Mean first passage time of active Brownian particles in two dimensions
Bibliographic record
Abstract
Abstract The mean first passage time (MFPT) is a key metric for understanding transport, search, and escape processes in stochastic systems. While well characterized for passive Brownian particles, its behavior in active systems—such as active Brownian particles (ABPs)—remains less understood due to their self-propelled, nonequilibrium dynamics. In this paper, we formulate and analyze an elliptic partial differential equation (PDE) to characterize the MFPT of ABPs in two-dimensional domains, including circular, annular, and elliptical regions. For annular regions, we analyze the MFPT of ABPs under various boundary conditions. Our results reveal rich behaviors in the MFPT of ABPs that differ fundamentally from those of passive particles. Notably, the MFPT exhibits non-monotonic dependence on the initial position and orientation of the particle, with maxima often occurring away from the domain center. We also find that increasing swimming speed can either increase or decrease the MFPT depending on the geometry and initial orientation. Asymptotic analysis of the PDE in the weak-activity regime provides insight into how activity modifies escape statistics of the particles in different geometries. Finally, our numerical solutions of the PDE are validated against Monte Carlo simulations.
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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".