Analytic Mathematical Model for Concentration Profile in a Parallel Plate Electrolyzer with Variable Current Density
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Bibliographic record
Abstract
The parallel plate electrolyzer is of interest in electrochemical applications. However, the modelling of an electrolyzer often involves numerical integration or use of infinite series that is computationally expensive. Using some simplifying assumptions, a novel analytical solution to the governing equation could be obtained using a similarity transformation. To obtain the solution, a mathematical limit evaluation is required rather than a simple substitution, resulting in a novel transcendental function that describes the constants of integration. However, the constants of integration could be excellently approximated by a rational function, with the coefficients obtainable by solving equations for special cases or linear regression. The quadratic and quartic regression were found to give a better fit. It is also demonstrated that the general solution reduces to constant current density and surface concentration under special cases. Using this approach, a simple mathematical model was developed to approximate the solutions that often require cumbersome numerical methods such as the finite element method.
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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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it