A water bridge refers to an experimental "flexible cable" made up of pure de-ionized water, which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the de-ionized water flexible cable maintain a tension that sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be...

We establish a new self-consistent system of equations for the gravitational and electromagnetic fields. The procedure is based on a non-minimal non-linear extension of the standard Einstein-Hilbert−Maxwell action. General properties of a threeparameter family of non-minimal linear models are discussed. In addition, we show explicitly, that a static spherically symmetric charged object can be d...

In December 1907, Minkowski expressed the Maxwell equations in the very beautiful and compact 4dimensional form: lor f = −s, lor F ∗ = 0. Here ‘lor’, an abbreviation of Lorentz, represents the 4dimensional differential operator. We study Minkowski’s derivation and show how these equations generalize to their modern premetric form in the framework of tensor and exterior calculus. After mentionin...

Attention is focused in this paper on: (i) definitions of alternate measures of “stress-resultants” and “stress-couples” in a finitely deformed shell (finite mid-plane stretches as well as finite rotations); (ii) mixed variational principles for shells, undergoing large mid-plane stretches and large rotations, in terms of a stress function vector and the rotation tensor. In doing so, both types...

We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In...

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in literature, their connection is often not entirely clear, some them introduced purely numerical techniques. Here we present a unifying ...

We investigate the formation of singularities in one-dimensional hyperbolic compressible Navier-Stokes equations, a model proposing relaxation leading to hyperbolization through nonlinear Cattaneo law for heat conduction as well constitutive Maxwell type relations stress tensor. By using entropy dissipation inequality, which gives lower energy estimates local solutions without any smallness con...

A model for the stress tensor in granular flows [Volfson, Tsimring, and Aranson, Phys. Rev. Lett. 90, 254301 (2003)] is correctly generalized to an objective form that is independent of the coordinate system. The objective representation correctly models the isotropic and anisotropic parts of the stress tensor, whereas the original model for stress tensor components is dependent on the coordina...