Bibliographic record
Abstract
A bimolecular elementary reaction requires that the two reactants meet. In solution, molecules are constantly bumping into other molecules, with the net effect that they wander randomly through the solution, which we call diffusion. In this chapter, we will study diffusion and its effect on chemical reactions, specifically focusing on the rate at which molecules meet each other. This will give us an upper bound on the reaction rate, which is useful for a number of purposes. Diffusion A molecule in solution is constantly surrounded by other molecules. All the molecules are constantly bumping into their neighbors. They move around the solution by sliding between their neighbors, much as you might slide between people tomake your way around a crowded room. This process is a form of diffusion , the random motion of molecules in space. The central quantity in describing diffusion is the flux , which is the rate at which molecules cross an imaginary surface in space per unit area of this surface. The flux therefore has units of number per unit time per unit area (e.g. mol s -1 m -2 ). We're going to focus on diffusion in one dimension, where it's a little easier to picture what is going on. Imagine that we have a tube of cross-sectional area A . The tube is narrow enough that we can treat the concentration across the tube as being constant.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.012 | 0.006 |
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".