A new equation for the mean free path of air
Bibliographic record
Abstract
A recent rigorous methodology for determining the mean free path, k, of air at ambient conditions [Tsalikis, D. G., Mavrantzas, V. G., & Pratsinis, S. E. (2023).Physics of Fluids, 35, 097131] is extended to pressures, P, from 0.5 to 5 atm and temperatures, T, from 100 to 3000 K that are of environmental and industrial relevance, allowing to derive a new simple equation for k as a function of T and P.This entails molecular dynamics (MD) simulations of air accounting for the actual shape and force field of nitrogen and oxygen and analysis of the computed microcanonical ensemble of free paths to derive k at any P and T. Simulations are rigorously validated by comparing MD-predicted air densities, diffusivities and viscosities at various temperatures and pressures against experimental measurements, theoretical expressions and ab initio simulations.At all T and P, the MD-computed k are systematically smaller (at least 40%) than those from classic kinetic theory and its variants.The new equation for k is: kT, P 0:033916 T 1:23 P -1 and can be also expressed in terms of the standard Jennings' expression, k ffi ffi ffi ffi ffi ffi ffi ffi p=8 p l u 1 ffi ffi ffi ffi qP p [Jennings, S. G. (1998).Journal of Aerosol Science, 19( 2), 159-166], relating k to air viscosity, l, and density, q, using just a new value for its numerical factor u, u 0.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.000 | 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".