Constructing tubular networks that occupy arbitrary regions in ℝ<sup>3</sup>
Bibliographic record
Abstract
Advances in additive manufacturing have enabled industry to relax many design constraints imposed by traditional construction methods. As such, it is now possible to design and build objects or devices with complex internal structures that conform to irregular external envelopes. In applications where fluid distribution or storage is an integral part of a larger system, additive manufacturing technologies allow "left over space" in an overall device volume to now be effectively utilized. Herein we describe a general algorithmic framework for the construction of branched networks of tubes which occupy a specified, and possibly quite complicated, region D ⊂ 3 as fully as possible. Such networks can be important in a variety of industrial applications ranging from heat exchangers to storage vessels to fluid distribution networks. Depending on the specific application of interest, such a design problem can be extremely ill-posed: For a given region D , our algorithm can produce an enormous number of networks, which generally requires that a much smaller number of "best" networks be isolated by ranking the networks based upon some problem-dependent properties ( e.g. , heat transfer rate, minimal friction losses, volume fraction, etc.). Some simple examples are presented to illustrate the algorithm and its output with comments added to illustrate its potential utility in industrial applications.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".