Related papers: Action functionals for relativistic perfect fluids
The Special Relativity allows the possibility of a class of particles, known tachyons, that have spacelike 4-velocities, i.e., which move with velocity greater than speed of light in vacuum. In this existence frame, the tachyons have energy…
The thermodynamic behaviour of a relativistic perfect simple fluid obeying the equation of state $p=(\gamma-1)\rho $, where $0 \le \gamma \le 2$ is a constant, has been investigated. Particular cases include: vacuum($p=-\rho $, $\gamma=0$),…
We perform a coarse-graining analysis of the paradigmatic active matter model, Active Brownian Particles, yielding a continuum description in terms of balance laws for mass, linear and angular momentum, and energy. The derivation of the…
In this paper we further develop the fluctuating hydrodynamics proposed in arXiv:1511.03646 in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In…
We investigate the initial-value problem for the relativistic Euler equations governing isothermal perfect fluid flows, and generalize an approach introduced by LeFloch and Shelukhin in the non-relativistic setting. We establish the…
We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
We develop a new theory of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a new fluid variable, the kinetic mass density, which is needed…
We consider a class of finite-dimensional dynamical systems whose equations of motion are derived from a non-local-in-time action principle. The action functional has a zeroth order piece derived from a local Hamiltonian and a perturbation…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
All possible action functionals on the space of surfaces in ${\bf R}^4$ that depend only on first and second derivatives of the functions, entering the equation of the surface, and satisfy the condition of invariance with respect to rigid…
We derive a new, exact formula for the estimate of the initial energy densities from a new family of finite and exact solution of relativistic perfect fluid hydrodynamics. The new formula depends non-trivially on the speed of sound and on…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
The response of an isolated granular fluid to small perturbations of the hydrodynamic fields is considered. The corresponding linear response functions are identified in terms of a formal solution to the Liouville equation including the…
We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…
Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic…
The log-homotopy particle flow filter resolves the Bayesian update by transporting particles along a continuous trajectory in pseudo-time. However, the governing partial differential equation for the flow velocity is fundamentally…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy…