We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.
We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the WKB representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical B
ogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented. The knowledge of the Hamiltonian structure for linear wave systems provides a basis for developing a theory of weakly nonlinear random waves in inhomogeneous media generalizing the theory of homogeneous wave turbulence.
Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as MEMS embedded in dielectric media, Casimir induced friction in nano-machinery, micro-fluidics and molecular electronics. Computation of such st
resses based on cavity QED generally require numerical analysis based on a regularization process. A new scheme is described that has the potential for wide applicability to systems involving realistic inhomogeneous media. From a knowledge of the spectrum of the stationary modes of the electromagnetic field the scheme is illustrated by estimating numerically the Casimir stress on opposite faces of a pair of perfectly conducting planes separated by a vacuum and the change in this result when the region between the plates is filled with an incompressible inhomogeneous non-dispersive dielectric.
This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly v
arying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.
We revisit the problem on the inner structure of shock waves in simple gases modelized by the Boltzmann kinetic equation. In cite{pomeau1987shock}, a self-similarity approach was proposed for infinite total cross section resulting from a power law in
teraction, but this self-similar form does not have finite energy. Motivated by the work of Pomeau, Bobylev and Cercignani started the rigorous study of the solutions of the spatial homogeneous Boltzmann equation, focusing on those which do not have finite energy cite{bobylev2002self,bobylev2003eternal}. In the present work, we provide a correction to the self-similar form, so that the solutions are more physically sound in the sense that the energy is no longer infinite and that the perturbation brought by the shock does not grow at large distances of it on the cold side in the soft potential case.
The formalism of SUSYQM (SUperSYmmetric Quantum Mechanics) is properly modified in such a way to be suitable for the description and the solution of a classical maximally superintegrable Hamiltonian System, the so-called Taub-Nut system, associated w
ith the Hamiltonian: $$ mathcal{H}_eta ({mathbf{q}}, {mathbf{p}}) = mathcal{T}_eta ({mathbf{q}}, {mathbf{p}}) + mathcal{U}_eta({mathbf{q}}) = frac{|{mathbf{q}}| {mathbf{p}}^2}{2m(eta + |{mathbf{q}}|)} - frac{k}{eta + |{mathbf{q}}|} quad (k>0, eta>0) , .$$ In full agreement with the results recently derived by A. Ballesteros et al. for the quantum case, we show that the classical Taub-Nut system shares a number of essential features with the Kepler system, that is just its Euclidean version arising in the limit $eta to 0$, and for which a SUSYQM approach has been recently introduced by S. Kuru and J. Negro. In particular, for positive $eta$ and negative energy the motion is always periodic; it turns out that the period depends upon $ eta$ and goes to the Euclidean value as $eta to 0$. Moreover, the maximal superintegrability is preserved by the $eta$-deformation, due to the existence of a larger symmetry group related to an $eta$-deformed Runge-Lenz vector, which ensures that in $mathbb{R}^3$ closed orbits are again ellipses. In this context, a deformed version of the third Keplers law is also recovered. The closing section is devoted to a discussion of the $eta<0$ case, where new and partly unexpected features arise.
Kira V. Khmelnytskaya
,Vladislav V. Kravchenko
,Hector Oviedo
.
(2007)
.
"On the solution of the static Maxwell system in axially symmetric inhomogeneous media"
.
Vladislav V. Kravchenko
هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا