Feasibility of streamline upwind Petrov-Galerkin angular stabilization of the linear Boltzmann transport equation with magnetic fields
Bibliographic record
Abstract
To accurately model dose in a magnetic field, the Lorentz force must be included in the traditional linear Boltzmann transport equation (LBTE). Both angular and spatial stabilization are required to deterministically solve this equation. In this work, a streamline upwind Petrov-Galerkin (SUPG) method is applied to achieve angular stabilization of the LBTE with magnetic fields. The spectral radius of the angular SUPG method is evaluated using a Fourier analysis method to characterize the convergence properties. Simulations are then performed on homogeneous phantoms and two heterogeneous slab geometry phantoms containing water, bone, lung/air and water for 0.5 T parallel and 1.5 T perpendicular magnetic field configurations. Fourier analysis determined that the spectral radius of the SUPG scheme is unaffected by magnetic field strength and the SUPG free parameter, indicating that the Gauss-Seidel source iteration method is unconditionally stable and the convergence rate is not degraded with increasing magnetic field strength. 100% of simulation points passed a 3D gamma analysis at a 2%/2 mm (3%/3 mm) gamma criterion for both magnetic field configurations in the homogeneous phantom study, with the exception of the 1.5 T perpendicular magnetic field in the pure lung phantom where a 77.4% (87.0%) pass rate was achieved. Simulations in the lung slab geometry phantom resulted in 100% of points passing a 2%/2 mm gamma analysis in a 0.5 T parallel magnetic field, and 97.7% (98.8%) of points passing a 2%/2 mm (3%/3 mm) gamma criterion in a 1.5 T perpendicular magnetic field. For the air slab geometry phantom, 72.1% (79.2%) of points passed a 2%/2 mm gamma criterion in a 0.5 T parallel magnetic field and 90.3% (92.8%) passed the same gamma criterion in a 1.5 T perpendicular magnetic field. While the novel SUPG angular stabilization method shows feasibility in some cases, it was found that the accuracy of this method was degraded for very low density media such as air.
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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 | 0.002 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".