Asymptotic Analysis of Perturbations to Travelling Wave Solutions of Nonlinear Advection-Reaction-Diffusion Equations of Fisher Type
Bibliographic record
Abstract
In this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type.First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium solutions and plotting their trajectories in phase portraits.We then describe the derivation of some exact expressions for travelling wave solutions which had been obtained by previous researcher using other methods.We examine some situations where the exact travelling wave solutions are perturbed.First we perturb the initial condition and then derive approximate expressions for the perturbations.The goal of the thesis is to investigate the case where the constant speed of the background medium is perturbed by a smallamplitude spatially and temporally localized perturbation.This situation occurs in atmospheric fluid flows when atmospheric waves interact and cause localized perturbations in the background flow speed.The perturbations in the flow speed affect the propagation of chemical species in the atmosphere.The approximate asymptotic solutions derived here show that the form of the perturbation can be exponentially decaying or oscillatory and this depends on the spatial and temporal width of the background speed perturbation.iiiDedication I would like to dedicate my thesis to my mother and father, my sisters and brothers, and my husband and daughters (Jawaher, Rhahf and Ghina).They have always been my inspiration in my life and my motivation to achieve all that I have achieved.Without their support and love I would not be where I am today.I hope that someday my daughters will grow up and read this and realize the work and time that I spent during the most precious years of their lives in order to help bring prosperity to
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".