Related papers: A Dyad Theory of Hydrodynamics and Electrodynamics
The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small…
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative…
The equations of hydrodynamics including mass, linear momentum, angular momentum, and energy are derived by coarse-graining the microscopic equations of motion for systems consisting of rotary dumbbells driven by internal torques.
We numerically construct dynamical asymptotically-AdS$_4$ metrics by evaluating the fluid/gravity metric on numerical solutions of dissipative hydrodynamics in (2+1) dimensions. The resulting numerical metrics satisfy Einstein's equations…
The dyadic Green function for a homogeneous electromagnetic medium inspired by the spatiotemporally nonhomogeneous constitutive equations of gravitationally affected vacuum is derived.
We use covariant methods to analyse the nonlinear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous…
A planar superfluid is considered and interpreted in terms of electromagnetism and gravity. It has previously been suggested that the superfluid flow can be regarded as analogous to an electromagnetic field and that a non-vanishing density…
Viscous flow of interacting electrons in two dimensional materials features a bunch of exotic effects. A model resembling the Navier-Stokes equation for classical fluids accounts for them in the so called hydrodynamic regime. We performed a…
Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
We argue that the well-known problem of the instabilities associated with the self-forces (radiation reaction forces) in classical electrodynamics are possibly stabilized by the introduction of gravitational forces via general relativity.
In this paper the possibility of the generation of the thermal waves in 2D electron gas is investigated. In the frame of the quantum heat transport theory the 2D quantum hyperbolic heat transfer equation is formulated and numerically…
At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications spanning from…
The geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhury equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) are…
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves…
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…