High Energy Astrophysical Phenomena · arXiv:1006.2663 v1 · submitted 14 Jun 2010
The relativistic kinetic dispersion relation: Comparison of the relativistic Bhatnagar-Gross-Krook model and Grad's 14-moment expansion
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“Thus, our calculation indicates that keeping these second-order terms does not simply correspond to improving the physical description of the relativistic hydrodynamics.”
from the abstract · picked out as the main claim by a classifier
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Abstract
In this paper, we study the Cauchy problem of the linearized kinetic equations for the models of Marle and Anderson-Witting, and compare these dispersion relations with the 14-moment theory. First, we propose a modification of the Marle model to improve the resultant transport coefficients in accord with those obtained by the full Boltzmann equation. Using the modified Marle model and Anderson-Witting model, we calculate dispersion relations that are kinetically correct within the validity of the BGK approximation. The 14-moment theory that includes the time derivative of dissipation currents has causal structure, in contrast to the acausal first-order Chapman-Enskog approximation. However, the dispersion relation of the 14-moment theory does not accurately describe the result of the kinetic equation. Thus, our calculation indicates that keeping these second-order terms does not simply correspond to improving the physical description of the relativistic hydrodynamics.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: hedged possibility 0.92
What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.69 · human participants 0.01 · controlled comparison 0.27 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.96 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| In this paper, we study the Cauchy problem of the linearized kinetic equations for the models of Marle and Anderson-Witting, and compare these dispersion relations with the 14-moment theory. | contribution 0.97 | 0.86 | 0.05 | asserted 0.87 |
| First, we propose a modification of the Marle model to improve the resultant transport coefficients in accord with those obtained by the full Boltzmann equation. | contribution 0.81 | 0.93 | 0.04 | asserted 0.97 |
| Using the modified Marle model and Anderson-Witting model, we calculate dispersion relations that are kinetically correct within the validity of the BGK approximation. | method 0.65 | 0.95 | 0.08 | asserted 1.00 |
| The 14-moment theory that includes the time derivative of dissipation currents has causal structure, in contrast to the acausal first-order Chapman-Enskog approximation. | background 0.90 | 0.12 | 0.08 | asserted 1.00 |
| However, the dispersion relation of the 14-moment theory does not accurately describe the result of the kinetic equation. | result 0.95 | 0.58 | 0.24 | asserted 1.00 |
| Thus, our calculation indicates that keeping these second-order terms does not simply correspond to improving the physical description of the relativistic hydrodynamics. | interpretation 0.99 | 0.91 | 0.76 | hedged possibility 0.92 |
What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.84
What was examined, and what was not
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- figures and tables
- references and citing sentences
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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, 4,983 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
How the literature uses it
4 arXiv papers cite this in 6 sentences
Papers citing it · 5 sentences without a confident label
Contests it 1 paper
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Recently turned out that the original Israel-Stewart theory [ref] does not reproduce the results of the kinetic equation quantitatively [ref] .
Temperature dependence of transport coefficients of QCD in high-energy heavy-ion collisions · Relativistic viscous hydrodynamic equation and algorithm · contest 0.77
What it cites · 2 sentences without a confident label
Compares with 1 paper
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However, our results of nonrelativistic case ($ζ= 100$) reproduce the dispersion relation of nonrelativistic BGK [ref] that agrees with experimental data [ref] even in short-wavelength regime.
Analysis of the Relaxation Process using Non-Relativistic Kinetic Equation · MARLE MODEL · 0.94
Cites as background 1 paper
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Recently, a new approach to relativistic dissipative fluid equation has been shown by Tsumura, Kunihiro, and Ohnishi [ref] .
Second-order Relativistic Hydrodynamic Equations for Viscous Systems; how does the dissipation affect the internal energy? · INTRODUCTION · 0.84
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