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Wrinkling of an elastic sheet floating on a liquid sphere

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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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Peter Bella, Carlos Román

Analysis of PDEs · Submitted 27 Jun 2023

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

The authors' main claim The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds.

how it is stated · asserted 1.00 read the record →

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arXiv ID2306.15504 (version 3)
Pith IDGNQH7FFV, Pith's permanent record of this paper and its review
CitationCarlos Rom\'an, Peter Bella. "Wrinkling of an elastic sheet floating on a liquid sphere." arXiv:2306.15504 (2023). https://pith.science/paper/GNQH7FFV
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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, 5,550 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.29 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. This generalizes the previous work [P. Bella and R.V. Kohn. Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate.

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 A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. background 0.98 0.27 0.10 asserted 1.00
s1 We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. method 0.98 0.91 0.05 asserted 0.97
s2 Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. method 0.79 0.94 0.09 asserted 1.00
s3 The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. method 0.44 0.92 0.19 asserted 1.00
s4 This generalizes the previous work [P. Bella and R.V. Kohn. contribution 0.62 0.39 0.03 asserted 0.80
s5 Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. background 0.95 0.04 0.03 unclear 0.88
s6 A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate. contribution 0.78 0.54 0.09 asserted 0.91

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. This generalizes the previous work [P. Bella and R.V. Kohn. Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate.

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