Discrete-time modeling and analysis of a class of linear thermodynamic distributed parameter systems
Bibliographic record
Abstract
Significant contributions have been made in continuous-time thermodynamic modeling, analysis, control, and estimation of distributed parameter systems. Compared with continuous-time works, research on discrete-time approaches is relatively limited. This contribution studies discrete-time modeling and analysis of a class of linear thermodynamic distributed parameter systems described by coupled hyperbolic partial differential equations (PDE) that can describe various applications in practice. Based on the Cayley-Tustin time discretization approach, the continuous-time infinite-dimensional model is converted to a discrete-time infinite dimensional model, where no spatial discretization or model order reduction is performed. We show that under this transformation, an approximation of the total internal entropy production is preserved, and the difference between the supply rates of the continuous- and discrete-time systems converges to zero as the time discretization interval tends to zero. Finally, the proposed analysis is illustrated through a counter-current heat exchanger with two state variables.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".