Fabrication of Topologically Complex Three-Dimensional Microstructures: Metallic Microknots
Bibliographic record
Abstract
This paper describes a method for fabricating three-dimensional (3D) microstructures with complex topologies trefoil, figure eight, and cinquefoil knots, a chain with complex links, Borromean rings, a Möbius strip, and a torus. This method is based on the strategy of decomposing these structures into figures that can be printed on the surfaces of cylinders and planes that contact one another. Any knot can be considered as a pattern of crossings of lines, in which one line crosses “over” or “under” the second. We map these “over” and “under” crossings onto the surface of a cylinder and show that only two cylinders, in tangential contact (with axes parallel) and with lines allowed to cross from the surface of one to the surface of the second, are required to make any knot (or, in a combinatorial mathematical sense, any graph) in a topography that consists only of smooth curves. To form free-standing metal microstructures, we begin by printing appropriate patterns onto a continuous metal film on two cylinders using microcontact printing: these patterns are developed into patterns of exposed metal by etching or by covering with polymer. The cylinders are aligned (using a new procedure) with a slight separation between them. The metallic patterns on them are used as cathodes for electrodeposition, which strengthens the metal features and also welds them into a continuous structure. When electrodeposition and welding are complete, the cylindrical templates are dissolved, and the topologically complex, 3D, free-standing metallic structures are released.
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 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".