We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than pr...

Certain configurations of D-branes, for example wrong dimensional branes or the brane-antibrane system, are unstable to decay. This instability is described by the appearance of a tachyonic mode in the spectrum of open strings ending on the brane(s). The decay of these unstable systems is described by the rolling of the tachyon field from the unstable maximum to the minimum of its potential. We...

The experimental method of caustics was used for the evaluation of the stress-singularities created by concentrated oblique load applied at the apex of a wedge or on the horizontal straight boundary of a half-plane. The wedge was considered to be elastic, isotropic and under generalized plane stress conditions. According to the method of caustics, the light rays impinging normally at the thin p...

background: the incidence of caustic ingestion injuries in developed countries has been decreasing, while it still remains a great concern in developing countries including iran. in this study we focused on alkali esophageal injuries in children which occur frequently in southern iran, due to both, unsafe products and unfamiliarity of families with the alkali consumption hazards. methods : in a...

In this paper, a new technique is presented for interactive rendering of caustics fully processed on GPU. Without any pre-computation required, the algorithm can directly render refractive caustics from complex deformable transparent objects onto an opaque receiver surface. By the technique we accurately trace the path of the photons and calculate the energy carried by the photons emitted from ...

We study combinatorics of billiard partitions which arose recently in the description periodic trajectories ellipsoidal billiards d-dimensional Euclidean and pseudo-Euclidean spaces. Such uniquely codify sets caustics, up to their types, generate trajectories. The period a trajectory is largest part while winding numbers are remaining summands corresponding partition. In order take into account...

Abstract As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) widely used modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits applicability. A new framework, called metaplectic (MGO), has recently been developed allows caustics certain types to be modeled accurately within the framework. Here...

In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and geometric invariants of curves under the action of the Lorentz group. c ©2016 A...

The display of realistic natural scenes is one of the most important research areas in computer graphics. The rendering of water is one of the essential components. This paper proposes an efficient method for rendering images of scenes within water. For underwater scenery, the shafts of light and caustics are attractive and important elements. However, computing these effects is difficult and t...