry phases - Scenario A (AS): High hygroscopicity (kappa=0.61) leads to faster activation
- Scenario B (Sucrose): Lower hygroscopicity (kappa=0.10) leads to slower activation
- Scenario C (Mixed): Competition for water vapor with AS activating first
Key Scientific Findings¶
- kappa-dependent activation: Higher kappa materials activate at lower supersaturation
- Size-dependent activation: Larger dry particles activate before smaller ones
- Water uptake: Higher kappa leads to higher water mass fraction during humid phases
- Mass evolution: Dilution and wall loss cause overall mass decrease over cycles
- Wall loss insight: Size-binned losses highlight faster removal for larger droplets
- Gallery recap: Four-panel summary compares activation, size, mass balance, and hydration
Next Steps¶
- Sensitivity studies: vary kappa, dilution coefficient, RH levels
- Extended cycle counts: 10+ cycles for long-term evolution
- Different size distributions: polydisperse populations
- Internal mixing: particles with both AS and sucrose