Jump Conditions for Hyperbolic Systems of Forced Conservation Laws with an Application to Gravity Currents
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Weak solutions to systems of nonlinear hyperbolic conservation laws admit discontinuities that result from either an initial value or as part of the temporally developing solution itself. The propagation of such shocks or jumps is affected by forcing terms for the nonlinear system in a way that has not been investigated fully in standard references. Jump conditions for systems of conservation laws with discontinuous forcing terms are derived herein, following the method used to derive the Rankine–Hugoniot jump conditions, and the generalized results are illustrated for the one‐dimensional inviscid Burger's equation with discontinuous forcing. The main application of this type of jump condition, and the primary motivation for its study, is its application to a shallow‐water model of gravity currents previously described by the authors. Specifically, a new result relation between the front and height at a gravity current front is obtained by using the existing model. Front speeds for gravity currents resulting from instantaneous release are calculated numerically and used to determine the suitability of the jump conditions, which are then compared with existing theoretical expressions and experimental observations. New numerical results are portrayed for the gravity current model, suggesting that the standard method of modeling shallow‐water gravity currents with a simple Froude number front condition may tend to suppress some of the finer details of the flow resolved by the numerical scheme used by the authors.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 it