Diffusing Diffusivity: A Model for Anomalous, yet Brownian, Diffusion
Bibliographic record
Abstract
Wang et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 15160 (2009)] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution G(x,t), with roughly exponential tails at short times, a situation they termed “anomalous yet Brownian” diffusion. The diversity of systems in which this is observed calls for a generic model. We present such a model where there is diffusivity memory but no direction memory in the particle trajectory, and we show that it leads to both a linear MSD and a non-Gaussian G(x,t) at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression “diffusing diffusivity”. G(x,t) is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 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".