Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Ground-state ABCD reaction
Why this work is in the frame
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Bibliographic record
Abstract
In the presence of an external electric field, the ground-state \documentclass[12pt]{minimal}\begin{document}$A+B^q \rightleftharpoons C^q + D$\end{document}A+Bq⇌Cq+D diffusion-influenced reversible reaction for a geminate pair, a neutral and a charged particle, is investigated in three dimensions. The probability density functions, the rates of reactions, and the survival probabilities of individual particles are analytically derived in the Laplace domain in terms of series solutions. The long-time kinetics of probability density functions and rates of reactions in rescaled forms shows a kinetic transition behavior from a t−3/2 power law to a t−3/2et increase when the condition \documentclass[12pt]{minimal}\begin{document}$D_1F_1^2 \le D_2F_2^2$\end{document}D1F12≤D2F22, which depends on the diffusivities of particles and the external electric fields, changes to \documentclass[12pt]{minimal}\begin{document}$D_1F_1^2 > D_2F_2^2$\end{document}D1F12>D2F22. In the transition region \documentclass[12pt]{minimal}\begin{document}$D_1F_1^2 = D_2F_2^2$\end{document}D1F12=D2F22, the long-time behavior also shows a t−3/2 power law decay but with a different value of the prefactor. The rescaled survival probabilities only exhibit an exponentially increasing behavior at long times with no dependence on the various values of parameters.
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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 | 0.000 |
| 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