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Frozen spatial chaos induced by boundaries

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Victor M. Eguiluz, Emilio Hernandez-Garcia, Oreste Piro, Salvador Balle (Instituto Mediterraneo de Estudios Avanzados IMEDEA, Mallorca (Spain))

chao-dyn · Submitted 9 Jun 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics.

how it is stated · asserted 0.73 read the record →

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arXiv IDchao-dyn/9906014 (version 1)
Pith IDCSAIJOCI, Pith's permanent record of this paper and its review
CitationEmilio Hernandez-Garcia, Mallorca (Spain)), Oreste Piro, Salvador Balle (Instituto Mediterraneo de Estudios Avanzados IMEDEA, Victor M. Eguiluz. "Frozen spatial chaos induced by boundaries." arXiv:chao-dyn/9906014 (1999). https://pith.science/paper/CSAIJOCI
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,940 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. result 0.79 0.94 0.92 asserted 0.73
s1 We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. method 0.68 0.88 0.05 asserted 0.98
s2 Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures. method 1.00 0.62 0.05 asserted 0.96

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from simulation or computation 0.68.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.

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