In this chapter we introduce the fundamental concepts in Newtonian and complex fluid mechanics, beginning with the basic underlying assumptions in continuum mechanical modeling. The equations of mass and momentum conservation are derived, and the Cauchy stress tensor makes its first of many appearances. The Navier–Stokes equations are derived, along with their inertialess limit, the Stokes equa...

The order-disorder duality structure is exploited in order to obtain a quantum description of anyons and vortices in: a) the Maxwell theory; b) the Abelian Higgs Model; c) the Maxwell-Chern-Simons theory; d) the Maxwell-Chern-Simons-Higgs theory. A careful construction of a charge bearing order operator(σ) and a magnetic flux bearing disorder operator (vortex operator) (μ) is performed, paying ...

Maxwell-type models for non-linear kinetic equations have many applications in physics, dynamics of granular gases, economics, and other areas where statistical modeling is relevant. They model the evolution of probability measures (distribution functions) and relate to a class of non-linear space homogeneous Boltzmann equations for binary interactions where scattering probability rates of the ...

In the framework of designing laboratory tests of relativistic gravity, we investigate the gravita-tional field produced by the magnetic field of a solenoid. Observing this field might provide a mean of testing whether stresses gravitate as predicted by Einstein's theory. A previous study of this problem by Braginsky, Caves and Thorne predicted that the contribution to the gravitational field r...

In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...

We show that the Maxwell equations for arbitrary inhomogeneous media are equivalent to a single quaternionic equation which can be considered as a generalization of the Vekua equation for generalized analytic functions.

The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the cognoscenti of differential forms on manifolds; namely, that charge conservation implies the inhomogeneous Maxwell equations. This is the reciprocal statement of one which is very well known among physicists: charge conservation, written in the...

The coupled Maxwell-Lorentz system describes feed-back action of electromagnetic fields in classical electrodynamics. When applied to point-charge sources (viewed as limiting cases of charged fluids) the resulting nonlinear weakly hyperbolic system lies beyond the scope of classical distribution theory. Using regularized derivatives in the framework of Colombeau algebras of generalized function...

The continuous extension of the discrete duality symmetry of the SchwarzSen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the non—local duality transformation generator found in the Hamiltonian formulation of Maxwell...

We consider a modified antenna’s problem with power-type constitutive laws. This consists in a new nonlinear hyperbolic system that extends a Duvaut-Lions model. Using the Galerkin approximation, properties of the natural functional spaces, and exploring the L-L ′ duality, we prove the existence of solutions, in a generalized sense, passing to the limit in a family of approximated problems and ...