Ionospheric Gravity Wave Interactions and Their Representation in Terms of Stochastic Partial Differential Equations
Bibliographic record
Abstract
Phenomena in nature that involve diffusion and convection of matter and propagation of waves, e.g., the propagation of waves in geophysical flows, can exhibit randomness properties and thus need to be modeled by stochastic partial differential equations (SPDEs). For example in the ionosphere, the region in the upper atmosphere where there are high concentrations of ions and electrons, wave interactions are influenced by electromagnetic forces that fluctuate randomly in time, and are thus modeled by SPDEs. In this thesis we model interactions between atmospheric waves and the ionosphere induced by upward propagating atmospheric gravity waves (AGWs) starting with the equations of conservation of mass, momentum and energy, and Maxwell's equations. Two important problems are examined: the problem in which the ionosphere is treated as a deterministic medium and the wave interactions are governed by nonlinear partial differential equations (PDEs), and the problem in which the ionosphere is a random medium and the governing equations are nonlinear stochastic partial differential equation (SPDEs) driven by the Brownian motion. In the stochastic case we make use of numerical methods based on Wiener Chaos expansions (WCE) which are effective methods for solving SPDEs driven by Brownian motion. The accuracy of this method is accessed by comparing the results with the exact analytical or semi-analytical solutions for some problems involving stochastic evolution equations comprising the stochastic heat and stochastic advection-diffusion equations, and the stochastic Burgers' equation. In the the deterministic case, we derive analytical solutions for some special simplified configurations and then carry out numerical simulations for time-dependent nonlinear configurations. The results of the simulations of our analytical and numerical models are compared with the conclusions from previous studies which are mainly observations. Our results explain several observed phenomena arising from the interactions of the atmospheric gravity waves with the ionosphere.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".