Exponential Stability of Maxwell’s Equations
Bibliographic record
Abstract
The control of electromagnetic systems, which is governed by Maxwell's equations, is of interest for various reasons such as controlling plasma in a nuclear fusion reactor or magnetically trapping antiparticles for observation. Proving that a controlled system is exponentially stable is of particular interest, as exponential stability infers that the system will converge asymptotically to a steady state solution. A tool called the multiplier method is considered, which allows for exponential stability to be demonstrated by defining an auxiliary functional and proving it is bounded by the system energy and the energy's time derivative in a particular way. If an appropriate bound is shown, exponential stability is not only guaranteed, but the exponential function which bounds the L2 norm of the system variables will be fully determined in terms of the systems parameters. Currently, there is ongoing work into generalizing the multiplier method approach for a class of problems known as Port-Hamiltonian systems. This thesis aims to contribute to this work by formulating Maxwell's equations as a Port-Hamiltonian system, and using this formulation as a basis for determining how to choose the auxiliary functional needed in the multiplier method.
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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 | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 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".