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Flow through randomly curved manifolds

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M. Mendoza, S. Succi, H. J. Herrmann

Fluid Dynamics · Submitted 9 May 2012

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

The authors' main claim We have found that the relation between the flow through campylotic (generically curved) media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system exhibits two distinct functional expressions (hysteresis), depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall Ricci curvature.

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arXiv ID1205.1906 (version 2)
Pith IDAXUHWN6H, Pith's permanent record of this paper and its review
CitationH. J. Herrmann, M. Mendoza, S. Succi. "Flow through randomly curved manifolds." arXiv:1205.1906 (2012). https://pith.science/paper/AXUHWN6H
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,119 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.02 · states quantitative result 0.13 · compares with prior results 0.10 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We have found that the relation between the flow through campylotic (generically curved) media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system exhibits two distinct functional expressions (hysteresis), depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall Ricci curvature. Furthermore, the flow through such systems as a function of the number of curvature perturbations presents a sublinear behavior for large concentrations due to the interference between curvature perturbations that, consequently, produces a less curved space. For the purpose of this study, we have developed and validated a lattice kinetic model capable of describing fluid flow in arbitrarily curved manifolds, which allows to deal with highly complex spaces in a very compact and efficient way.

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 have found that the relation between the flow through campylotic (generically curved) media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system exhibits two distinct functional expressions (hysteresis), depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall Ricci curvature. result 1.00 0.95 0.75 asserted 1.00
s1 Furthermore, the flow through such systems as a function of the number of curvature perturbations presents a sublinear behavior for large concentrations due to the interference between curvature perturbations that, consequently, produces a less curved space. result 0.99 0.87 0.19 asserted 1.00
s2 For the purpose of this study, we have developed and validated a lattice kinetic model capable of describing fluid flow in arbitrarily curved manifolds, which allows to deal with highly complex spaces in a very compact and efficient way. method 0.91 0.95 0.06 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.73 · evidence from simulation or computation 1.00.

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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 have found that the relation between the flow through campylotic (generically curved) media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system exhibits two distinct functional expressions (hysteresis), depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall Ricci curvature. Furthermore, the flow through such systems as a function of the number of curvature perturbations presents a sublinear behavior for large concentrations due to the interference between curvature perturbations that, consequently, produces a less curved space. For the purpose of this study, we have developed and validated a lattice kinetic model capable of describing fluid flow in arbitrarily curved manifolds, which allows to deal with highly complex spaces in a very compact and efficient way.

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