Lava Delta Formation: Mathematical Modeling and Laboratory Experiments
Bibliographic record
Abstract
Abstract We analyze the dynamics of evolving lava‐fed deltas through the use of shallow‐layer mathematical models and analog laboratory experiments. Numerical and asymptotic solutions are calculated for the cases of planar and three‐dimensional flows fed by a point source upstream of the shoreline. We consider several modes of delta formation: a reduction in the driving buoyancy force; an enhanced viscosity of the submerged material; and the production of a granular subaqueous platform, over which a subaerial current can propagate. These modes of delta formation result in different behaviors. Under a steady supply of fluid upstream, the buoyancy‐driven case develops a solution with a steady subaerial delta and a subaqueous current which propagates at a constant speed, while the granular platform model extends the delta indefinitely. We determine a late‐time power‐law relation for the shoreline extent with time in this case. When the viscosity contrast is large, the model with an enhanced subaqueous viscosity is shown to mimic the initial dynamics of the granular platform model, but ultimately reaches a steady shoreline extent at sufficiently late times, as for the buoyancy‐driven model. The distinct behaviors of these models are further illustrated through laboratory experiments, utilizing the gelling reaction of sodium alginate solution in the presence of calcium ions as a novel analog for the abrupt rheological changes that occur when lava makes contact with water. These experiments provide quantitative verification of the buoyancy‐driven model in the absence of the reaction, and demonstrate the effects of a subaqueous platform qualitatively in its presence.
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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 | 0.001 | 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".