Analytical Solution of Heat Pulse Method in a Parallelepiped Sample Space with Inclined Needles
Bibliographic record
Abstract
The heat pulse method enables estimation of soil thermal diffusivity ( k ), volumetric heat capacity ( C ), thermal conductivity, and water content. The heater needle and temperature‐sensing needle may deflect during probe insertion into soils. The impact of needle deflection on estimates of C and k has not been fully studied theoretically or experimentally. We defined θ to be the polar angle of needle deviation from the z axis and φ to be the azimuthal angle in the x–y plane. Transient‐state analytical solutions were derived for an inclined and pulsed finite line source in a parallelepiped sample with zero surface temperature and adiabatic boundary conditions. For a heat pulse sensor with 6‐mm needle spacing and a heater needle of 4‐cm length in a given parallelepiped (5 by 5 by 5 cm, assumed to be filled with air‐dry sand), model errors in C and k were about −11.3 and 12.1%, respectively, for an inclined heater needle with θ = 1° and φ = 0°. Model errors in C and k were about −11.2 and 12.1%, respectively, for an inclined sensor needle with θ = 1° and φ = 180°. When −6 ≤ θ ≤ 6° for either the heater or the sensor needle, the temperature curves could be approximated rather well by a pulsed infinite line source model with a modified probe spacing that accounted for the inclination. For various heating durations and strengths, the errors in both k and C were relatively constant when all other parameters were fixed; however, the errors in both C and k decreased monotonically and slowly as k increased. The model errors in C and k were similar for four soil conditions with different thermal properties in the range −6 ≤ θ ≤ 2°.
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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 | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| 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 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".