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Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell

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Omri Gat, Baruch Meerson, Arkady Vilenkin

Fluid Dynamics · Submitted 13 May 2006

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

The authors' main claim We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory.

how it is stated · asserted 1.00 read the record →

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arXiv IDphysics/0605112 (version 1)
Pith IDOLPDXAMO, Pith's permanent record of this paper and its review
CitationArkady Vilenkin, Baruch Meerson, Omri Gat. "Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell." arXiv:physics/0605112 (2006). https://pith.science/paper/OLPDXAMO
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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, 4,138 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t=0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory. We solve this inverse problem analytically for an almost flat wedge, and numerically otherwise. The wedge solution is useful for analysis of pinch-off singularities.

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 Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t=0, a wedge shape. background 0.88 0.12 0.03 asserted 0.76
s1 As a wedge is scale-free, the fluid relaxation dynamics are self-similar. background 0.68 0.17 0.19 asserted 1.00
s2 We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory. result 0.81 0.96 0.59 asserted 1.00
s3 We solve this inverse problem analytically for an almost flat wedge, and numerically otherwise. method 0.84 0.96 0.10 asserted 1.00
s4 The wedge solution is useful for analysis of pinch-off singularities. interpretation 0.97 0.51 0.13 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.92.

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  • T body sentences
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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

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t=0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory. We solve this inverse problem analytically for an almost flat wedge, and numerically otherwise. The wedge solution is useful for analysis of pinch-off singularities.

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