First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps
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Bibliographic record
Abstract
We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated by two examples of cellular transport. The first is the intracellular process through which proteins transit from the cytosol to the interior of the nucleus through nuclear pore complexes that are distributed on the nuclear surface. The second is the problem of chemoreception, in which cells sense their surroundings through diffusive contact with receptors distributed on the cell exterior. Using a matched asymptotic analysis in terms of small absorbing pore radius, we derive and numerically verify a high order expansion for the capacitance of the structured target which incorporates surface effects and gives explicit information on interpore interaction through a Coulomb-type discrete energy with additional logarithmic dependencies. In the large $N$ dilute surface trap fraction limit, a single homogenized Robin boundary condition $ \partial_n v + \kappa v = 0$ is derived in which $\kappa$ depends on the total absorbing fraction, the characteristic pore scale, and parameters relating to interpore interactions.
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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 | 0.000 | 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 it