A Mean-Field Free-Energy Lattice Boltzmann Model for Liquid-Vapor Interfaces
Bibliographic record
Abstract
A nonlocal pressure equation is proposed for liquid-vapor interfaces based on mean-field theory. The new nonlocal pressure equation is shown to be a generalized form of the nonlocal pressure equation of the van der Waals theory or the “square-gradient theory”. The proposed nonlocal pressure is implemented in the mean-field free-energy lattice Boltzmann method (LBM) proposed by Zhang et al (2004). The modified LBM is applied to simulate equilibrium interface properties and the interface dynamics of capillary waves. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, and the dispersion relation between frequency and wave number describing the dynamics of capillary waves. It is shown that the modified LBM gives very good agreement with the theories. In addition, preliminary calculations of phase transition and binary droplet coalescence are also presented.
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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) | 0.000 | 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".