Bibliographic record
Abstract
A model that rapidly computes the secular evolution of a gravitating disk-planet system is developed. The disk is treated as a nested set of gravitating rings, with the rings'/planets' time evolution being governed by the classical Laplace-Lagrange solution for secular evolution but modified to account for the disk's finite thickness h . The Lagrange planetary equations for this system yield a particular class of spiral wave solutions, usually called apsidal density waves and nodal bending waves. There are two varieties of apsidal waves—long waves and short waves. Planets typically launch long density waves at the disk's nearer edge or else at a secular resonance in the disk, and these waves ultimately reflect downstream at a more distant disk edge or else at a Q barrier in the disk, whereupon they return as short density waves. Planets also launch nodal bending waves, and these have the interesting property that they can stall in the disk, that is, their group velocity plummets to zero upon approaching a region in the disk that is too thick to support further propagation of bending waves. The rings model is used to compute the secular evolution of a Kuiper Belt having a variety of masses, and it is shown that the early massive belt was very susceptible to the propagation of low-amplitude apsidal and nodal waves launched by the giant planets. For instance, these waves typically excited orbits to e ~ sin i ~ 0.01 in a primordial Kuiper Belt of mass M KB ~ 30 Earth masses. Although these orbital disturbances are quite small, the resulting fractional variations in the disk's surface density due to the short density waves is usually large, typically of order unity. This epoch of apsidal and nodal wave propagation probably lasted throughout the Kuiper Belt's first ~10 7 to ~5 × 10 8 yr, with the waves being shut off between the time when the large R ≳ 100 km Kuiper Belt objects first formed and when the belt was subsequently eroded and stirred up to its present configuration.
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.
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 | 0.000 |
| 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 | 0.000 |
| 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".