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The Construction of Zonal Models of Dispersion in Channels via Matched Centre Manifolds

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S.D. Watt (University of Melbourne), A.J. Roberts (University of Southern Queensland)

chao-dyn · Submitted 2 Dec 1994

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

The authors' main claim We expect the proposed principle of matched centre manifold evolution to be useful in a wide range of modelling problems.

how it is stated · hedged possibility 0.82 read the record →

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arXiv IDchao-dyn/9412002 (version 1)
Pith IDNAQOP2EP, Pith's permanent record of this paper and its review
CitationA.J. Roberts (University of Southern Queensland), S.D. Watt (University of Melbourne). "The Construction of Zonal Models of Dispersion in Channels via Matched Centre Manifolds." arXiv:chao-dyn/9412002 (1994). https://pith.science/paper/NAQOP2EP
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,726 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.64 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion via the new principle of matching their long-term evolution with that of the original problem. Using centre manifold techniques this is done straightforwardly and systematically. Furthermore, this approach provides correct initial and boundary conditions for the zonal models. We expect the proposed principle of matched centre manifold evolution to be useful in a wide range of modelling problems.

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 Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. background 1.00 0.04 0.03 asserted 1.00
s1 However, often we need multi-mode models to resolve finer details in space and time. gap 0.57 0.07 0.03 asserted 0.79
s2 Here we construct zonal models of dispersion via the new principle of matching their long-term evolution with that of the original problem. contribution 0.95 0.95 0.42 asserted 1.00
s3 Using centre manifold techniques this is done straightforwardly and systematically. method 0.99 0.81 0.07 asserted 1.00
s4 Furthermore, this approach provides correct initial and boundary conditions for the zonal models. result 0.52 0.85 0.15 asserted 1.00
s5 We expect the proposed principle of matched centre manifold evolution to be useful in a wide range of modelling problems. interpretation 0.56 0.19 0.37 hedged possibility 0.82

What kind of paper the classifier reports this is: method or tool 0.96 · evidence from proof or derivation 0.99.

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
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  • P abstract
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  • 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

Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion via the new principle of matching their long-term evolution with that of the original problem. Using centre manifold techniques this is done straightforwardly and systematically. Furthermore, this approach provides correct initial and boundary conditions for the zonal models. We expect the proposed principle of matched centre manifold evolution to be useful in a wide range of modelling problems.

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