Local fractal and multifractal characteristics of soil number-based particle size distributions
Bibliographic record
Abstract
【Objective】 The inner structures of soil particle size distribution(PSD) were judged thoroughly by quantitative methods to increase the accuracy of soil hydraulic parameters estimation from soil PSD functions.【Method】 Volume-based PSD data of four loess soils including Hongjiao soil,Lou soil,Heilu soil and Sand loess were measured by laser diffractometry and used to determine soil number-based PSD.The power law domain of particles size and the corresponding fractal dimensions were defined.Multifractal calculations were conducted within the particle range that followed the power law and the multifractal parameters were obtained.【Result】 The fractal analysis showed that the lower particle limits of the power law domain for the four soils were close to 0.5 μm,while the upper limits differed a lot for different soils.The calculated fractal dimensions ranged from 2.17 to 3.43.From the multifractal analysis,the generalized dimension,Dq value of Hongjiao soil had the most obvious variations along regions of q and indicated stronger heterogeneous distribution of number-based PSD.The curves of τ(q)-q for all 4 soils were concave downwards and quite different from straight lines,indicating the number-based PSD of all 4 soils had multifractal distributions.Widths of f(α) spectra for Hongjiao soil,Lou soil,Heilu soil and Sand loess were 4.30,1.96,1.74 and 1.25,respectively.The asymmetric coefficients of the spectra were-0.924,0.516,0.141 and 0.490,respectively,indicating that the multifractal structures of Hongjiao soil were more complicated than the other soils,its asymmeric extent was also the largest.【Conclusion】 Multifractal theory can depict number-based soil particle size distributions more in detail.Combining fractal with multifractal theory can understand the inner structures of soil PSD more comprehensively.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 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) | 0.001 | 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".