A wide range of transformation media designed with conformal mapping are currently being studied extensively due to their favorable properties: isotropy, moderate index requirements, low loss and broad bandwidth. For optical frequency operation, the transformation media are commonly fabricated on high index semiconductor thin films. These 2D implementations, however, inevitably introduces waveg...

We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) fI CP 1 . We also extend this picture to the N = 2k superconformal mechanics described in terms of Lobache...

It is challenging to realise the perfect manipulation of water waves within a broad range of frequencies. By extending conformal transformation principles to water waves, their propagation can be controlled via gradually varying water depths, permitting the realisation of a desired refractive index profile for linear water surface waves. Wave bending, directional wave emission and wave focusing...

We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) fI CP 1 . We also extend this picture to the N = 2k superconformal mechanics described in terms of Lobache...

Over the past years, invisibility cloaks have been extensively discussed since transformation optics emerges. Generally, the electromagnetic parameters of invisibility cloaks are complicated tensors, yet difficult to realize. As a special method of transformation optics, conformal mapping helps us design invisibility cloak with isotropic materials of a refractive index distribution. However, fo...

After a study of the Hamiltonian group of gauge transformations, whose infinitesimal generators are the 14 first class constraints of a new formulation of canonical tetrad gravity on globally hyperbolic, asymptotically flat at spatial infinity, spacetimes with simultaneity spacelike hypersurfaces Στ diffeomorphic to R3, the multitemporal equations associated with the constraints generating spac...

After a study of the Hamiltonian group of gauge transformations, whose infinitesimal generators are the 14 first class constraints of a new formulation of canonical tetrad gravity on globally hyperbolic, asymptotically flat at spatial infinity, spacetimes with simultaneity spacelike hypersurfaces Στ diffeomorphic to R3, the multitemporal equations associated with the constraints generating spac...

A new formalism is introduced for the transfer of polarized radiation. Stokes parameters are shown to be four– vectors in a Minkowski-like space and, most strikingly, the radiative transfer equation (RTE) turns out to be an infinitesimal transformation under the Poincaré (plus dilatations) group. A solution to the transfer equation as a finite element of this group is proposed.

The Burgers equation with linear damping has been subjected to Lie's group theoretic method of infinitesimal transformation to derive its solutions. To the best of our knowledge, we are the first to obtain a new similarity variable for an equation of the Burgers type and therefore provide new solutions.