We assert that the physics underlying the extraordinary light transmission (reflection) in nanostructured materials can be understood from rather general principles based on the formal scattering theory developed in quantum mechanics. The Maxwell equations in passive (dispersive and absorptive) linear media are written in the form of the Schrödinger equation to which the quantum mechanical reso...

The equations of the linearized first post-Newtonian approximation to general relativity are often written in ‘‘gravitoelectromagnetic’’ Maxwell-like form, since that facilitates physical intuition. Damour, Soffel, and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlineari...

Integrating factors and adjoint equations are determined for linear and nonlinear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by...

We develop in this paper an efficient and robust spectral-Galerkin method to solve the three-dimensional time-harmonic Maxwell equations in exterior domains. We first reduce the problem to a bounded domain by using the capacity operator which characterizes the nonreflecting boundary condition. Then, we adapt the transformed field expansion (TFE) approach to reduce the problem to a sequence of M...

New method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector (E + iB)/ √ 2 is multiplied by a complex scalar function φ. Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeroes of the ...

Magnetostatic Maxwell equations and the Landau-Lifshitz-Gilbert (LLG) equation are combined to a multiscale method, which allows to extend the problem size of traditional micromagnetic simulations. By means of magnetostatic Maxwell equations macroscopic regions can be handled in an averaged and stationary sense, whereas the LLG allows to accurately describe domain formation as well as magnetiza...

The torsion modified Maxwell-Proca equations when applied to describe a plasma is shown to lead to a correction to the Debye screening length. For hot new born neutron stars the torsion correction is shown to be significant. This effect may provide an indirect evidence for Torsion. Indian Institute of Astrophysics, Bangalore India, and Universita degli Studi di Ferrara, Dipartimento di Fisica, ...

It is shown how the phase-space kinetic theory of polymeric liquid mixtures leads to a set of extended Maxwell-Stefan equations describing multicomponent diffusion. This expression reduces to standard results for dilute solutions and for undiluted polymers. The polymer molecules are modeled as flexible bead-spring structures. To obtain the Maxwell-Stefan equations, the usual expression for the ...

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

In this paper the Maxwell field theory is considered on the Zn symmetric algebraic curves. As a first result, a large family of nondegenerate metrics is derived for general curves. This allows to treat many differential equations arising in quantum mechanics and field theory on Riemann surfaces as differential equations on the complex sphere. The examples of the scalar fields and of an electron...