Symmetry analysis of the 1+1 dimensional relativistic imperfect fluid dynamics
C Alexa, D Vrinceanu
讨论了二维相对论性非理想流体的流动。计算了能量动量张量守恒方程在超相对论极限下的对称群。得到了不可压缩流体的群不变解
The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the incompressible fluid are obtained
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This paper tries to obtain a simple picture of several aspects of the mode structure in relativistic non-equilibrium thermodynamics. Its pedagogical focus is on the relation between long-wavelength perturbation modes of the causal Müller-Israel-Stewart (MIS) theory and those of the traditional Eckart theory. Principally, this issue was clarified in a series of papers by Hiscock and Lindblom (see [8-10]). Here, I put together some essential features which do not require the entire formalism of the complete theory.
The Imperfect Fluid behind Kinetic Gravity Braiding
本文给出了具有动力学引力辫的非正则标量场理论的标准流体动力学描述。特别是，这一图景适用于最简单的伽利略和k-本质。流体变量不仅具有明确的物理意义，而且大大简化了系统的分析。流体携带的电荷对应于场空间的位移。该移位充电电流包含负责电荷扩散的空间部分。而且，在不可压缩极限下，运动方程变成标准扩散方程。流体确实是不完美的，因为能量既不沿着场梯度流动，也不沿着移位电流流动。流体的涡度为零，没有耗散：没有熵产生，能量动量完全守恒，温度为零，没有剪切粘度。然而，在理想流体周围的膨胀中，人们可以识别以体积粘度的方式校正压力的项。我们关闭制定的非平凡的条件，这个不完美的流体的热力学平衡。
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $ρ$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational principle. This leads to the Euler equation and the equation of continuity in reparametrization invariant form.
Oscillating Shock Profiles in Relativistic Fluid Dynamics
研究了具有粘性的相对纯辐射流体模型，发现冲击波的连续轮廓在任何变量下均振荡，与经典流体动力学中状态变量单调性不同。
Non-relativistic conformal symmetries in fluid mechanics
自由不可压缩流体的对称性跨越伽利略群，并伴随着空间和时间的独立膨胀。当流体是可压缩的，对称性被扩大到扩展的薛定谔群，这也涉及到，此外，薛定谔扩展。虽然不可压缩的流体动力学可以推导出一个适当的非相对论性限制的共形不变的相对论性理论，最近讨论的共形伽利略群，从相对论共形群收缩，是不是一个对称。这可以用非相对论极限的微妙之处来解释。
Relativistic particle, fluid and plasma mechanics coupled to gravity
在这篇介绍性的评论文章中，我们探讨了粒子运动的特殊相对论方程和爱因斯坦著名公式$E=mc^2$的推导。其次，我们研究了狭义相对论电磁场方程和带电粒子洛伦兹运动方程的推广。然后我们引入了作为对称二阶张量场的狭义相对论性引力场。在静态引力存在下的粒子运动进行了探索，可用于研究行星动力学，揭示近日点的变化。接下来，我们研究了由无压等离子体和中性理想流体组成的耦合到引力场的系统。在这个领域，我们推导出相对论欧拉方程。最后，我们研究了理想流体等离子体的相对论动力学，并将其推广到粘性流，导出了相对论纳维-斯托克斯方程。
Recent developments in mathematical aspects of relativistic fluids
本文综述相对论流体数学研究的最新进展，围绕相对论 Euler 方程介绍波–输运表述、激波形成、低正则性解、物理真空边界及黏性流体等主题，并指出开放问题。
Generic stability of dissipative non-relativistic and relativistic fluids
研究了具有质量通量的非相对论流体和以能量矢量的绝对值为内能的特殊相对论流体均相平衡的线性稳定性。它被证明，在这两种情况下，由于纯粹的热力学限制的平衡是渐近稳定的，唯一的要求是热力学稳定性和非负性的传输系数。
Numerical tests of causal relativistic dissipative fluid dynamics
本文提出了求解具有体粘和剪切粘的因果相对论耗散流体动力学Israel-Stewart（IS）方程的数值方法。然后，我们测试这些方法研究黎曼问题（1+1）-和（2+1）维几何。本文研究的数值格式适用于实际的相对论耗散流体的（3+1）维模拟。
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by Stückelberg. This covariant approach leads to a relativistic formulation of the first and second laws of thermodynamics. The internal energy density and the pressure of a relativistic perfect fluid carry inertia, which leads to a relativistic coupling between heat and work. The relativistic continuity equation for the relativistic inertia is derived. The relativistic corrections in the Euler equation and in the continuity equations for the …
Theories of Relativistic Dissipative Fluid Dynamics
本文综述相对论耗散流体动力学理论，梳理其在高能核物理与天体物理中的应用，并比较迄今提出的各类因果、稳定理论。
