Transition to Chaos in Five-Dimensional Porous-Medium Thermal-Hydrodynamic Model with Low Prandtl Number
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Bibliographic record
Abstract
In this paper, we investigate the transition to a chaotic regime of thermal convection in a five-dimensional model with low Prandtl number in a porous medium. The mathematical formulation of the model includes the heat equation coupled with the equations of motion under the Boussinesq–Darcy approximation. A system of five ordinary differential equations is derived using a spectral method. This system is solved numerically by using the fourth-order Runge–Kutta method. The results show that from a subcritical value of the Rayleigh number, a transition from steady convection to chaos via a Hopf bifurcation produces a limit cycle which can be associated with a homoclinic explosion. Furthermore, we find that for certain values of Rayleigh number and shape parameter which measures the ratio between the dimensions of the computational domain, the transition from periodic oscillatory convection to chaotic convection can occur via a period-doubling.
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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 | 0.001 |
| 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)
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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