Spectral Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems (12w5073) Paul Binding (University of Calgary),
Bibliographic record
Abstract
Linearised stability analysis of stationary and periodic solutions of both finite and infinite dimensional dynam-ical systems is a central issue in many (physical) applications. Such systems usually depend on parameters, so an important question is what happens to stability when the parameters are varied. This implies that one has to study the spectrum of a linear operator and its dependence on parameters. Moreover, systems arising in physics and other applications often possess special structure, for example Hamiltonian systems. Therefore spectrum and Jordan structure no longer suffice to characterize equivalent systems (under smooth coordinate transformations) but additional invariants are needed. Identifying and interpreting these in infinite dimen-sional systems seems more involved than in finite dimensional situations. For example, one may consider the symplectic or Krein signature for imaginary eigenvalues in linear finite dimensional Hamiltonian systems. When such eigenvalues meet as the parameters vary, the existence of additional invariants causes non-generic behaviour. In particular, a collision of eigenvalues on the imaginary axis may have dynamical consequences since the stability may change, depending on the additional invariants. At such a collision the boundary of the so called stability domain in parameter space may have singularities. This phenomenon occurs in nu-merous applications and it may have various physical consequences and interpretations. On the other hand stability questions can also be studied by index theory (Morse index, Maslov index). These approaches are
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.019 | 0.006 |
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".