Time-dependent diffusion in one-dimensional disordered media decorated by permeable membranes: Theoretical findings backed by simulations and a new disorder class
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Bibliographic record
Abstract
As the diffusion of fluids is hindered by semipermeable membranes, the long-time behavior of the diffusion coefficient is influenced by the arrangement of the membranes. We develop methods that predict this long-time instantaneous diffusivity from bulk diffusivity, the membranes' locations, and their permeabilities. We studied this problem theoretically and expressed the instantaneous diffusivity analytically as an infinite sum. An independent numerical scheme was employed. Several types of disorder in the membranes' positions were considered including a new disorder family that generalizes hyperuniform and short-range disorders. Our theoretical and numerical findings are in excellent agreement. Our methods provide an alternative means for studying time-dependent diffusion processes.
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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