3 The permittivity of space-time is a metric on u(1). 8 3.1 Electrostatics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 The electric field. . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.2 The dielectric displacement. . . . . . . . . . . . . . . . . . 8 3.1.3 The dielectric operator and the dielectric coefficient. . . . 9 3.1.4 The dielectric coefficient. . . . . . . ...

this paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. the two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low reynolds number. the exact solutions of reduced momentum equation and magnetic force function have been computed in wave fra...

A volume-surface integral equation (VSIE) formulation is developed for determining the electromagnetic TM scattering by a two-dimensional conducting cylinder coated with an inhomogeneous dielectric/magnetic material. The electric field integral equations (EFIEs) are utilized to derive the VSIE. The surface EFIE is applied to the conducting surface, while the volume EFIE is applied to the coatin...

A virtually complete description of the topology of stationary incompressible Euler flows and the magnetic field satisfying the magnetostatic equation is given by a theorem due to Arnol'd. We apply this theorem to describe the topology of stationary states of plasmas with significant fluid flow, obeying the Hall magnetohydrodynamics model equations. In the context of the integrability (nonchaot...

This paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. The two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low Reynolds number. The exact solutions of reduced momentum equation and magnetic force function have been computed in wave...

For electromagnetic analysis using Method of Moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor 0 equal to the solid angle external to the surface at the testing points, which is2 everywhere on the surface of the obj...

We derive the quantum Boltzmann equation for the two-dimensional electron gas in a magnetic field such that the filling factor n@1. This equation describes all of the effects of the external fields on the impurity collision integral including Shubnikov–de Haas oscillations, the smooth part of the magnetoresistance, and nonlinear transport. Furthermore, we obtain quantitative results for the eff...

a new hybrid modal-moment method is proposed to calculate fields penetrated through small apertures on rectangular metallic enclosures. first, the method of moments is used to numerically solve the governing electric field integral equation for the equivalent two-dimensional surface-current distributions on the surface of metallic enclosure including any number of rectangular apertures of arbit...

We take the Gauss’ linking integral of two curves as a starting point to discuss the connection between the equation of continuity and the inhomogeneous Maxwell equations. Gauss’ formula has been discussed before, as being derivable from the line integral of a magnetic field generated by a steady current flowing through a loop. We argue that a purely geometrical result such as Gauss’ formula ca...