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Toward a mathematical analysis for a model of suspension flowing down an inclined plane

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Kaname Matsue, Kyoko Tomoeda

Analysis of PDEs · Submitted 1 Sep 2017

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

The authors' main claim We present a method to find shock waves, rarefaction waves for the Riemann problem of this system.

how it is stated · asserted 1.00 read the record →

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arXiv ID1709.00409 (version 1)
Pith ID7JS53YPN, Pith's permanent record of this paper and its review
CitationKaname Matsue, Kyoko Tomoeda. "Toward a mathematical analysis for a model of suspension flowing down an inclined plane." arXiv:1709.00409 (2017). https://pith.science/paper/7JS53YPN
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,630 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows over the sediment [Murisic et al., J. Fluid. Mech. {\bf{717}}, 203--231 (2013)]. We present a method to find shock waves, rarefaction waves for the Riemann problem of this system. Our method is mainly based on [Smoller, Springer-Verlag, New York, second edition, (1994)].

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 consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows over the sediment [Murisic et al., J. Fluid. background 0.62 0.39 0.05 asserted 0.85
s1 Mech. {\bf{717}}, 203--231 (2013)]. background 0.99 0.04 0.02 unclear 0.96
s2 We present a method to find shock waves, rarefaction waves for the Riemann problem of this system. contribution 0.76 0.94 0.44 asserted 1.00
s3 Our method is mainly based on [Smoller, Springer-Verlag, New York, second edition, (1994)]. method 0.90 0.07 0.03 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.85 · evidence from proof or derivation 0.94.

What was examined, and what was not

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  • full text
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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
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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 consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows over the sediment [Murisic et al., J. Fluid. Mech. {\bf{717}}, 203--231 (2013)]. We present a method to find shock waves, rarefaction waves for the Riemann problem of this system. Our method is mainly based on [Smoller, Springer-Verlag, New York, second edition, (1994)].

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