Numerical investigation of the spreading-receding cycle in a concentration-dependent lattice gas automaton diffusion model
Bibliographic record
Abstract
This work forms the second part of a numerical study about the dynamics of diffusive fronts in concentration-dependent diffusion processes. We previously demonstrated that one-dimensional spreading of a density front in a concentration-dependent microscopically heterogeneous, macroscopically homogeneous isotropic lattice gas automaton (LGA) substantially deviates from the t(1/2) relation expected from Fick's law over large periods of time. The time exponent was found to be larger than 1/2 , i.e., spreading of the density front is enhanced with respect to standard Fickian diffusion. In this note, we specifically investigate the dynamics of receding by using the same LGA model. We show here that the receding process essentially scales as t(1/2). The LGA simulations of diffusive fronts thus lead to the paradoxical result of Fick's-compatible receding and anomalous superdiffusive spreading for the same microscopic random structure and the same boundary conditions. The results also suggest that hysteresis of the spreading-receding cycle could arise from the contrasted dynamics between spreading and receding. A conceptual model of "offer and demand" which includes both the diffusivity gradient dD(rho)/d(rho) and the conditions applied at boundaries as main parameters is proposed to tentatively account for the dynamics of diffusive fronts in concentration-dependent diffusion processes.
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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 | 0.002 |
| 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".