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Record W2038132635 · doi:10.1103/physreve.63.041116

Branching and annihilating Lévy flights

2001· article· en· W2038132635 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenuePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2001
Typearticle
Languageen
FieldMathematics
TopicStochastic processes and statistical mechanics
Canadian institutionsSimon Fraser University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsRenormalization groupSigmaPhysicsUniversality (dynamical systems)Critical exponentCritical dimensionStatistical physicsBranching (polymer chemistry)Branching processMathematical physicsMonte Carlo methodPhase transitionMathematicsQuantum mechanicsStatistics

Abstract

fetched live from OpenAlex

We consider a system of particles undergoing the branching and annihilating reactions $\stackrel{\ensuremath{\rightarrow}}{A}(m+1)A$ and $A+\stackrel{\ensuremath{\rightarrow}}{A}\ensuremath{\emptyset},$ with m even. The particles move via long-range L\'evy flights, where the probability of moving a distance r decays as ${r}^{\ensuremath{-}d\ensuremath{-}\ensuremath{\sigma}}.$ We analyze this system of branching and annihilating L\'evy flights using field theoretic renormalization group techniques close to the upper critical dimension ${d}_{c}=\ensuremath{\sigma}$ with $\ensuremath{\sigma}<2.$ These results are then compared with Monte Carlo simulations in $d=1.$ For $\ensuremath{\sigma}$ close to unity in $d=1,$ the critical point for the transition from an absorbing to an active phase occurs at zero branching. However, for $\ensuremath{\sigma}$ bigger than about $3/2$ in $d=1,$ the critical branching rate moves away from zero with increasing $\ensuremath{\sigma},$ and the transition lies in a different universality class, inaccessible to controlled perturbative expansions. We measure the exponents in both universality classes and examine their behavior as a function of $\ensuremath{\sigma}.$

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.877
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.025
GPT teacher head0.361
Teacher spread0.336 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it