Random Sequential Adsorption of 3D Rods

A computational study of how rods pack under sequential, irreversible placement — and what that reveals about entanglement transitions.

GitHub: rod-placement

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Background

Random Sequential Adsorption (RSA) is a classical model for irreversible deposition: objects are placed one at a time, uniformly at random, and accepted only if they do not overlap with previously placed objects. For spheres in 2D and 3D, RSA is well-studied. For elongated rods in 3D with periodic boundary conditions, the problem is richer — aspect ratio, orientation distribution, and density all interact to determine whether the packing becomes entangled.

This project implements an RSA simulation for 3D rods inside a periodic box, with the goal of measuring how packing statistics depend on rod geometry and density.

Simulation setup

Rods are modeled as line segments (spherocylinders) with a given aspect ratio \(\ell / d\). A rod is placed by:

1. Sampling a random center position uniformly in the periodic box
2. Sampling a random orientation from the unit sphere
3. Checking overlap with all previously placed rods
4. Accepting if no overlap; rejecting and retrying otherwise

The simulation tracks the number of attempts per successful placement, which diverges as the packing approaches jamming. The distribution of attempt counts is a sensitive probe of the local geometry and correlations.

Key metrics

• Attempts per rod: How many random trials are needed to place each successive rod? This grows rapidly near the jamming density.
• Attempts distribution: The full histogram of attempts reveals the heterogeneity of available space.
• Normalized cumulative analysis: Comparing multiple runs with different random seeds or parameters.
• Entanglement onset: At what density does the packing first exhibit macroscopic entanglement?

Workflow

The project is designed for high-throughput parametric studies on HPC clusters:

• submit_from_parameter_sets.py — Generates and submits SLURM jobs across a parameter grid (aspect ratio \(\times\) target density)
• post_analyze_attempts.py — Analyzes a single completed run
• combined_analysis.py — Aggregates statistics across an ensemble of runs
• process_collection.py — Main tool for batch processing result collections

Large simulation outputs (runs/) are kept separate from lightweight analysis results (analysis/) to facilitate sharing and archiving.

Findings in context

The RSA simulations feed into a larger picture of the entanglement transition. By varying aspect ratio and density, we map out the boundary between jammed-but-unentangled and jammed-and-entangled phases. The onset of entanglement in RSA packings correlates with the caging number crossing a threshold — a result consistent with equilibrium simulations and experiments on physical rod packings.

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