The electromagnetic fields scattered when a plane wave is incident on an oblate spheroid in the side-on orientation may be calculated using a generalization of Mie theory, and the results may be decomposed in a Debye series expansion. A number of optical caustics are observed in the computed scattered intensity for the one internal reflection portion of the Debye series for scattering angles in...

A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. ¿From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity. Several popular schemes are analyzed and are shown ...

We introduce an asymptotic formula for calculating quantum mechanical and quantum theoretical models with caustics, like the Nambu–Jona-Lasinio(NJL) model. This asymptotic formula is given by the form attached the extra term, which suppresses the divergence induced because of caustics, to the leading term of the WKB approximation. This formula guarantees validity of the mean field approximation...

We study classical and quantum caustics for systems with quadratic Lagrangians of the form L = 1 2 ẋ − 1 2 λ(t)x − μ(t)x. After deriving the transition amplitude on caustics in a closed form, we consider the Gaussian slit experiment and point out that the focusing around caustics is stabilized against initial momentum fluctuations by quantum effect. PACS codes: 02.30.Hg; 03.65.-w; 03.65.Sq

We present a real-time GPU caustics rendering technique in dynamic scenes under multiple directional lights taking into account light occlusion. Our technique renders caustics cast on receiver objects as well as volumetric caustics. We precompute caustic patterns of caustic objects for several directional lights and store them in caustic images. During the rendering, we interpolate the precompu...

Cold dark matter haloes are populated by caustics, which are yet to be resolved in N-body simulations or observed in the Universe. Secondary infall model provides a paradigm for the study of caustics in typical haloes assuming that they have had no major mergers and have grown only by smooth accretion. This is a particular characteristic of the smallest dark matter haloes of about 10−5 M⊙, whic...

Cold dark matter haloes are populated by high-density structures with sharplypeaked profiles known as caustics which have not yet been resolved by 3dimensional numerical simulations. Here, we derive semi-analytic expressions for the density profiles near caustics in haloes which form by self-similar accretions of dark matter with infinitesimal velocity dispersion. A simple rescaling shows that ...

This paper provides a complete theoretical treatment of the point-mass lens perturbed by constant external shear, often called the Chang-Refsdal lens. We show that simple invariants exist for the products of the (complex) positions of the four images, as well as moment sums of their signed magnifications. The image topographies and equations of the caustics and critical curves are also studied....

There are at least four versions of Hořava-Lishitz gravity in the literature. We consider the version without the detailed balance condition with the projectability condition and address one aspect of the theory: avoidance of caustics for constant time hypersurfaces. We show that caustics cannot form with codimension one in the absence of matter source if λ deviates from 1 near would-be caustic...