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In this work, we perform a phenomenological derivation of the first- and second-order relativistic hydrodynamics of dissipative fluids. To set the stage, we start with a review of the ideal relativistic hydrodynamics from energy-momentum…
We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed…
Extended theories are widely used in the literature to describe relativistic fluids. The motivation for this is mostly due to the causality issues allegedly present in the first order in the gradients theories. However, the decay of…
This work considers a compressible, viscous, heat-conducting fluid exhibiting thermal relaxation according to Christov's constitutive heat transfer law (C. I. Christov, Mech. Research Comm. 36 (2009)), which is of Cattaneo type. The…
A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase flow is described. Thermodynamic consistency is ensured by introducing a non-ideal pressure tensor directly into the collision operator. We also…
We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of $C^2$…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
We survey some results on non-uniform hyperbolicity, geometric pressure and equilibrium states in one-dimensional real and complex dynamics. We present some relations with Hausdorff dimension and measures with refined gauge functions of…
A thermodynamically consistent model of non-classical coupled non-linear thermoelasticity capable of accounting for thermal wave propagation is proposed. The heat flux is assumed to consist of both additive energetic and dissipative…
We study equilibrium states for an open class of non-uniformly expanding local homeomorphisms defined by a mild condition such that for some iterate each point admits at least one contracting inverse branch. We prove the existence and…
We investigate the formal stability of finite-amplitude non-zonal flows bifurcating from the trivial state in the unforced 2D Euler equations on the sphere. To bypass the degeneracy of the spherical Laplacian and filter out the…
The macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow for a suitable mechanical system. Turbulent fluctuations (intermittency) then correspond to thermal fluctuations,…
We propose a new model which describes relativistic hydrodynamics and generalizes the standard Euler system of isentropic perfect fluids. Remarkably, our system admits a convex extension which allows us to transform it to a symmetric…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
In a previous paper [I. Bena, M. Malek Mansour, and F. Baras, ``Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime", Phys. Rev. E 59, 5503 - 5510 (1999)] the statistical properties of the linearized Kolmogorov flow have been…
We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories.…
Relativistic heat transport in electron-two-temperature plasmas with density gradients has been investigated. The Legendre expansion analysis of relativistically modified kinetic equations shows that strong inhibition of heat flux appears…
This article surveys recent progress of results in topology and dynamics based on techniques of closed one-forms. Our approach allows us to draw conclusions about properties of flows by studying homotopical and cohomological features of…
In this work, based on the cluster expansion of the energy functional, we have extracted a formalism for calculation of the thermodynamic properties of fluids with non-spherical molecules. The salient feature of the extracted formalism is…
In the causal theory of relativistic dissipative fluid dynamics, there are conditions on the equation of state and other thermodynamic properties such as the second-order coefficients of a fluid that need to be satisfied to guarantee that…