Effects of Anisotropy in Tridimensional Diffusion: Flow Patterns and Transport Efficiency
Bibliographic record
Abstract
Modeling diffusive processes via a constant effective diffusivity value taken to represent realistic uncertainty or heterogeneity is entrenched in scientific and engineering applications. This brings forth the question, to what extent does the flow pattern changes when symmetry is broken by anisotropy. This study supplies the answer by deriving a class of tridimensional solutions to the steady nonlinear diffusion equation in a spherical domain divided into an arbitrary number of meridian sectors with distinct diffusivities and generation rates. The new family of solutions permits flexible modeling, where traditionally only isotropic radial transport was considered. The flow patterns support an extensive variety of topological terrain via tesseral and sectoral harmonics. The anisotropy gives rise to an unconventional type of a fixed point combining both node and saddle attributes. The contours are nonsmooth on the contiguity planes between sectors and might or might not be localized in the polar angle and/or azimuthal angle , implying a particle might remain confined to a relatively small neighborhood or meander over the sphere. The impact on motion trajectories and thus transport efficiency implies that the energy required to sustain a steady flow is starkly underestimated when symmetry is assumed for simplicity despite the presence of anisotropy.
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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) | 0.000 | 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".