Electricity flows in circuits that bring us power and information. The current flow is defined by the Maxwell equations are as exact universal any science. Maxwell-Ampere law defines source of magnetic field a current. In vacuum, like between stars, there no charges to carry displacement current, \(\varepsilon_0\ \partial\mathbf{E}/\partial t\). Inside matter, flux charge added This total obeys...

We use a rigorous numerical code based on the method of moments to test the accuracy and validity domains of two popular first-order approximations, namely the Kirchhoff and the small-slope approximation (SSA), in the case of two-dimensional rough surfaces. The experiment is performed on two representative types of surfaces: surfaces with Gaussian spectrum, which are the paradigm of single-scal...

A theoretical model is developed to describe the interferometric coherency between pairs of SAR images of rough soil surfaces. The model is derived using a dyadic form for surface reflectivity in the Kirchhoff approximation. This permits the combination of Kirchhoff theory and spotlight synthetic aperture radar (SAR) image formation theory. The resulting model is used to describe the interferom...

In this paper, we derive a sharp observability inequality for Kirchhoff plate equations with lower order terms in an unbounded domain Ω of lR. More precisely, when the observation is assumed to be located in a subdomain ω such that Ω \ ω is bounded and the observation time T > 0 is sufficiently large, we establish an observability estimate with an explicit observability constant for Kirchhoff p...

Real filaments are not perfectly homogeneous. Most of them have various materials composition and shapes making their stiffnesses not constant along the arclength. We investigate the existence of circular and helical equilibrium solutions of an intrinsically straight rod with varying bending and twisting stiffnesses, within the framework of the Kirchhoff model. The planar ring equilibrium solut...

Abstract A bicycle path is a pair of trajectories in R n , the ‘front’ and ‘back’ tracks, traced out by endpoints moving line segment fixed length (the ‘bicycle frame’) tangent...