A Mathematical Model of Sap Exudation in Maple Trees Governed by Ice Melting, Gas Dissolution, and Osmosis
Bibliographic record
Abstract
We develop a mathematical model for sap exudation in a maple tree that is based on a purely physical mechanism for internal pressure generation in trees in the leafless state. There has been a long-standing controversy in the tree physiology literature over precisely what mechanism drives sap exudation, and we aim to cast light on this issue. Our model is based on the work of Milburn and O'Malley [Can. J. Bot., 62 (1984), pp. 2101--2106], who hypothesized that elevated sap pressures derive from compressed gas that is trapped within certain wood cells and subsequently released when frozen sap thaws in the spring. We also incorporate the extension of Tyree [in Tree Sap, M. Terazawa, C. A. McLeod, and Y. Tamai, eds., Hokkaido University Press, Sapporo, Japan, 1995, pp. 37--45], who argued that gas bubbles are prevented from dissolving because of osmotic pressure that derives from differences in sap sugar concentrations and the selective permeability of cell walls. We derive a system of differential-algebraic equations based on conservation principles that is used to test the validity of the Milburn--O'Malley hypothesis and also to determine the extent to which osmosis is required. This work represents the first attempt to derive a detailed mathematical model of sap exudation at the microscale.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".