Laminar flow velocity profile measurement from magnetic resonance spin echoes at incomplete polarization
Bibliographic record
Abstract
Laminar flow velocity profiles are directly related to the rheological properties of the flowing fluids. Magnetic resonance spin echo measurements at complete polarization, with a flow-oriented magnetic field gradient, can be utilized to determine the velocity profile of laminar flow in a circular pipe. However, fluids with a long spin-lattice relaxation time will not have time to completely polarize before signal acquisition in typical applications. This will restrict applications of the method, and modification of the original methodology is required to work with the general case of incomplete polarization. In this paper, magnetic resonance spin echo measurements at incomplete polarization with a flow-oriented magnetic field gradient are employed to determine the velocity profile of laminar flow in a circular pipe. The governing equations describing phase shifts and magnitude changes of odd echoes for laminar flows were derived, at incomplete polarization, based on the flow behavior index, an effective polarization length, spin-lattice relaxation time, and the average velocity. The objective function for least squares minimization was constructed, based on the first odd echo phase shifts and magnitude changes at different echo times, to solve for the flow behavior index and average velocity. The Nelder–Mead algorithm was employed to minimize the objective function. Discrete simulations for three kinds of laminar flows in a circular pipe, that is, shear-thickening flow, Poiseuille flow, and shear-shinning flow, were employed to validate the proposed method. Magnetic resonance experiments for Poiseuille flow were undertaken for further verification.
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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 | 0.000 | 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) | 0.001 | 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 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".