Biased random walks on a lattice: Exact numerical method to study the effect of alternating fields in disordered and asymmetric systems of obstacles
Bibliographic record
Abstract
The migration of a particle in a system of obstacles under the action of an external field is often modeled using lattice Monte Carlo algorithms. For example, such simulation methods have been used to study the electrophoresis of charged molecules in sieving gels and the separation of particles using ratchet systems. In the case of constant fields or low-frequency alternating fields, the Monte Carlo simulation method can be mapped onto a numerical or algebraic matrix problem that can be solved exactly. In this Rapid Communication, we generalize this matrix approach to treat periodic time-dependent fields. The evolution of the spatial distribution function during a period is computed using a sequence of transfer matrices, and a steady-state closure relation allows us to calculate the exact mean velocity of the particle during a complete cycle. As an example, we examine the properties of a simple spatially asymmetric ratchet system in the presence of periodic alternating fields (symmetric and asymmetric) as well as random telegraph signals.
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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 | 0.000 |
| 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".