Anomalous spreading of a density front from an infinite continuous source in a concentration-dependent lattice gas automaton diffusion model
Bibliographic record
Abstract
A two-dimensional lattice gas automaton (LGA) is used for simulating concentration-dependent diffusion in a microscopically random heterogeneous structure. The heterogeneous medium is initialized at a low density ρ 0 and then submitted to a steep concentration gradient by continuous injection of particles at a concentration ρ 1 >ρ 0 from a one-dimensional source to model spreading of a density front. Whereas the nonlinear diffusion equation generally used to describe concentration-dependent diffusion processes predicts a scaling law of the type ϕ = xt −1/2 in one dimension, the spreading process is shown to deviate from the expected t 1/2 scaling. The time exponent is found to be larger than ½, i.e. diffusion of the density front is enhanced with respect to standard Fickian diffusion. It is also established that the anomalous time exponent decreases as time elapses: anomalous spreading is thus not a timescaling process. We demonstrate that occurrence of anomalous spreading results from the diffusivity gradient (d D (ρ)/dρ) existing in the concentration-dependent LGA diffusion model. Standard Fickian diffusion appears as a special case which only occurs when (d D (ρ)/dρ)≈0. Decrease of the anomalous exponent with time may indicate that anomalous diffusion is only transient. In any case, the LGA system possesses a very long transitory regime and spreading remains an anomalous superdiffusive process over large period of time. A simple qualitative model, based on the supply and demand principle, is proposed to account for anomalous spreading. A correspondence is finally established between LGA simulations and experimental measurements of one-dimensional water absorption in non-saturated porous materials in which evidence of anomalous spreading was recently reported.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".