Analytical resolution of the Poisson–Boltzmann equation for a cylindrical polyion immersed in an electrolyte solution: using the optimal linearization method
Bibliographic record
Abstract
By using the optimal linearization method (OLM), the potential of the electrical double layer created by a highly charged cylindrical polyion immersed in an electrolyte reservoir, which is represented by the so-called Poisson–Boltzmann equation (PBE), has been solved analytically under general potential conditions. For this system, three regions must be considered. The first one is in the near-neighborhood of the polyion and it is deprived of coions because of the repulsion phenomenon between the polyion and the coions, as proposed by Fuoss et al. (Proc. Natl. Acad. Sci. 37, 579 (1951). doi: 10.1073/pnas.37.9.579 ). For the second region, where the potential is slightly lower, we propose an OLM for solving the PBE. In the last region, where the potential is sufficiently low, the approximation of Debye–Hückel is adopted. This method allowed us to overcome some shortcomings in the analytical calculation of the electrostatic potential created by a polyion in an electrolyte solution.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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 | 0.001 |
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".