RSA generation scaling

This benchmark measures the time to generate periodic random sequential adsorption (RSA) configurations as the box volume, and therefore the requested particle count, increases. The radius, target packing fraction, and stopping criteria remain fixed.

The timings are specific to the machine and build configuration. They describe RSA insertion cost, not equilibrium sampling or agreement with an analytical hard-sphere model.

from time import perf_counter

import matplotlib.pyplot as plt
import numpy as np

from PackLab import monte_carlo, samplers, ureg

Define a fixed RSA workload

radius = 100 * ureg.nanometer
target_packing_fraction = 0.08
box_lengths = np.linspace(3.0, 5.0, 10) * ureg.micrometer
sampler = samplers.ConstantRadiusSampler(radius=radius)

Time configuration generation at increasing box sizes

sphere_counts = []
elapsed_seconds = []

for index, box_length in enumerate(box_lengths):
    domain = monte_carlo.PackingDomain(
        box_length,
        box_length,
        box_length,
        use_periodic_boundaries=True,
    )
    options = monte_carlo.RSAOptions()
    options.random_seed = 2026 + index
    options.maximum_attempts = 50_000
    options.maximum_consecutive_rejections = 10_000
    options.target_packing_fraction = target_packing_fraction

    started = perf_counter()
    result = monte_carlo.RSASimulator(domain, sampler, options).run()
    elapsed_seconds.append(perf_counter() - started)
    sphere_counts.append(result.statistics.sphere_count)
    print(
        f"{box_length.to('micrometer').magnitude:.1f} µm box: "
        f"{sphere_counts[-1]:4d} spheres in {elapsed_seconds[-1]:.3f} s"
    )

3.0 µm box:  516 spheres in 0.001 s
3.2 µm box:  639 spheres in 0.001 s
3.4 µm box:  781 spheres in 0.002 s
3.7 µm box:  942 spheres in 0.002 s
3.9 µm box: 1124 spheres in 0.002 s
4.1 µm box: 1328 spheres in 0.003 s
4.3 µm box: 1555 spheres in 0.004 s
4.6 µm box: 1806 spheres in 0.004 s
4.8 µm box: 2083 spheres in 0.005 s
5.0 µm box: 2388 spheres in 0.007 s

Display generation time against the realised workload

figure, axis = plt.subplots(figsize=(6, 4))
_ = axis.plot(sphere_counts, elapsed_seconds, "o-", color="#d97706")
_ = axis.set(
    xlabel="accepted sphere count",
    ylabel="wall-clock time (s)",
    title="Periodic RSA generation scaling",
)
axis.grid(alpha=0.25)
figure.tight_layout()