Review of the percolation threshold for spherocylinder-based systems in a continuum model
Bibliographic record
Abstract
This study presents a comprehensive review and comparative analysis of various methods for determining the percolation threshold in systems of spherocylinders—a critical parameter in the design of advanced composite materials. We evaluated a range of approaches, including analytical models based on excluded volume theory (soft- and hard-core), computational Monte Carlo simulations, and established experimental techniques. A central focus was reconciling the discrepancies between theoretical models, which often assume infinite aspect ratios, and experimental results from fillers with finite aspect ratios. Our analysis reveals that while traditional analytical bounds and hard-core models exhibit limited predictive accuracy, computational soft-core simulations for finite-sized fillers provide robust predictions that align well with experimental data. Moreover, empirical approximations fitted to numerical results demonstrate strong agreement across all aspect ratio regimes. The primary contribution of this work is a novel interpolation formula that unifies the distinct asymptotic behaviours observed at very low and very high aspect ratios. This formula shows excellent agreement with extensive simulation data and serves as a highly accurate, unified predictive tool. By clarifying the strengths and weaknesses of existing methods, this investigation provides a reliable framework for accurately predicting the percolation threshold in spherocylinder-based systems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".