arXiv 0806.37252008-06cond-mat.stat-mechhep-thnucl-th

Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics

T. Koide, T. Kodama

备注：: 15 pages, no figure. Discussions are added in the concluding remarks. Accepted for publication in Phys. Rev. E
发表信息：: Phys.Rev.E78:051107,2008
DOI：: 10.1103/PhysRevE.78.051107

英文摘要：

A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Shock propagation and stability in causal dissipative hydrodynamics

We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by introducing an additional viscosity which is related to the coarse-graining scale of the theory.

2008-05-12cond-mat.stat-mechhep-phnucl-th

Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory

We present a new formalism for the theory of relativistic dissipative hydrodynamics. Here, we look for the minimal structure of such a theory which satisfies the covariance and causality by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). It can readily be applied to the full three-dimensional hydrodynamical calculations. We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.

2007-03-22cond-mat.stat-mechhep-phnucl-th

Shear viscosity coefficient and relaxation time of causal dissipative hydrodynamics in QCD

The shear viscosity coefficient and the corresponding relaxation time for causal dissipative hydrodynamics are calculated based on the microscopic formula proposed in [T. Koide and T. Kodama, Phys. Rev. \textbf{E 78}, 051107 (2008)]. Here, the exact formula is transformed into a more compact form and applied it to evaluate these transport coefficients in the chiral perturbation theory and perturbative QCD. It is shown that in the leading order calculation, the causal shear viscosity coefficient $η$ reduces to that of the ordinary Green-Kubo-Nakano formula, and the relaxation time $τ_π$ is rela…

2009-06-30cond-mat.stat-mechhep-phhep-th

Extensivity of Irreversible Current and Stability in Causal Dissipative Hydrodynamics

We extended our formulation of causal dissipative hydrodynamics [T. Koide \textit{et al.}, Phys. Rev. \textbf{C75}, 034909 (2007)] to be applicable to the ultra-relativistic regime by considering the extensiveness of irreversible currents. The new equation has a non-linear term which suppresses the effect of viscosity. We found that such a term is necessary to guarantee the positive definiteness of the inertia term and stabilize numerical calculations in ultra-relativistic initial conditions. Because of the suppression of the viscosity, the behavior of the fluid is more close to that of the id…

2009-01-26cond-mat.stat-mechhep-phnucl-th

Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics

The microscopic formulae of the bulk viscosity $ζ$ and the corresponding relaxation time $τ_Π$ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition and $τ_Π$ and $ζ$ are related as $τ_Π=ζ/[β\{(1/3-c_{s}^{2})(ε+P)-2(ε-3P)/9\}]$, where $ε$, $P$ and $c_{s}$ are the ene…

2010-10-21cond-mat.stat-mechhep-phnucl-th

Shear viscosity, Bulk viscosity and Relaxation Times of Causal Dissipative Relativistic Fluid-Dynamics at Finite Temperature and Chemical Potential

The microscopic formulas for the shear viscosity $η$, the bulk viscosity $ζ$, and the corresponding relaxation times $τ_π$ and $τ_Π$ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potential by using the projection operator method. The non-triviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition for the bulk viscous pressure.We show that, when the operator definition for the bulk viscous pressure $Π$ is appropriately chosen, the leading-order result of the ratio, $ζ$ over $τ_Π$, coinc…

2012-08-09cond-mat.stat-mechhep-phhep-th

更多相关论文收起更多论文

Kernel/Metric Correspondence of Dissipative Systems in Information Theory

We study the kernel/metric correspondence pointed out in our previous work in a dissipative system which is accompanying fractional Brownian motion. We also give some comments on information causality.

2016-09-10cond-mat.stat-mech

Non-Newtonian Properties of Relativistic Fluids

We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the ne…

2010-09-23cond-mat.stat-mechhep-phnucl-th

The causality and stability of relativistic spin-hydrodynamics

We study the causality and stability of relativistic hydrodynamics with the inclusion of the spin degree of freedom as a hydrodynamic field. We consider two specific models of spin-hydrodynamics for this purpose. A linear mode analysis for static background shows that a first-order dissipative spin-hydrodynamics remains acausal and admits instabilities. Besides, it is found that the inclusion of the spin field in hydrodynamics leads to new kinds of linear modes in the system. These new modes also exhibit instability and acausal behavior. The second model of the spin-hydrodynamics that we have …

2023-03-24cond-mat.stat-mechhep-phhep-th

Emergence of extended Newtonian gravity from thermodynamics

Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to …

2021-11-09astro-ph.GAcond-mat.stat-mechgr-qc

Large-scale structure from superdiffusion in a driven dissipative system

A system far from equilibrium is characterized by unconventional many-body dynamical effects, which can lead to anomalous density fluctuations and mass transport. Interestingly, these structural and dynamic features often emerge simultaneously in driven dissipative systems. Here we seek an origin of their co-existence by numerical simulations of a two-dimensional driven granular gas. We reveal a causal link between superdiffusive transport and giant density fluctuations. The kinetic dissipation upon particle collisions depends on the relative velocity of colliding particles, and is responsible…

2010-03-08cond-mat.stat-mech

A fluid particle model

We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of a dissipative particle dynamics algorithm that incorporates shear forces between dissipative particles. The inclusion of these non-central shear forces requires the consideration of angular velocities of the dissipative particles in order to comply with the conservation of angular momentum. It is shown that the equilibrium statistical mechanics requirement …

1997-09-02cond-mat.softcond-mat.stat-mech

受限Riesz气体：从牛顿动力学到涌现流体动力学

Confined Riesz gas: From Newtonian Dynamics to Emergent Hydrodynamics

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）

本研究通过大规模牛顿模拟与基于密度、速度、温度三场构建的流体动力学框架相结合，定量验证了受限Riesz气体从微观到宏观演化的对应关系，并证明该涌现流体动力学描述在较宽的输运系数窗口内具有鲁棒性，为幂律相互作用系统建立了牛顿动力学与连续介质理论之间的桥梁。

2026-10-06cond-mat.stat-mech