Related papers: Approximate Analytical Solutions to the Relativist…
We consider the hydrodynamics of relativistic conformal field theories at finite temperature and its slow motions limit, where it reduces to the incompressible Navier-Stokes equations. The symmetries of the equations and their solutions are…
Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for distribution function close to equilibrium, we derive hydrodynamic evolution equations for the…
In this paper we approximate the thermodynamic limit of finite-gap solutions to any integrable equations in the focusing NLS hierarchy (fNLS, mKdV, ...) with an associated multisoliton solutions using the Riemann-Hilbert Problem approach.…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
The problem of equilibrium of a plasma in a Tokamak is a free boundary problemdescribed by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the…
In the present work, we obtain the hydrostatic equilibrium configurations of neutron stars in the recently proposed $f(R,\mathcal{L},T)$ theory of gravity, for which $R$ is the Ricci scalar, $\mathcal{L}$ is the matter lagrangian density,…
We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…
We present a model of a slowly rotating Tolman VII (T-VII) fluid sphere, at second order in the angular velocity. The structure of this configuration is obtained by integrating the Hartle-Thorne equations for slowly rotating relativistic…
In this paper, we have solved 1D special relativistic hydrodynamical equations using different numerical method in computational gas dynamics. The numerical solutions of these equations for smooth wave cases give better solution when we use…
We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic…
We have designed and developed, from scratch, a global circulation model named THOR that solves the three-dimensional non-hydrostatic Euler equations. Our general approach lifts the commonly used assumptions of a shallow atmosphere and…
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
We show that the 1D planar ultrarelativistic shock-tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the…
The first static spherically symmetric perfect fluid solution with constant density was found by Schwarzschild in 1918. Generically, perfect fluid spheres are interesting because they are first approximations to any attempt at building a…
This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entropy instead of the total energy. The presented procedure is…
Standard reduced models often fail to adequately describe the complex geometric response of tokamak plasmas to strong toroidal rotation. In this work, we present VEQ-R, a computationally efficient spectral solver designed to calculate…
Charged static and rotating objects as solutions of the Einstein-Maxwell field equations are obtained and studied in the present work. The full spacetime geometry is obtained by matching two spacetime regions, an interior region containing…
We complete our previous investigation concerning the structure and the stability of "isothermal" spheres in general relativity. This concerns objects that are described by a linear equation of state $P=q\epsilon$ so that the pressure is…
The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and…
First post-Newtonian (1PN) hydrostatic equations for an irrotational fluid which have been recently derived are solved for an incompressible star. The 1PN configurations are expressed as a deformation of the Newtonian irrotational Riemann…