Stochastic self-assembly of incommensurate clusters
Why this work is in the frame
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Bibliographic record
Abstract
Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated mass-action Becker-Döring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can "emulsify" the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic mass-action equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic Monte-Carlo simulations. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.
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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 it