Bibliographic record
Abstract
The fundamental problem of turbulence is that of closing the infinite sequence of equations that result from the application of Reynolds averaging to the governing relations for momentum, heat and mass transfer.These equations model the moments of the turbulent probability density, PDF, such as the first, second, third, and higher order moments, each equation depending on higher order moments.The ability to relate the set of moments of order n to moments of n+1 would permit closure to a finite system of equations as we could truncate the sequence of equations.The concept of the Shannon entropy allows us to model the degree of uncertainty of a PDF.The Shannon entropy is related to the concept of thermodynamic entropy.The maximum entropy method determines the PDF that maximizes the entropy subject to a number of constraints.The most usual method is to use a finite number of lower order moments.A maximum entropy PDF is often used to approximate the shape of a PDF as the solution has desirable features such as being positive definite.The maximum entropy method is of great value as an approximation method in general.An examination of the behavior of the moments generate from a maximum entropy for a single degree of freedom fit to real, turbulent PDFs for velocity, skin-friction, and temperature fluctuations have been carried out to examine the methods ability predictive capability.In this examination experimentally determined data sets that contained data for all moments up to the sixth order were compiled from the literature.The maximum entropy method was applied using the first four moments.The fifth and sixth moments computed from the maximum entropy approximations were compared and found to compare very favorably with those measured.The presentation will start with a review of the maximum entropy method for a finite number of moments and a discussion of the computational
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".