Random walk and diffusion of hard spherical particles in quenched systems: Reaching the continuum limit on a lattice
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Bibliographic record
Abstract
Lattice Monte Carlo methods are widely used to study diffusion problems such as the random walk of a probe particle among fixed obstacles. However, the diffusion coefficient D found with such methods generally depends on the type of lattice used. In order to obtain experimentally relevant results, one often needs to consider the continuum limit, i.e., the limit where the size of the lattice parameter is infinitely small compared to the size of both the probe particle and the obstacles. A numerical procedure to reach this limit for a single particle diffusing between quenched impenetrable obstacles is presented. As an example, the case of a system of periodic spherical obstacles is treated and a general relation between the diffusion coefficient D, the total obstructed volume f, and the dimensionality d of the problem is proposed.
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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