Theoretical fractional formulation of a three-dimensional radio frequency ion trap (Paul-trap) for optimum mass separation
Bibliographic record
Abstract
We investigate the dynamics of an ion confined in a Paul-trap supplied by a fractional periodic impulsional potential. The Cantor-type cylindrical coordinate method is a powerful tool to convert differential equations on Cantor sets from cantorian-coordinate systems to Cantor-type cylindrical coordinate systems. By applying this method to the classical Laplace equation, a fractional Laplace equation in the Cantor-type cylindrical coordinate is obtained. The fractional Laplace equation is solved in the Cantor-type cylindrical coordinate, then the ions is modelled and studied for confined ions inside a Paul-trap characterized by a fractional potential. In addition, the effect of the fractional parameter on the stability regions, ion trajectories, phase space, maximum trapping voltage, spacing between two signals and fractional resolution is investigated and discussed.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".