Related papers: A quaternionic unification of electromagnetism and…
By constructing a hydrodynamic canonical formalism, we show that the occurrence of an arbitrary density-dependent gauge potential in the meanfield Hamiltonian of a Bose-condensed fluid invariably leads to nonlinear flow-dependent terms in…
In this article, we combine V. Arnold's celebrated approach via the Euler-Arnold equation -- describing the geodesic flow on a Lie group equipped with a right-invariant metric \cite{Arnold66} -- with his formulation of the motion of a…
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit,…
We derive the system of hydrodynamic equations governing the collective motion of massless fermions in graphene. The obtained equations demonstrate the lack of Galilean- and Lorentz invariance, and contain a variety of nonlinear terms due…
We present a quaternion wavefunction formulation that reduces the incompressible Euler equations to a single nonlinear Schr\"odinger-type equation with a holomorphic constraint, revealing hidden geometric structure connecting quantum and…
The free motion of charged colloids within ionic solutions and in the vicinity of charged boundaries, is a phenomenon that occurs in various natural, biological and industrial settings. Here, we develop an electrohydrodynamic lubrication…
We treat the Christoffel coefficients as operators and introduce new mappings for quaternionic products to connect with the theory of electrodynamics in general spacetime. By utilizing the directional operator of the covariant derivative,…
We consider the dominant equations for the motion of the non-Newtonian fluid in a domain from an energetic point of view. We apply our energetic variational approaches and the first law of thermodynamics to derive the generalized…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity.…
Using recently developed consistent and robust first order relativistic hydrodynamics of a dissipative fluid we propose a generalization but weak version of Tolman-Ehrenfest relation and Klein's law on a general background spacetime. These…
In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the…
The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
We discuss several geometric PDEs and their relationship with Hydrodynamics and classical Electrodynamics. We start from the Euler equations of ideal incompressible fluids that, geometrically speaking, describe geodesics on groups of…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
In the framework of the classical Maxwell-Lorentz electrodynamics the energy conservation law is reconsidered.
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be…