From conduction to convection of thermally relativistic fluids between two parallel walls under gravitational force
从理论和数值两方面讨论了重力作用下两平行壁间热相对论流体的热传导和对流。在理论讨论中，我们假设洛伦兹收缩被忽略，时空是平坦的。为了了解重力作用下两平行壁之间热相对论流体的热传导和对流，我们采用直接模拟蒙特卡罗方法求解相对论性玻尔兹曼方程。数值结果表明，当流场处于稀薄区和连续区之间的过渡区时，在两壁附近形成了强烈的非平衡态，这使得我们不能在相对论Navier-Stokes-Fourier方程的框架内讨论热相对论流体在重力作用下的热传导向热对流的转变，而在非相对论极限下，两壁附近不会形成这种强非平衡态。
Non-Newtonian Properties of Relativistic Fluids
我们表明，相对论流体的行为作为非牛顿流体。首先，我们讨论了扩散方程中的非因果传播问题，并引入了修正的Maxwell-Cattaneo-Vernotte（MCV）方程。利用修正的MCV方程，我们得到了因果耗散相对论（CDR）流体动力学，其中不存在无限速度的非物理传播。我们进一步指出，违反因果关系和不稳定性的问题是密切相关的，相对论性的纳维-斯托克斯方程作为相对论性流体理论是不够的。最后，讨论了计算CDR流体动力学输运系数的新的微观公式。微观公式的结果与玻尔兹曼方程的结果一致，即，格拉德矩法。
Hadamard-Papapetrou method of field discontinuities is here employed in order to determine the effective metric that describes the propagation of acoustic perturbations in isentropic fluids. It is shown that, when dissipative effects are present, small perturbations in fastly moving fluids have a natural description in terms of an effective acoustic geometry. As an application of our results, a model for an acoustic black hole in viscous fluid is investigated.
We extend the effective theory approach to the ideal fluid limit where the polarization of the fluid is non-zero. After describing and motivating the equations of motion, we expand them around the hydrostatic limit, obtaining the sound wave and vortex degrees of freedom. We discuss how the presence of polarization affects the stability and causality of the ideal fluid limit.
At low Reynolds numbers, the wind flow in the wake of a single wind turbine is generally not turbulent. However, turbines in wind farms affect each other's wakes so that a turbulent flow can arise. In the present work, an analogue of this effect for the massless charge carrier flow around obstacles in graphene is outlined. We use a relativistic hydrodynamic simulation to analyze the flow in a sample containing impurities. Depending on the density of impurities in the sample, we indeed find evidence for potentially turbulent flow and discuss experimental consequences.
Fluid turbulence and eddy viscosity in relativistic heavy-ion collisions
本文导出了具有相对论性状态方程的可压缩湍流的涡粘性。可压缩性允许的声音模式，但在剪切模式中的涡粘性被发现是相同的不可压缩流体。对于两个空间维度（这是相对论性重离子碰撞动力学的相关情况），剪切模式中的涡动粘度为负，将有效粘度降低到其微观值以下。这可以解释在RHIC中发现的微小粘度。推测了大型强子对撞机实验上可获得的椭圆流系数的含义。
Two Dimensional Turbulence in a Massless Fluid with a Relativistic Lattice Boltzmann Model
本文提出一种相对论格子玻尔兹曼模型，用于模拟二维无质量流体的湍流行为，并通过零平均搅拌力验证其流动特性，有望应用于石墨烯和Kagome晶格中的电子流体定量模拟。
We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations, and are obtained from standard relativistic hydrodynamics in the limit of infinite or vanishing velocity of light. All dissipative phenomena such as friction and heat conduction are included in our description. Part of our work consists in designing the appropriate coordinate frames for relativistic spacetimes, invariant under Galilean or Carrollian diffeomor…
Variational Principle for Relativistic Fluid Dynamics
本文讨论了狭义和广义相对论流体力学的变分原理在求这些问题近似解中的应用。我们表明，有效的拉格朗日函数可以得到适当的动力学变量，如系统的密度分布的Ancilians。作为一个例子，球形液滴运动的相对论版本（Rayleigh-Plesset方程）推导出一个简单的拉格朗日。对于广义相对论情形，给出了球对称系统的最一般拉格朗日量。
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