Singularities cancellation on wave fronts

Stable singularities of wave-fronts in general relativity

A wave-front in a space-time M is a family of null geodesics orthogonal to a smooth spacelike two-surface in M; it is of some interest to know how a wave-front can fail to be a smoothly immersed surface in M. In this paper we see that the space of null geodesics N of M, considered as a contact manifold, provides a natural setting for an efficient study of the stable singularities arising in the...

Reaction-diffusion wave fronts on comblike structures.

From the Hamilton-Jacobi formalism, an explicit expression for the speed of wave front propagation along the backbone of comblike structures is obtained. This expression, through the waiting-time distribution function, takes into account the number of sites and their distribution in the secondary branches. Our theoretical results are supported by numerical simulations of the reaction random-wal...

Singlarities of Wave Fronts

In this paper, we discuss the recognition problem for Ak-type singularities on wave fronts. We give computable and simple criteria of these singularities, which will play a fundamental role in generalizing the authors’ previous work “the geometry of fronts” for surfaces. The crucial point to prove our criteria for Ak-singularities is to introduce a suitable parametrization of the singularities ...

Institute for Mathematical Physics Stable Singularities of Wave Fronts in General Relativity

Optical Wave Fronts

In recent years, the formation of laser beams with specific intensity and phase distributions has attracted considerable attention. The formation of such laser beams has been efficiently achieved by various intracavity mode selection techniques1 or by external conversion of a given laser beam distribution into the desired one. Recently Machavariani et al. presented a new method for efficiently ...