PDE Backstepping Boundary Observer Design for Microfluidic Systems
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Bibliographic record
Abstract
In this brief, we explore the use of conformal mapping theory to reduce the complexity in PDE backstepping boundary observer design. The technique is applied to a genetic analysis microchip that features a collocated sensor-actuator architecture in which the temperature of the reaction chamber is the spatially distributed control variable. The size and structure of the microchip do not allow for sensor placement within the reaction chamber, making temperature estimation mandatory. The PDE backstepping boundary observer design is chosen to provide real-time data from the temperature inside the microchip. The standard PDE backstepping boundary observer design results in a partial differential equation for the kernel function with double the spatial dimension of the original problem, which makes the design intractable for the problems with dimensions higher than one. We show that the spatial domain of the original problem can be reduced with the use of the conformal mapping. The resulting observer is tested and experimentally validated, shown excellent performance with respect to the spacial L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> norm of the estimation error.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 | 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 it