High Energy Physics - Theory · arXiv:1007.4302 v2 · submitted 25 Jul 2010
One-Dimensional Approximation of Viscous Flows
The paper says
“This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.”
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The paper
Abstract
Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: hedged possibility 0.97
What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.67 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. | background 1.00 | 0.25 | 0.06 | asserted 0.93 |
| In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. | contribution 0.67 | 0.97 | 0.12 | asserted 1.00 |
| This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence. | contribution 0.40 | 0.28 | 0.35 | hedged possibility 0.97 |
What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00
What was examined, and what was not
Sources read
- arXiv listing abstract v2
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- 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
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,079 input tokens, $0.0001 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 1 Pith paper
Reviewed papers on Pith that cite this one. The full citation record
- Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship hep-th · Jun 2010
How the literature uses it
2 arXiv papers cite this in 2 sentences
What it cites · 26 sentences without a confident label
Compares with 5 papers
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One sees from Eq. ([ref]) that the wavenumber of the onset of instability [$k_c>0$, $ω(k_c) = 0$] is given by $k_c = √(n)/r_0$, irrespective of the viscosity, which generalizes the result of the inviscid case [ref] and is similar to the dimensional dependence of Gregory-Laflamme instability [ref] .
High and Low Dimensions in The Black Hole Negative Mode · Instability of viscous flows · 0.95
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One sees from Eq. ([ref]) that the wavenumber of the onset of instability [$k_c>0$, $ω(k_c) = 0$] is given by $k_c = √(n)/r_0$, irrespective of the viscosity, which generalizes the result of the inviscid case [ref] and is similar to the dimensional dependence of Gregory-Laflamme instability [ref] .
On Black-Brane Instability In an Arbitrary Dimension · Instability of viscous flows · 0.95
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One sees from Eq. ([ref]) that the wavenumber of the onset of instability [$k_c>0$, $ω(k_c) = 0$] is given by $k_c = √(n)/r_0$, irrespective of the viscosity, which generalizes the result of the inviscid case [ref] and is similar to the dimensional dependence of Gregory-Laflamme instability [ref] .
Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings · Instability of viscous flows · 0.95
Cites as background 9 papers
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While in this paper we will focus on a non-relativistic and incompressible limit for simplicity, the generalizations to relativistic and compressible cases would be straightforward (but see, , [ref] for non-relativistic and incompressible fluids obtained via the fluid/gravity correspondence or the membrane paradigm).
The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity · Introduction · 0.88
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While in this paper we will focus on a non-relativistic and incompressible limit for simplicity, the generalizations to relativistic and compressible cases would be straightforward (but see, , [ref] for non-relativistic and incompressible fluids obtained via the fluid/gravity correspondence or the membrane paradigm).
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations · Introduction · 0.88
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While in this paper we will focus on a non-relativistic and incompressible limit for simplicity, the generalizations to relativistic and compressible cases would be straightforward (but see, , [ref] for non-relativistic and incompressible fluids obtained via the fluid/gravity correspondence or the membrane paradigm).
The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics · Introduction · 0.88
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