Related papers: Reciprocal Transformations in Relativistic Gasdyna…
Recent years have seen much development in analyzing the structure of relativistic hydrodynamics. In this proceeding, some of the developments are highlighted including issues related to pseudo-gauge transformations and spin hydrodynamics.
A class of generalized nonlinear p-Laplacian evolution equations is studied. These equations model radial diffusion-reaction processes in $n\geq 1$ dimensions, where the diffusivity depends on the gradient of the flow. For this class, all…
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with…
The Lorentz covariant statistical physics and thermodynamics is formulated within the preferred frame approach. The transformation laws for geometrical and mechanical quantities such as volume and pressure as well as the Lorentz-invariant…
We couple a nonlinear evolution equation with an associated one and derive the action principle. This allows us to write the Lagrangian density of the system in terms of the original field variables rather than Casimir potentials. We find…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
New mathematical and numerical results are given for the coupling of the temperature equation of a fluid with Radiative Transfer: existence and uniqueness and a convergent monotone numerical scheme. The technique is shown to be feasible for…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the…
Considering a system of non-interacting particles characterized by the number N of its constituents and by its Kelvin temperature T, we reduce the transformation of the Kelvin temperature to the transformation mass
We show that the relativistic expressions for momentum and energy as well as the way in which they transform could be derived without involving collisions and conservation laws. Our approach involves relativistic kinematics via the addition…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
The principle of Random Galilean Transformation (RGT) Invariance is applied to the random motion of particles in a turbulent gas to construct a kinetic equation for the transport of the particle phase space probability…
The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred…
The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…