Related papers: Homogeneity and plane-wave limits
We describe various aspects of plane wave backgrounds. In particular, we make explicit a simple criterion for singularity by establishing a relation between Brinkmann metric entries and diffeomorphism-invariant curvature information. We…
We analyze the wave equation in families of pp-wave geometries developing strong localized scale-invariant singularities in certain limits. For both cases of well-localized pp-waves and the so-called null-cosmologies, we observe an…
A closed-form expression for the amplitudes of source waves in 2D discrete lattice with local and linear (waveguides) defects is derived. The numerical implementation of this analytic expression is demonstrated by several examples.
Patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization. The…
We study the propagation of Maxwellian electromagnetic waves in curved spacetimes in terms of the appropriate geometrical optics limit, notions of signal speed, and minimal coupling prescription from Maxwellian theory in flat spacetime. In…
We study the homogeneous wave equation with radially symmetric data in four or higher space dimensions. Using some new integral representations for the Riemann operator, we establish weighted decay estimates for the solution.
Starting from well-known absolute instruments for perfect imaging, we introduce a type of rotational-symmetrical compact closed manifolds, namely geodesic lenses. We demonstrate that light rays confined on geodesic lenses are closed…
We considered the experimental realization of a Tamm medium that is optically equivalent to the collision of two linearly polarized gravitational plane waves as a piecewise homogeneous metamaterial. Our formulation was based on the…
We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…
Inhomogeneity generated waves, discovered more than a decade ago, play an important role in processes like energy transfer, turbulence generation, heating, etc. To understand the nature of these waves we developed the formalism that looks…
We study the dynamics of an inertial particle coupled to forcing, dissipation, and noise in the small mass limit. We derive an expression for the limiting (homogenized) joint distribution of the position and (scaled) velocity degrees of…
In this work, we demonstrate that the interaction of electromagnetic waves with a microstructured material formed by metallic wires connected to a metallic surface can be described using homogenization methods provided an additional…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
We consider non-linear plane gravitational waves as propagating space-time defects, and construct the Burgers vector of the waves. In the context of classical continuum systems, the Burgers vector is a measure of the deformation of the…
The paper 0705.0332v1 seeks to study the effect of non-trivial spatial curvature in homogeneous and isotropic models. We note that the space considered is not homogeneous, and that the equations of motion used are inconsistent with the…
For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally…
The geometric optics approximation traditionally used to study the propagation of gravitational waves on a curved background, breaks down in the vicinity of compact and extended astrophysical objects, where wave-like effects like diffusion…
We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.
Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded.…
In this paper, theoretical and numerical studies of perfect/nearly-perfect conversion of a plane wave into a surface wave are presented. The problem of determining the electromagnetic properties of an inhomogeneous lossless boundary which…