Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows
Bibliographic record
Abstract
Abstract Modeling the evolution of composition in a convecting mantle is difficult since the associated chemical diffusivity is very small. Consequently, compositional evolution is often modeled using the advection equation which is prone to overdiffusion and spurious oscillations unless special numerical schemes are employed. Similar errors can also occur while modeling the evolution of temperature, since mantle convection is advection dominated. One numerical scheme designed to minimize such errors is the tracer ratio method, in which Lagrangian tracers are used to track each composition in the system in addition to carrying local temperature values that are time dependent. However, tracer spacing may become very uneven during evolution, which can contribute to errors in mass and energy conservation. In this study, a tracer repositioning algorithm designed to promote even tracer coverage is presented and tested using over 400 calculations in a large thermal Rayleigh number/buoyancy ratio parameter space. In particular, the effect of tracer repositioning on mass and energy conservation errors is examined. In most cases, we find that energy errors are roughly an order of magnitude less than mass errors, regardless of tracer repositioning. However, in situations with substantial entrainment of compositionally distinct material, mass errors can be reduced by up to an order of magnitude if tracers are repositioned during model evolution. We also find that for a fixed buoyancy ratio, entrainment of basal material decreases as the thermal Rayleigh number increases.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".